How to Write a For Loop in Python

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The for loop is one of the basic tools in Python. You will likely encounter them at the very beginning of your Python journey. In this article, I’ll give you a brief overview of the for loop in Python and demonstrate with examples how you can use it to iterate over different types of sequences.

What Is a For Loop in Python?

Python is a powerful programming language that can be used for just about anything , and the for loop is one of its fundamental tools. You should understand it well and master it to build applications in Python.

A for loop allows you to iterate over a sequence that can be either a list, a tuple, a set, a dictionary, or a string . You use it if you need to execute the same code for each item of a sequence.

To explain the syntax of the for loop, we’ll start with a very basic example. Let’s say we want to keep track of the home countries of our students. So, we have the list new_students_countries , which contains the countries of origin for our three new students.

We use the for loop to access each country in the list and print it:

Here, for each country in the list new_students_countries , we execute the print() command. As a result, we get the name of each country printed out in the output.

Let’s go over the syntax of the for loop:

  • It starts with the for keyword, followed by a value name that we assign to the item of the sequence ( country in this case).
  • Then, the in keyword is followed by the name of the sequence that we want to iterate.
  • The initializer section ends with “ : ”.
  • The body of the loop is indented and includes the code that we want to execute for each item of the sequence.

Practice writing for loops with the course Python Basics. Part 1 . It has 95 interactive exercises that cover basic Python topics, including loops.

Now that we’re familiar with the syntax, let’s move on to an example where the usefulness of the for loop is more apparent.

We continue with our example. We have the list new_students_countries with the home countries of the new students. We now also have the list students_countries with the home countries of the existing students. We will use the for loop to check each country in new_students_countries to see if we already have students from the same country:

As you can see, we start by initializing the variable new_countries with 0 value. Then, we iterate over the list new_students_countries , and check for each country in this list if it is in the list students_countries . If it is not, it is a new country for us, and we increase new_countries by 1.

Since there are three items in new_students_countries , the for loop runs three times. We find that we already have students from Germany, while Great Britain and Italy are new countries for our student community.

For Loops to Iterate Over Different Sequence Types

For loops and sets.

As mentioned before, for loops also work with sets . Actually, sets can be an even better fit for our previous example; if we have several new students from the same new country, we don’t want them to be counted multiple times as if we have more new countries than we actually have.

So, let’s consider the set new_students_countries with the countries for four new students, two of whom come from Italy. Except for replacing a list with a set, we can use the same code as the above:

Because we use a set instead of a list, we have correctly counted that only two new countries are added to our student community, even though we have three students coming from new countries.

For Loops and Tuples

We may also iterate over a tuple with the for loop. For example, if we have a tuple with the names of the new students, we can use the following code to ask the home country of each student:

For Loops and Dictionaries

There are many different ways to iterate over a dictionary; it is a topic for a separate discussion by itself. In this example, I iterate through the dictionary items, each of which are basically tuples. So, I specify in the loop header to unpack these tuples into key and value. This gives me access to both dictionary keys and dictionary values in the body of the loop.

If you want to refresh your knowledge about dictionaries and other data structures, consider joining our course Python Data Structures in Practice .

For Loops and Strings

While iterating over sequences like lists, sets, tuples, and dictionaries sounds like a trivial assignment, it is often very exciting for Python beginners to learn that strings are also sequences , and hence, can also be iterated over by using a for loop.

Let’s see an example of when you may need to iterate over a string.

We need each new student to create a password for his or her student account. Let’s say we have a requirement that at least one character in the password must be uppercase. We may use the for loop to iterate over all of the characters in a password to check if the requirement is met:

Here, we initialize the variable uppercase as False . Then, we iterate over every character ( char ) of the string password to check if it is uppercase. If the condition is met, we change the uppercase variable to True .

For Loops to Iterate Over a Range

If you are familiar with other programming languages, you’ve probably noticed that the for loop in Python is different. In other languages, you typically iterate within a range of numbers (from 1 to n, from 0 to n, from n to m), not over a sequence. That said, you can also do this in Python by using the range() function.

For Loops With range()

First, you can use the range() function to repeat something a certain number of times. For example, let’s say you want to create a new password ( password_new ) consisting of 8 random characters. You can use the following for loop to generate 8 random characters and merge them into one string called password_new :

In addition to the required stop argument (here, 8), the range() function also accepts optional start and step arguments. With these arguments, you can define the starting and the ending numbers of the sequence as well as the difference between each number in the sequence. For example, to get all even numbers from 4 to 10, inclusive, you can use the following for loop:

Note that we use 11, not 10, as the upper bound. The range() function does not include the upper bound in the output .

You may also use the range() function to access the iteration number within the body of the for loop. For example, let’s say we have a list of the student names ordered by their exam results, from the highest to the lowest. In the body of our for loop, we want to access not only the list values but also their index. We can use the range() function to iterate over the list n times, where n is the length of the list. Here, we calculate n by len(exam_rank) :

Note that we use i+1 to print meaningful results, since the index in Python starts at 0.

For Loops With enumerate()

A “Pythonic” way to track the index value in the for loop requires using the enumerate() function. It allows you to iterate over lists and tuples while also accessing the index of each element in the body of the for loop:

When combining the for loop with enumerate() , we have access to the current count ( place in our example) and the respective value ( student in our example) in the body of the loop. Optionally, we can specify the starting count argument to have it start from 1 as we have done, or from any other number that makes sense in your case.

Time to Practice For Loops in Python!

This is a general overview of the Python for loop just to quickly show you how it works and when you can use it. However, there is much more to learn, and even more importantly, you need lots of practice to master the Python for loop.

A good way to start practicing is with the Python courses that can be either free or paid. The course Python Basics. Part 1 is one of the best options for Python newbies. It covers all basic topics, including the for loop, the while loop, conditional statements, and many more. With 95 interactive exercises, this course gives you a strong foundation for becoming a powerful Python user. Here is a review of the Python Basics Course for those interested in learning more details.

If you’re determined to become a Python programmer, I recommend starting with the track Learn Programming with Python . It includes 5 courses with hundreds of interactive exercises, covering not only basics but also built-in algorithms and functions. They can help you write optimized applications and real Python games.

Thanks for reading and happy learning!

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The for statement creates a loop that consists of three optional expressions, enclosed in parentheses and separated by semicolons, followed by a statement (usually a block statement ) to be executed in the loop.

An expression (including assignment expressions ) or variable declaration evaluated once before the loop begins. Typically used to initialize a counter variable. This expression may optionally declare new variables with var or let keywords. Variables declared with var are not local to the loop, i.e. they are in the same scope the for loop is in. Variables declared with let are local to the statement.

The result of this expression is discarded.

An expression to be evaluated before each loop iteration. If this expression evaluates to true , statement is executed. If the expression evaluates to false , execution exits the loop and goes to the first statement after the for construct.

This conditional test is optional. If omitted, the condition always evaluates to true.

An expression to be evaluated at the end of each loop iteration. This occurs before the next evaluation of condition . Generally used to update or increment the counter variable.

A statement that is executed as long as the condition evaluates to true. You can use a block statement to execute multiple statements. To execute no statement within the loop, use an empty statement ( ; ).

The following for statement starts by declaring the variable i and initializing it to 0 . It checks that i is less than nine, performs the two succeeding statements, and increments i by 1 after each pass through the loop.

Initialization block syntax

The initialization block accepts both expressions and variable declarations. However, expressions cannot use the in operator unparenthesized, because that is ambiguous with a for...in loop.

Optional for expressions

All three expressions in the head of the for loop are optional. For example, it is not required to use the initialization block to initialize variables:

Like the initialization block, the condition part is also optional. If you are omitting this expression, you must make sure to break the loop in the body in order to not create an infinite loop.

You can also omit all three expressions. Again, make sure to use a break statement to end the loop and also modify (increase) a variable, so that the condition for the break statement is true at some point.

However, in the case where you are not fully using all three expression positions — especially if you are not declaring variables with the first expression but mutating something in the upper scope — consider using a while loop instead, which makes the intention clearer.

Lexical declarations in the initialization block

Declaring a variable within the initialization block has important differences from declaring it in the upper scope , especially when creating a closure within the loop body. For example, for the code below:

It logs 0 , 1 , and 2 , as expected. However, if the variable is defined in the upper scope:

It logs 3 , 3 , and 3 . The reason is that each setTimeout creates a new closure that closes over the i variable, but if the i is not scoped to the loop body, all closures will reference the same variable when they eventually get called — and due to the asynchronous nature of setTimeout , it will happen after the loop has already exited, causing the value of i in all queued callbacks' bodies to have the value of 3 .

This also happens if you use a var statement as the initialization, because variables declared with var are only function-scoped, but not lexically scoped (i.e. they can't be scoped to the loop body).

The scoping effect of the initialization block can be understood as if the declaration happens within the loop body, but just happens to be accessible within the condition and afterthought parts. More precisely, let declarations are special-cased by for loops — if initialization is a let declaration, then every time, after the loop body is evaluated, the following happens:

  • A new lexical scope is created with new let -declared variables.
  • The binding values from the last iteration are used to re-initialize the new variables.
  • afterthought is evaluated in the new scope.

So re-assigning the new variables within afterthought does not affect the bindings from the previous iteration.

A new lexical scope is also created after initialization , just before condition is evaluated for the first time. These details can be observed by creating closures, which allow to get hold of a binding at any particular point. For example, in this code a closure created within the initialization section does not get updated by re-assignments of i in the afterthought :

This does not log "0, 1, 2", like what would happen if getI is declared in the loop body. This is because getI is not re-evaluated on each iteration — rather, the function is created once and closes over the i variable, which refers to the variable declared when the loop was first initialized. Subsequent updates to the value of i actually create new variables called i , which getI does not see. A way to fix this is to re-compute getI every time i updates:

The i variable inside the initialization is distinct from the i variable inside every iteration, including the first. So, in this example, getI returns 0, even though the value of i inside the iteration is incremented beforehand:

In fact, you can capture this initial binding of the i variable and re-assign it later, and this updated value will not be visible to the loop body, which sees the next new binding of i .

This logs "0, 0, 0", because the i variable in each loop evaluation is actually a separate variable, but getI and incrementI both read and write the initial binding of i , not what was subsequently declared.

Using for without a body

The following for cycle calculates the offset position of a node in the afterthought section, and therefore it does not require the use of a statement section, a semicolon is used instead.

Note that the semicolon after the for statement is mandatory, because it stands as an empty statement . Otherwise, the for statement acquires the following console.log line as its statement section, which makes the log execute multiple times.

Using for with two iterating variables

You can create two counters that are updated simultaneously in a for loop using the comma operator . Multiple let and var declarations can also be joined with commas.

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In programming, a loop is used to repeat a block of code until the specified condition is met.

C programming has three types of loops:

  • do...while loop

We will learn about for loop in this tutorial. In the next tutorial, we will learn about while and do...while loop.

The syntax of the for loop is:

  • How for loop works?
  • The initialization statement is executed only once.
  • Then, the test expression is evaluated. If the test expression is evaluated to false, the for loop is terminated.
  • However, if the test expression is evaluated to true, statements inside the body of the for loop are executed, and the update expression is updated.
  • Again the test expression is evaluated.

This process goes on until the test expression is false. When the test expression is false, the loop terminates.

To learn more about test expression (when the test expression is evaluated to true and false), check out relational and logical operators .

for loop Flowchart

Flowchart of for loop in C programming

Example 1: for loop

  • i is initialized to 1.
  • The test expression i < 11 is evaluated. Since 1 less than 11 is true, the body of for loop is executed. This will print the 1 (value of i ) on the screen.
  • The update statement ++i is executed. Now, the value of i will be 2. Again, the test expression is evaluated to true, and the body of for loop is executed. This will print 2 (value of i ) on the screen.
  • Again, the update statement ++i is executed and the test expression i < 11 is evaluated. This process goes on until i becomes 11.
  • When i becomes 11, i < 11 will be false, and the for loop terminates.

Example 2: for loop

The value entered by the user is stored in the variable num . Suppose, the user entered 10.

The count is initialized to 1 and the test expression is evaluated. Since the test expression count<=num (1 less than or equal to 10) is true, the body of for loop is executed and the value of sum will equal to 1.

Then, the update statement ++count is executed and count will equal to 2. Again, the test expression is evaluated. Since 2 is also less than 10, the test expression is evaluated to true and the body of the for loop is executed. Now, sum will equal 3.

This process goes on and the sum is calculated until the count reaches 11.

When the count is 11, the test expression is evaluated to 0 (false), and the loop terminates.

Then, the value of sum is printed on the screen.

We will learn about while loop and do...while loop in the next tutorial.

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for loop to repeat specified number of times

Description

for index = values , statements , end executes a group of statements in a loop for a specified number of times. values has one of the following forms:

initVal : endVal — Increment the index variable from initVal to endVal by 1 , and repeat execution of statements until index is greater than endVal .

initVal : step : endVal — Increment index by the value step on each iteration, or decrements index when step is negative.

valArray — Create a column vector, index , from subsequent columns of array valArray on each iteration. For example, on the first iteration, index = valArray (:,1) . The loop executes a maximum of n times, where n is the number of columns of valArray , given by numel( valArray (1,:)) . The input valArray can be of any MATLAB ® data type, including a character vector, cell array, or struct.

collapse all

Assign Matrix Values

Create a Hilbert matrix of order 10.

Decrement Values

Step by increments of -0.2 , and display the values.

Execute Statements for Specified Values

Repeat statements for each matrix column.

To programmatically exit the loop, use a break statement. To skip the rest of the instructions in the loop and begin the next iteration, use a continue statement.

Avoid assigning a value to the index variable within the loop statements. The for statement overrides any changes made to index within the loop.

To iterate over the values of a single column vector, first transpose it to create a row vector.

Extended Capabilities

C/c++ code generation generate c and c++ code using matlab® coder™..

Usage notes and limitations:

Suppose that the loop end value is equal to or close to the maximum or minimum value for the loop index data type. In the generated code, the last increment or decrement of the loop index might cause the index variable to overflow. The index overflow might result in an infinite loop. See Loop Index Overflow (MATLAB Coder) .

HDL Code Generation Generate VHDL, Verilog and SystemVerilog code for FPGA and ASIC designs using HDL Coder™.

Do not use for loops without static bounds.

Do not use the & and | operators within conditions of a for statement. Instead, use the && and || operators.

HDL Coder™ does not support nonscalar expressions in the conditions of for statements. Instead, use the all or any functions to collapse logical vectors into scalars.

Thread-Based Environment Run code in the background using MATLAB® backgroundPool or accelerate code with Parallel Computing Toolbox™ ThreadPool .

This function fully supports thread-based environments. For more information, see Run MATLAB Functions in Thread-Based Environment .

Version History

Introduced before R2006a

end | break | continue | parfor | return | switch | colon | if

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Mathematics LibreTexts

1.1: Four Ways to Represent a Function

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Learning Objectives

  • Determine whether a relation represents a function.
  • Find the value of a function.
  • Determine whether a function is one-to-one.
  • Use the vertical line test to identify functions.
  • Graph the functions listed in the library of functions.

A jetliner changes altitude as its distance from the starting point of a flight increases. The weight of a growing child increases with time. In each case, one quantity depends on another. There is a relationship between the two quantities that we can describe, analyze, and use to make predictions. In this section, we will analyze such relationships.

Determining Whether a Relation Represents a Function

A relation is a set of ordered pairs. The set of the first components of each ordered pair is called the domain and the set of the second components of each ordered pair is called the range. Consider the following set of ordered pairs. The first numbers in each pair are the first five natural numbers. The second number in each pair is twice that of the first.

\[\{(1, 2), (2, 4), (3, 6), (4, 8), (5, 10)\}\tag{1.1.1}\]

The domain is \(\{1, 2, 3, 4, 5\}\). The range is \(\{2, 4, 6, 8, 10\}\).

Note that each value in the domain is also known as an input value, or independent variable , and is often labeled with the lowercase letter \(x\). Each value in the range is also known as an output value, or dependent variable , and is often labeled lowercase letter \(y\).

A function \(f\) is a relation that assigns a single value in the range to each value in the domain. In other words, no \(x\)-values are repeated. For our example that relates the first five natural numbers to numbers double their values, this relation is a function because each element in the domain, {1, 2, 3, 4, 5}, is paired with exactly one element in the range, \(\{2, 4, 6, 8, 10\}\).

Now let’s consider the set of ordered pairs that relates the terms “even” and “odd” to the first five natural numbers. It would appear as

\[\mathrm{\{(odd, 1), (even, 2), (odd, 3), (even, 4), (odd, 5)\}} \tag{1.1.2}\]

Notice that each element in the domain, {even, odd} is not paired with exactly one element in the range, \(\{1, 2, 3, 4, 5\}\). For example, the term “odd” corresponds to three values from the range, \(\{1, 3, 5\},\) and the term “even” corresponds to two values from the range, \(\{2, 4\}\). This violates the definition of a function, so this relation is not a function.

Figure \(\PageIndex{1}\) compares relations that are functions and not functions.

[Three relations that demonstrate what constitute a function.]

A function is a relation in which each possible input value leads to exactly one output value. We say “the output is a function of the input.”

The input values make up the domain , and the output values make up the range .

How To: Given a relationship between two quantities, determine whether the relationship is a function

  • Identify the input values.
  • Identify the output values.
  • If each input value leads to only one output value, classify the relationship as a function. If any input value leads to two or more outputs, do not classify the relationship as a function.

Example \(\PageIndex{1}\): Determining If Menu Price Lists Are Functions

The coffee shop menu, shown in Figure \(\PageIndex{2}\) consists of items and their prices.

  • Is price a function of the item?
  • Is the item a function of the price?

A menu of donut prices from a coffee shop where a plain donut is $1.49 and a jelly donut and chocolate donut are $1.99.

  • Let’s begin by considering the input as the items on the menu. The output values are then the prices. See Figure \(\PageIndex{3}\).

[A menu of donut prices from a coffee shop where a plain donut is $1.49 and a jelly donut and chocolate donut are $1.99.]

Each item on the menu has only one price, so the price is a function of the item.

  • Two items on the menu have the same price. If we consider the prices to be the input values and the items to be the output, then the same input value could have more than one output associated with it. See Figure \(\PageIndex{4}\).

[Association of the prices to the donuts.]

Therefore, the item is a not a function of price.

Example \(\PageIndex{2}\): Determining If Class Grade Rules Are Functions

In a particular math class, the overall percent grade corresponds to a grade point average. Is grade point average a function of the percent grade? Is the percent grade a function of the grade point average? Table \(\PageIndex{1}\) shows a possible rule for assigning grade points.

For any percent grade earned, there is an associated grade point average, so the grade point average is a function of the percent grade. In other words, if we input the percent grade, the output is a specific grade point average.

In the grading system given, there is a range of percent grades that correspond to the same grade point average. For example, students who receive a grade point average of 3.0 could have a variety of percent grades ranging from 78 all the way to 86. Thus, percent grade is not a function of grade point average.

Exercise \(\PageIndex{2}\)

Table \(\PageIndex{2}\) lists the five greatest baseball players of all time in order of rank.

  • Is the rank a function of the player name?
  • Is the player name a function of the rank?

yes. (Note: If two players had been tied for, say, 4th place, then the name would not have been a function of rank.)

Using Function Notation

Once we determine that a relationship is a function, we need to display and define the functional relationships so that we can understand and use them, and sometimes also so that we can program them into computers. There are various ways of representing functions. A standard function notation is one representation that facilitates working with functions.

To represent “height is a function of age,” we start by identifying the descriptive variables \(h\) for height and \(a\) for age. The letters \(f\), \(g\),and \(h\) are often used to represent functions just as we use \(x\), \(y\),and \(z\) to represent numbers and \(A\), \(B\), and \(C\) to represent sets.

\[\begin{array}{ll} h \text{ is } f \text{ of }a \;\;\;\;\;\; & \text{We name the function }f \text{; height is a function of age.} \\ h=f(a) & \text{We use parentheses to indicate the function input.} \\ f(a) & \text{We name the function }f \text{ ; the expression is read as “ }f \text{ of }a \text{.”}\end{array}\]

Remember, we can use any letter to name the function; the notation \(h(a)\) shows us that \(h\) depends on \(a\). The value \(a\) must be put into the function \(h\) to get a result. The parentheses indicate that age is input into the function; they do not indicate multiplication.

We can also give an algebraic expression as the input to a function. For example \(f(a+b)\) means “first add \(a\) and \(b\), and the result is the input for the function \(f\).” The operations must be performed in this order to obtain the correct result.

Function Notation

The notation \(y=f(x)\) defines a function named \(f\). This is read as “\(y\) is a function of \(x\).” The letter \(x\) represents the input value, or independent variable. The letter \(y\), or \(f(x)\), represents the output value, or dependent variable.

Example \(\PageIndex{3}\): Using Function Notation for Days in a Month

Use function notation to represent a function whose input is the name of a month and output is the number of days in that month.

Using Function Notation for Days in a Month

The number of days in a month is a function of the name of the month, so if we name the function \(f\), we write \(\text{days}=f(\text{month})\) or \(d=f(m)\). The name of the month is the input to a “rule” that associates a specific number (the output) with each input.

The function 31 = f(January) where 31 is the output, f is the rule, and January is the input.

For example, \(f(\text{March})=31\), because March has 31 days. The notation \(d=f(m)\) reminds us that the number of days, \(d\) (the output), is dependent on the name of the month, \(m\) (the input).

Note that the inputs to a function do not have to be numbers; function inputs can be names of people, labels of geometric objects, or any other element that determines some kind of output. However, most of the functions we will work with in this book will have numbers as inputs and outputs.

Example \(\PageIndex{3B}\): Interpreting Function Notation

A function \(N=f(y)\) gives the number of police officers, \(N\), in a town in year \(y\). What does \(f(2005)=300\) represent?

When we read \(f(2005)=300\), we see that the input year is 2005. The value for the output, the number of police officers \((N)\), is 300. Remember, \(N=f(y)\). The statement \(f(2005)=300\) tells us that in the year 2005 there were 300 police officers in the town.

Exercise \(\PageIndex{3}\)

Use function notation to express the weight of a pig in pounds as a function of its age in days \(d\).

Instead of a notation such as \(y=f(x)\), could we use the same symbol for the output as for the function, such as \(y=y(x)\), meaning “\(y\) is a function of \(x\)?”

Yes, this is often done, especially in applied subjects that use higher math, such as physics and engineering. However, in exploring math itself we like to maintain a distinction between a function such as \(f\) , which is a rule or procedure, and the output y we get by applying \(f\) to a particular input \(x\) . This is why we usually use notation such as \(y=f(x),P=W(d)\) , and so on.

Representing Functions Using Tables

A common method of representing functions is in the form of a table. The table rows or columns display the corresponding input and output values. In some cases, these values represent all we know about the relationship; other times, the table provides a few select examples from a more complete relationship.

Table \(\PageIndex{3}\) lists the input number of each month (\(\text{January}=1\), \(\text{February}=2\), and so on) and the output value of the number of days in that month. This information represents all we know about the months and days for a given year (that is not a leap year). Note that, in this table, we define a days-in-a-month function \(f\) where \(D=f(m)\) identifies months by an integer rather than by name.

Table \(\PageIndex{4}\) defines a function \(Q=g(n)\) Remember, this notation tells us that \(g\) is the name of the function that takes the input \(n\) and gives the output \(Q\).

Table \(\PageIndex{5}\) displays the age of children in years and their corresponding heights. This table displays just some of the data available for the heights and ages of children. We can see right away that this table does not represent a function because the same input value, 5 years, has two different output values, 40 in. and 42 in.

How To: Given a table of input and output values, determine whether the table represents a function

  • Identify the input and output values.
  • Check to see if each input value is paired with only one output value. If so, the table represents a function.

Example \(\PageIndex{5}\): Identifying Tables that Represent Functions

Which table, Table \(\PageIndex{6}\), Table \(\PageIndex{7}\), or Table \(\PageIndex{8}\), represents a function (if any)?

Table \(\PageIndex{6}\) and Table \(\PageIndex{7}\) define functions. In both, each input value corresponds to exactly one output value. Table \(\PageIndex{8}\) does not define a function because the input value of 5 corresponds to two different output values.

When a table represents a function, corresponding input and output values can also be specified using function notation.

The function represented by Table \(\PageIndex{6}\) can be represented by writing

\[f(2)=1\text{, }f(5)=3\text{, and }f(8)=6 \nonumber\]

Similarly, the statements

\[g(−3)=5\text{, }g(0)=1\text{, and }g(4)=5 \nonumber\]

represent the function in Table \(\PageIndex{7}\).

Table \(\PageIndex{8}\) cannot be expressed in a similar way because it does not represent a function.

Exercise \(\PageIndex{5}\)

Does Table \(\PageIndex{9}\) represent a function?

Finding Input and Output Values of a Function

When we know an input value and want to determine the corresponding output value for a function, we evaluate the function. Evaluating will always produce one result because each input value of a function corresponds to exactly one output value.

When we know an output value and want to determine the input values that would produce that output value, we set the output equal to the function’s formula and solve for the input. Solving can produce more than one solution because different input values can produce the same output value.

Evaluation of Functions in Algebraic Forms

When we have a function in formula form, it is usually a simple matter to evaluate the function. For example, the function \(f(x)=5−3x^2\) can be evaluated by squaring the input value, multiplying by 3, and then subtracting the product from 5.

How To: Given the formula for a function, evaluate.

Given the formula for a function, evaluate.

  • Replace the input variable in the formula with the value provided.
  • Calculate the result.

Example \(\PageIndex{6A}\): Evaluating Functions at Specific Values

1. Evaluate \(f(x)=x^2+3x−4\) at

  • Evaluate \(\frac{f(a+h)−f(a)}{h}\)

Replace the x in the function with each specified value.

a. Because the input value is a number, 2, we can use simple algebra to simplify.

\[\begin{align*}f(2)&=2^2+3(2)−4\\&=4+6−4\\ &=6\end{align*}\]

b. In this case, the input value is a letter so we cannot simplify the answer any further.

\[f(a)=a^2+3a−4\nonumber\]

c. With an input value of \(a+h\), we must use the distributive property.

\[\begin{align*}f(a+h)&=(a+h)^2+3(a+h)−4\\&=a^2+2ah+h^2+3a+3h−4 \end{align*}\]

d. In this case, we apply the input values to the function more than once, and then perform algebraic operations on the result. We already found that

\[f(a+h)=a^2+2ah+h^2+3a+3h−4\nonumber\]

and we know that

\[f(a)=a^2+3a−4 \nonumber\]

Now we combine the results and simplify.

\[\begin{align*}\dfrac{f(a+h)−f(a)}{h}&=\dfrac{(a^2+2ah+h^2+3a+3h−4)−(a^2+3a−4)}{h}\\ &=\dfrac{(2ah+h^2+3h)}{h} \\ &=\dfrac{h(2a+h+3)}{h} & &\text{Factor out h.}\\ &=2a+h+3 & & \text{Simplify.}\end{align*}\]

Example \(\PageIndex{6B}\): Evaluating Functions

Given the function \(h(p)=p^2+2p\), evaluate \(h(4)\).

To evaluate \(h(4)\), we substitute the value 4 for the input variable p in the given function.

\[\begin{align*}h(p)&=p^2+2p\\h(4)&=(4)^2+2(4)\\ &=16+8\\&=24\end{align*}\]

Therefore, for an input of 4, we have an output of 24.

Exercise \(\PageIndex{6}\)

Given the function \(g(m)=\sqrt{m−4}\), evaluate \(g(5)\).

Example \(\PageIndex{7}\): Solving Functions

Given the function \(h(p)=p^2+2p\), solve for \(h(p)=3\).

\[\begin{array}{rl} h(p)=3\\p^2+2p=3 & \text{Substitute the original function}\\ p^2+2p−3=0 & \text{Subtract 3 from each side.}\\(p+3)(p−1)=0&\text{Factor.}\end{array} \nonumber \]

If \((p+3)(p−1)=0\), either \((p+3)=0\) or \((p−1)=0\) (or both of them equal \(0\)). We will set each factor equal to \(0\) and solve for \(p\) in each case.

\[(p+3)=0,\; p=−3 \nonumber \]

\[(p−1)=0,\, p=1 \nonumber\]

This gives us two solutions. The output \(h(p)=3\) when the input is either \(p=1\) or \(p=−3\). We can also verify by graphing as in Figure \(\PageIndex{6}\). The graph verifies that \(h(1)=h(−3)=3\) and \(h(4)=24\).

[Graph of a parabola with labeled points (-3, 3), (1, 3), and (4, 24).]

Exercise \(\PageIndex{7}\)

Given the function \(g(m)=\sqrt{m−4}\), solve \(g(m)=2\).

Evaluating Functions Expressed in Formulas

Some functions are defined by mathematical rules or procedures expressed in equation form. If it is possible to express the function output with a formula involving the input quantity, then we can define a function in algebraic form. For example, the equation \(2n+6p=12\) expresses a functional relationship between \(n\) and \(p\). We can rewrite it to decide if \(p\) is a function of \(n\).

How to: Given a function in equation form, write its algebraic formula.

  • Solve the equation to isolate the output variable on one side of the equal sign, with the other side as an expression that involves only the input variable.
  • Use all the usual algebraic methods for solving equations, such as adding or subtracting the same quantity to or from both sides, or multiplying or dividing both sides of the equation by the same quantity.

Example \(\PageIndex{8A}\): Finding an Equation of a Function

Express the relationship \(2n+6p=12\) as a function \(p=f(n)\), if possible.

To express the relationship in this form, we need to be able to write the relationship where \(p\) is a function of \(n\), which means writing it as \(p=[\text{expression involving }n]\).

\[\begin{align*}2n+6p&=12 \\ 6p&=12−2n && \text{Subtract 2n from both sides.} \\ p&=\dfrac{12−2n}{6} & &\text{Divide both sides by 6 and simplify.} \\ p&=\frac{12}{6}−\frac{2n}{6} \\ p&=2−\frac{1}{3}n\end{align*}\]

Therefore, \(p\) as a function of \(n\) is written as

\[p=f(n)=2−\frac{1}{3}n \nonumber\]

It is important to note that not every relationship expressed by an equation can also be expressed as a function with a formula.

Example \(\PageIndex{8B}\): Expressing the Equation of a Circle as a Function

Does the equation \(x^2+y^2=1\) represent a function with \(x\) as input and \(y\) as output? If so, express the relationship as a function \(y=f(x)\).

First we subtract \(x^2\) from both sides.

\[y^2=1−x^2 \nonumber\]

We now try to solve for \(y\) in this equation.

\[y=\pm\sqrt{1−x^2} \nonumber\]

\[\text{so, }y=\sqrt{1−x^2}\;\text{and}\;y = −\sqrt{1−x^2} \nonumber\]

We get two outputs corresponding to the same input, so this relationship cannot be represented as a single function \(y=f(x)\).

Exercise \(\PageIndex{8}\)

If \(x−8y^3=0\), express \(y\) as a function of \(x\).

\(y=f(x)=\dfrac{\sqrt[3]{x}}{2}\)

Are there relationships expressed by an equation that do represent a function but which still cannot be represented by an algebraic formula?

Yes, this can happen. For example, given the equation \(x=y+2^y\), if we want to express y as a function of x, there is no simple algebraic formula involving only \(x\) that equals \(y\). However, each \(x\) does determine a unique value for \(y\), and there are mathematical procedures by which \(y\) can be found to any desired accuracy. In this case, we say that the equation gives an implicit (implied) rule for \(y\) as a function of \(x\), even though the formula cannot be written explicitly.

Evaluating a Function Given in Tabular Form

As we saw above, we can represent functions in tables. Conversely, we can use information in tables to write functions, and we can evaluate functions using the tables. For example, how well do our pets recall the fond memories we share with them? There is an urban legend that a goldfish has a memory of 3 seconds, but this is just a myth. Goldfish can remember up to 3 months, while the beta fish has a memory of up to 5 months. And while a puppy’s memory span is no longer than 30 seconds, the adult dog can remember for 5 minutes. This is meager compared to a cat, whose memory span lasts for 16 hours.

The function that relates the type of pet to the duration of its memory span is more easily visualized with the use of a table (Table \(\PageIndex{10}\)).

At times, evaluating a function in table form may be more useful than using equations. Here let us call the function \(P\). The domain of the function is the type of pet and the range is a real number representing the number of hours the pet’s memory span lasts. We can evaluate the function \(P\) at the input value of “goldfish.” We would write \(P(goldfish)=2160\). Notice that, to evaluate the function in table form, we identify the input value and the corresponding output value from the pertinent row of the table. The tabular form for function P seems ideally suited to this function, more so than writing it in paragraph or function form.

How To: Given a function represented by a table, identify specific output and input values

1. Find the given input in the row (or column) of input values. 2. Identify the corresponding output value paired with that input value. 3. Find the given output values in the row (or column) of output values, noting every time that output value appears. 4. Identify the input value(s) corresponding to the given output value.

Example \(\PageIndex{9}\): Evaluating and Solving a Tabular Function

Using Table \(\PageIndex{11}\),

a. Evaluate \(g(3)\). b. Solve \(g(n)=6\).

a. Evaluating \(g(3)\) means determining the output value of the function \(g\) for the input value of \(n=3\). The table output value corresponding to \(n=3\) is 7, so \(g(3)=7\). b. Solving \(g(n)=6\) means identifying the input values, n,that produce an output value of 6. Table \(\PageIndex{12}\) shows two solutions: 2 and 4.

When we input 2 into the function \(g\), our output is 6. When we input 4 into the function \(g\), our output is also 6.

Exercise \(\PageIndex{1}\)

Using Table \(\PageIndex{12}\), evaluate \(g(1)\).

Finding Function Values from a Graph

Evaluating a function using a graph also requires finding the corresponding output value for a given input value, only in this case, we find the output value by looking at the graph. Solving a function equation using a graph requires finding all instances of the given output value on the graph and observing the corresponding input value(s).

Example \(\PageIndex{10}\): Reading Function Values from a Graph

Given the graph in Figure \(\PageIndex{7}\),

  • Evaluate \(f(2)\).
  • Solve \(f(x)=4\).

Graph of a positive parabola centered at (1, 0)

To evaluate \(f(2)\), locate the point on the curve where \(x=2\), then read the y-coordinate of that point. The point has coordinates \((2,1)\), so \(f(2)=1\). See Figure \(\PageIndex{8}\).

Graph of a positive parabola centered at (1, 0) with the labeled point (2, 1) where f(2) =1.

To solve \(f(x)=4\), we find the output value 4 on the vertical axis. Moving horizontally along the line \(y=4\), we locate two points of the curve with output value 4: \((−1,4)\) and \((3,4)\). These points represent the two solutions to \(f(x)=4\): −1 or 3. This means \(f(−1)=4\) and \(f(3)=4\), or when the input is −1 or 3, the output is 4. See Figure \(\PageIndex{9}\).

Graph of an upward-facing parabola with a vertex at (0,1) and labeled points at (-1, 4) and (3,4). A line at y = 4 intersects the parabola at the labeled points.

Exercise \(\PageIndex{10}\)

Given the graph in Figure \(\PageIndex{7}\), solve \(f(x)=1\).

\(x=0\) or \(x=2\)

Determining Whether a Function is One-to-One

Some functions have a given output value that corresponds to two or more input values. For example, in the stock chart shown in the Figure at the beginning of this chapter, the stock price was $1000 on five different dates, meaning that there were five different input values that all resulted in the same output value of $1000.

However, some functions have only one input value for each output value, as well as having only one output for each input. We call these functions one-to-one functions. As an example, consider a school that uses only letter grades and decimal equivalents, as listed in Table \(\PageIndex{13}\).

This grading system represents a one-to-one function, because each letter input yields one particular grade point average output and each grade point average corresponds to one input letter.

To visualize this concept, let’s look again at the two simple functions sketched in Figures \(\PageIndex{1a}\) and \(\PageIndex{1b}\). The function in part (a) shows a relationship that is not a one-to-one function because inputs \(q\) and \(r\) both give output \(n\). The function in part (b) shows a relationship that is a one-to-one function because each input is associated with a single output.

One-to-One Functions

A one-to-one function is a function in which each output value corresponds to exactly one input value.

Example \(\PageIndex{11}\): Determining Whether a Relationship Is a One-to-One Function

Is the area of a circle a function of its radius? If yes, is the function one-to-one?

A circle of radius \(r\) has a unique area measure given by \(A={\pi}r^2\), so for any input, \(r\), there is only one output, \(A\). The area is a function of radius\(r\).

If the function is one-to-one, the output value, the area, must correspond to a unique input value, the radius. Any area measure \(A\) is given by the formula \(A={\pi}r^2\). Because areas and radii are positive numbers, there is exactly one solution:\(\sqrt{\frac{A}{\pi}}\). So the area of a circle is a one-to-one function of the circle’s radius.

Exercise \(\PageIndex{11A}\)

  • Is a balance a function of the bank account number?
  • Is a bank account number a function of the balance?
  • Is a balance a one-to-one function of the bank account number?

a. yes, because each bank account has a single balance at any given time;

b. no, because several bank account numbers may have the same balance;

c. no, because the same output may correspond to more than one input.

Exercise \(\PageIndex{11B}\)

Evaluate the following:

  • If each percent grade earned in a course translates to one letter grade, is the letter grade a function of the percent grade?
  • If so, is the function one-to-one?

a. Yes, letter grade is a function of percent grade; b. No, it is not one-to-one. There are 100 different percent numbers we could get but only about five possible letter grades, so there cannot be only one percent number that corresponds to each letter grade.

Using the Vertical Line Test

As we have seen in some examples above, we can represent a function using a graph. Graphs display a great many input-output pairs in a small space. The visual information they provide often makes relationships easier to understand. By convention, graphs are typically constructed with the input values along the horizontal axis and the output values along the vertical axis.

The most common graphs name the input value \(x\) and the output \(y\), and we say \(y\) is a function of \(x\), or \(y=f(x)\) when the function is named \(f\). The graph of the function is the set of all points \((x,y)\) in the plane that satisfies the equation \(y=f(x)\). If the function is defined for only a few input values, then the graph of the function is only a few points, where the x-coordinate of each point is an input value and the y-coordinate of each point is the corresponding output value. For example, the black dots on the graph in Figure \(\PageIndex{10}\) tell us that \(f(0)=2\) and \(f(6)=1\). However, the set of all points \((x,y)\) satisfying \(y=f(x)\) is a curve. The curve shown includes \((0,2)\) and \((6,1)\) because the curve passes through those points

Graph of a polynomial.

The vertical line test can be used to determine whether a graph represents a function. If we can draw any vertical line that intersects a graph more than once, then the graph does not define a function because a function has only one output value for each input value. See Figure \(\PageIndex{11}\) .

Three graphs visually showing what is and is not a function.

Howto: Given a graph, use the vertical line test to determine if the graph represents a function

  • Inspect the graph to see if any vertical line drawn would intersect the curve more than once.
  • If there is any such line, determine that the graph does not represent a function.

Example \(\PageIndex{12}\): Applying the Vertical Line Test

Which of the graphs in Figure \(\PageIndex{12}\) represent(s) a function \(y=f(x)\)?

Graph of a polynomial (a), a downward-sloping line (b), and a circle (c).

If any vertical line intersects a graph more than once, the relation represented by the graph is not a function. Notice that any vertical line would pass through only one point of the two graphs shown in parts (a) and (b) of Figure \(\PageIndex{12}\). From this we can conclude that these two graphs represent functions. The third graph does not represent a function because, at most x-values, a vertical line would intersect the graph at more than one point, as shown in Figure \(\PageIndex{13}\).

Graph of a circle.

Exercise \(\PageIndex{12}\)

Does the graph in Figure \(\PageIndex{14}\) represent a function?

[Absolute function f(x)=|x|.]

Using the Horizontal Line Test

Once we have determined that a graph defines a function, an easy way to determine if it is a one-to-one function is to use the horizontal line test . Draw horizontal lines through the graph. If any horizontal line intersects the graph more than once, then the graph does not represent a one-to-one function.

Howto: Given a graph of a function, use the horizontal line test to determine if the graph represents a one-to-one function

  • Inspect the graph to see if any horizontal line drawn would intersect the curve more than once.
  • If there is any such line, determine that the function is not one-to-one.

Example \(\PageIndex{13}\): Applying the Horizontal Line Test

Consider the functions shown in Figure \(\PageIndex{12a}\) and Figure \(\PageIndex{12b}\). Are either of the functions one-to-one?

The function in Figure \(\PageIndex{12a}\) is not one-to-one. The horizontal line shown in Figure \(\PageIndex{15}\) intersects the graph of the function at two points (and we can even find horizontal lines that intersect it at three points.)

Graph of a polynomial with a horizontal line crossing through 2 points

The function in Figure \(\PageIndex{12b}\) is one-to-one. Any horizontal line will intersect a diagonal line at most once.

Exercise \(\PageIndex{13}\)

Is the graph shown in Figure \(\PageIndex{13}\) one-to-one?

No, because it does not pass the horizontal line test.

Identifying Basic Toolkit Functions

In this text, we will be exploring functions—the shapes of their graphs, their unique characteristics, their algebraic formulas, and how to solve problems with them. When learning to read, we start with the alphabet. When learning to do arithmetic, we start with numbers. When working with functions, it is similarly helpful to have a base set of building-block elements. We call these our “toolkit functions,” which form a set of basic named functions for which we know the graph, formula, and special properties. Some of these functions are programmed to individual buttons on many calculators. For these definitions we will use x as the input variable and \(y=f(x)\) as the output variable.

We will see these toolkit functions, combinations of toolkit functions, their graphs, and their transformations frequently throughout this book. It will be very helpful if we can recognize these toolkit functions and their features quickly by name, formula, graph, and basic table properties. The graphs and sample table values are included with each function shown in Table \(\PageIndex{14}\).

Key Equations

  • Constant function \(f(x)=c\), where \(c\) is a constant
  • Identity function \(f(x)=x\)
  • Absolute value function \(f(x)=|x|\)
  • Quadratic function \(f(x)=x^2\)
  • Cubic function \(f(x)=x^3\)
  • Reciprocal function \(f(x)=\dfrac{1}{x}\)
  • Reciprocal squared function \(f(x)=\frac{1}{x^2}\)
  • Square root function \(f(x)=\sqrt{x}\)
  • Cube root function \(f(x)=3\sqrt{x}\)

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Python Functions is a block of statements that return the specific task. The idea is to put some commonly or repeatedly done tasks together and make a function so that instead of writing the same code again and again for different inputs, we can do the function calls to reuse code contained in it over and over again.

Some Benefits of Using Functions

  • Increase Code Readability 
  • Increase Code Reusability

Python Function Declaration

The syntax to declare a function is:

Python Functions

Syntax of Python Function Declaration

Types of Functions in Python

There are mainly two types of functions in Python .

  • Built-in library function: These are Standard functions in Python that are available to use.
  • User-defined function: We can create our own functions based on our requirements.

Creating a Function in Python

We can define a function in Python, using the def keyword. We can add any type of functionalities and properties to it as we require.

Calling a  Python Function

After creating a function in Python we can call it by using the name of the function followed by parenthesis containing parameters of that particular function.

Python Function with Parameters

If you have experience in C/C++ or Java then you must be thinking about the return type of the function and data type of arguments. That is possible in Python as well (specifically for Python 3.5 and above).

Defining and calling a function with parameters

The following example uses arguments and parameters that you will learn later in this article so you can come back to it again if not understood.

Note: The following examples are defined using syntax 1, try to convert them in syntax 2 for practice.

Python Function Arguments

Arguments are the values passed inside the parenthesis of the function. A function can have any number of arguments separated by a comma.

In this example, we will create a simple function in Python to check whether the number passed as an argument to the function is even or odd.

Types of Python Function Arguments

Python supports various types of arguments that can be passed at the time of the function call. In Python, we have the following 4 types of function arguments.

  • Default argument
  • Keyword arguments (named arguments)
  • Positional arguments
  • Arbitrary arguments (variable-length arguments *args and **kwargs)

Let’s discuss each type in detail. 

Default Arguments

A default argument is a parameter that assumes a default value if a value is not provided in the function call for that argument. The following example illustrates Default arguments. 

Like C++ default arguments, any number of arguments in a function can have a default value. But once we have a default argument, all the arguments to its right must also have default values.

Keyword Arguments

The idea is to allow the caller to specify the argument name with values so that the caller does not need to remember the order of parameters.

Positional Arguments

We used the Position argument during the function call so that the first argument (or value) is assigned to name and the second argument (or value) is assigned to age. By changing the position, or if you forget the order of the positions, the values can be used in the wrong places, as shown in the Case-2 example below, where 27 is assigned to the name and Suraj is assigned to the age.

Arbitrary Keyword  Arguments

In Python Arbitrary Keyword Arguments, *args, and **kwargs can pass a variable number of arguments to a function using special symbols. There are two special symbols:

  • *args in Python (Non-Keyword Arguments)
  • **kwargs in Python (Keyword Arguments)

Example 1: Variable length non-keywords argument

Example 2: Variable length keyword arguments

The first string after the function is called the Document string or Docstring in short. This is used to describe the functionality of the function. The use of docstring in functions is optional but it is considered a good practice.

The below syntax can be used to print out the docstring of a function:

Example: Adding Docstring to the function

Python Function within Functions

A function that is defined inside another function is known as the inner function or nested function . Nested functions can access variables of the enclosing scope. Inner functions are used so that they can be protected from everything happening outside the function.

Anonymous Functions in Python

In Python, an anonymous function means that a function is without a name. As we already know the def keyword is used to define the normal functions and the lambda keyword is used to create anonymous functions.

Recursive Functions in Python

Recursion in Python refers to when a function calls itself. There are many instances when you have to build a recursive function to solve Mathematical and Recursive Problems.

Using a recursive function should be done with caution, as a recursive function can become like a non-terminating loop. It is better to check your exit statement while creating a recursive function.

Here we have created a recursive function to calculate the factorial of the number. You can see the end statement for this function is when n is equal to 0. 

Return Statement in Python Function

The function return statement is used to exit from a function and go back to the function caller and return the specified value or data item to the caller. The syntax for the return statement is:

The return statement can consist of a variable, an expression, or a constant which is returned at the end of the function execution. If none of the above is present with the return statement a None object is returned.

Example: Python Function Return Statement

Pass by Reference and Pass by Value

One important thing to note is, in Python every variable name is a reference. When we pass a variable to a function, a new reference to the object is created. Parameter passing in Python is the same as reference passing in Java.

When we pass a reference and change the received reference to something else, the connection between the passed and received parameters is broken. For example, consider the below program as follows:

Another example demonstrates that the reference link is broken if we assign a new value (inside the function). 

Exercise: Try to guess the output of the following code. 

Quick Links: 

  • Quiz on Python Functions
  • Difference between Method and Function in Python
  • Recent articles on Python Functions .

FAQs- Python Functions

Q1. what is function in python.

Python function is a block of code, that runs only when it is called. It is programmed to return the specific task. You can pass values in functions called parameters. It helps in performing repetitive tasks.

Q2. What are the 4 types of Functions in Python?

The main types of functions in Python are: Built-in function User-defined function Lambda functions Recursive functions

Q3. How to define function in Python?

To define a function in Python you can use the def keyword and then write the function name. You can provide the function code after using ‘:’. Basic syntax to define a function is: def function_name(): Function code

Q4. What are the parameters of a function in Python?

Parameters in Python are the variables that take the values passed as arguments when calling the functions. A function can have any number of parameters. You can also set default value to a parameter in Python.

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Python Program to Swap Two Elements in a List [4 Methods]

Swapping two elements in Python from a list refers to exchanging their positions. In other words, if we want to take two elements at specific indices in the list and swap their places. So that we can change the position of the elements within the list.

In this Python tutorial , I will demonstrate how to write a Python Program to swap two elements in a list .

Here, we will cover different methods to swap two elements in a list in Python, such as using comma assignment, temporary variables, pop() function, and enumerate() function .

To better understand the problem, let’s consider an example. Suppose we have a list of numbers with elements [1, 2, 3, 4, 5], and we want to swap the elements at indices 1 and 3.

After swapping, the updated list should be [1, 4, 3, 2, 5], where the element at index 1 (which is 2) is swapped with the element at index 3 (which is 4).

Let’s begin to implement these methods one by one with various examples.

Table of Contents

Swap Two Elements in a List in Python Using Comma Assignment

We can swap the positions of the elements because the positions of the elements are known.

Here is the complete Python program to swap two elements in a list using a comma assignment .

Here, I have used comma assignment in this Python program to perform simultaneous assignments or swapping of elements in a list.

Here, we call a Python function named swap_position with arguments list_of_elements, position1-1, and position2-1 . The -1 adjusts the positions since indexing typically starts from 0 .

Refer to the below screenshot, it provides the output of the Python program to swap two elements in a list using comma assignment.

Swap two elements in a list in Python

Swap Two Elements in a List Using the Temp Variable

We will see how to swap two elements in a Python list using a temp variable . This is the source code of Python to swap two elements in a list using a temp variable.

We will use a temp variable to store the element’s values in Python.

The image below shows the output of the Python program to swap two elements in a list using the temp variable.

Python program to swap two elements in a list

Swap Two Elements in a List Using the Enumerate Function

In Python, enumerate is a built-in function that adds a counter to an iterable and returns it as an enumerate object (iterator with index and the value).

Here is the complete Python program to swap two elements in a list using the enumerate function.

Here, using the enumerate function to iterate over the elements of the list and by using conditional if statements in Python, we will check if the current index is equal to the value of the specified position.

You can refer to the screenshot below to see the output of the Python program to swap two elements in a list using the enumerate function.

Swap two elements in a list in Python using the enumerate function

Python Program to Swap Two Elements in a List Using the Pop Function

The pop() function in Python is used to remove the element at the specified position. This is the complete Python code to swap two elements in a list using the pop function.

The pop() function is used here to remove and return the element at the specified index in Python. Since indices typically start from 0, -1 adjusts the order’s index.

Refer to the screenshot below; it provides the output of the Python program to swap two elements in a list using the pop() function in Python .

How to swap two elements in a list using pop() function in Python

In this post, we have shown how to write a Python Program to swap two elements in a list . Additionally, we have discussed the different approaches for swapping two elements in Python and provided a step-by-step explanation of each example.

Methods we explained in this Python tutorial to swap two elements in a list in Python include comma assignment, temporary variables, enumerate() function, and pop() function .

You may also like to read:

  • How to Swap Two Numbers in Python Using Function
  • Python Program to Check Armstrong Number
  • Python Program for Selection Sort

Bijay - Python Expert

I am Bijay Kumar, a Microsoft MVP in SharePoint. Apart from SharePoint, I started working on Python, Machine learning, and artificial intelligence for the last 5 years. During this time I got expertise in various Python libraries also like Tkinter, Pandas, NumPy, Turtle, Django, Matplotlib, Tensorflow, Scipy, Scikit-Learn, etc… for various clients in the United States, Canada, the United Kingdom, Australia, New Zealand, etc. Check out my profile .

How-To Geek

How to use take in excel to extract data.

Extract specific data from your Excel table.

Quick Links

Prepare your table in excel, how to use take to extract the first and/or last rows and/or columns in excel, how to use take to extract a specific column in excel, how to use take with average in excel.

Excel's TAKE function will let you extract the first, last, or specific columns or rows from a table. For example, you might want to extract the data from the last three days or display the top ranked individuals. Let's look into this in more detail.

Excel's TAKE function only works in Microsoft 365 or Excel for the web.

Before you can use TAKE and CHOOSE, you will need to format and name your table . We will use this table of data as our example:

Data unformatted-2

Ensure you have included a row that includes headings for your columns. Now, select any cell within your table and click "Format As Table" in the "Styles" group of the "Home" tab.

Excel sheet with the 'Format As Table' option highlighted.

Click your preferred layout and, in the dialog box that opens, check "My Table Has Headers" and click "OK".

Now that Excel recognizes your data as a formatted table, you need to change the table name (for later use). In the "Table Design" tab on the ribbon, head to the "Properties" group and change the "Table Name" field to one that works for you.

Excel sheet highlighting where the table name can be amended.

You're now ready to extract data.

Excel's TAKE function is mostly used to extract the first or last few rows or columns from your table. The formula you'll need to use is:

=TAKE(X,Y,Z)

where X is the table name, Y is the number of rows to extract, and Z is the number of columns to extract. Simply place a "-" in front of Y or Z to change that part of the formula from the first rows or columns to the last rows or columns.

If the number of rows or columns that you want to extract might change, instead of typing digits for Y and Z, you can place the number in another cell and type the appropriate cell reference.

In our example, we want to find out the names of the top five employees based on profit per month.

First, create a place on your worksheet where you want the data to be extracted, and type an appropriate header. In our case, we've chosen cell J2 and the header "Top 5."

Excel sheet with a table of data and a place for our first formula to be inserted.

Second, start to type the formula as follows:

The next part of your formula is the table name. Begin typing the name of your table in your formula, and then double-click when you see it appear in the suggestions box. Then, add a comma.

Excel sheet with the first part of the TAKE formula typed into a cell and the table name appearing as an option to include within the formula.

=TAKE(Employees,

You now need to tell Excel how many of the first or last rows you want to include in your extracted data. In our case, we want the top five employees. Therefore, we type "5" and add a comma. If we wanted the last five rows, we'd type "-5". To extract all rows, simply don't include the number, and add the comma.

=TAKE(Employees,5,

Finally, finish your formula by telling Excel how many of the first or last columns you want to include. We'll go for just the first column, as we want only the employees' names, and close the parentheses and press Enter. Again, type "-" if you want to extract the last x columns. To extract all columns, miss out the number and press Enter.

=TAKE(Employees,5,1)

You will now see the desired outcome. Now, if you change or reorder the data in your table, the TAKE formula you have just added will automatically adjust to extract the updated information. For example, we want to reorder the column containing profit per month:

Excel sheet showing the result of using the TAKE formula in conjunction with an ordered column of data in the table.

If you were to add more data to your table, the TAKE formula would account for this. For example, if we added another employee's data to the bottom of the table in an additional row (by dragging the corner handle of the table downwards one row and completing their figures), the TAKE formula would include this when looking for the criteria you set.

If you want to extract a specific column, follow the steps above but add the column name to your formula in place of the number of columns .

Let's say that, in our example above, we need to work out how many months each of the five longest serving employees have been at the company. This would be our formula:

=TAKE(Employees[Months of service],5)

where "Employees" is the table's name, "[Months of service]" is the column name (notice the lack of a comma in between these two parts of the formula), and "5" is the number of rows we want to extract from the named column. Remember to filter the corresponding column in your table.

Excel sheet showing the length of the longest five payrolls using TAKE and a named column within the formula.

If you want to use TAKE with Excel's AVERAGE function , follow the steps above but nest the TAKE formula within your AVERAGE formula .

For example, let's say we want to work out the average earnings of the top five employees. This would be our formula:

=AVERAGE( TAKE(Employees,5,-1) )

where the AVERAGE formula surrounds the TAKE formula, which includes "Employees" (table name), "5" (we want to take the top 5 rows), and "-1" (we want to take the last column).

Excel sheet with the top five average calculated through the AVERAGE and TAKE functions being used together.

You now have a fundamental understanding of how the TAKE formula works in Excel. You can now go one step further—extract columns or rows from multiple ranges by using Excel's VSTACK and HSTACK functions , or combine TAKE with Excel's SORTBY function to see it work without you sorting your table's columns. Finally, you can use Excel's DROP function, which excludes certain cells and rows from your extracted data and works with exactly the same syntax as the TAKE function.

Function Transformations

Transformation of functions means that the curve representing the graph either "moves to left/right/up/down" or "it expands or compresses" or "it reflects". For example, the graph of the function f(x) = x 2 + 3 is obtained by just moving the graph of g(x) = x 2 by 3 units up. Function transformations are very helpful in graphing the functions just by moving/expanding/compressing/reflecting the curve without actually needing to graph it from scratch.

In this article, we will see what are the rules of function transformations and we will see how to do transformations of different types of functions along with examples.

What are Function Transformations?

A function transformation either "moves" or "resizes" or "reflects" the graph of the parent function. There are mainly three types of function transformations :

  • Translation

Among these transformations, only dilation changes the size of the original shape but the other two transformations change the position of the shape but not the size of the shape. We can see what each of these transformations of functions mean in the table below.

In math words, the transformation of a function y = f(x) typically looks like y = a f(b(x + c)) + d. Here, a, b, c, and d are any real numbers and they represent transformations. Note that all outside numbers (that are outside the brackets) represent vertical transformations and all inside numbers represent horizontal transformations. Also, note that addition/subtraction indicates translation and multiplication/division represents dilation. Any minus sign multiplies means that it is a reflection. Here,

  • 'a' represents the vertical dilation
  • 'b' represents the horizontal dilation
  • 'c' represents the horizontal translation
  • 'd' represents the vertical translation

Let us learn each of these function transformations in detail.

Translation of Functions

A translation occurs when every point on a graph (representing a function) moves by the same amount in the same direction. There are two types of translations of functions.

  • Horizontal translations
  • Vertical translations

Horizontal Translation of Functions :

In this translation, the function moves to the left side or right side. This changes a function y = f(x) into the form y = f(x ± k), where 'k' represents the horizontal translation . Here,

  • if k > 0, then the function moves to the left side by 'k' units.
  • if k < 0, then the function moves to the right by 'k' units.

Horizontal translation of functions

Here, the original function y = x 2 (y = f(x)) is moved to 3 units right to give the transformed function y = (x - 3) 2 (y = f(x - 3)).

Vertical Translation of Functions :

In this translation, the function moves to either up or down. This changes a function y = f(x) into the form f(x) ± k, where 'k' represents the vertical translation . Here,

  • if k > 0, then the function moves up by 'k' units.
  • if k < 0, then the function moves down by 'k' units.

vertical translation of functions

Here, the original function y = x 2 (y = f(x)) is moved to 2 units up to give the transformed function y = x 2 + 2 (y = f(x) + 2).

Dilation of Functions

A dilation is a stretch or a compression. If a graph undergoes dilation parallel to the x-axis, all the x-values are increased by the same scale factor. Similarly, if it is dilated parallel to the y-axis, all the y-values are increased by the same scale factor. There are two types of dilations.

Horizontal Dilation

Vertical Dilation

The horizontal dilation (also known as horizontal scaling ) of a function either stretches/shrinks the curve horizontally. It changes a function y = f(x) into the form y = f(kx), with a scale factor '1/k', parallel to the x-axis. Here,

  • If k > 1, then the graph shrinks.
  • If 0 < k < 1, then the graph stretches.

In this dilation, there will be changes only in the x-coordinates but there won't be any changes in the y-coordinates. Every old x-coordinate is multiplied by 1/k to find the new x-coordinate. In the following graph, the original function y = x 3 is stretched horizontally by a scale factor of 3 to give the transformed function graph y = (x/3) 3 . For example, the point (1,1) of the original graph is transformed to (3, 1) of the new graph.

horizontal dilation of functions

The vertical dilation (also known as vertical scaling ) of a function either stretches/shrinks the curve vertically. It changes a function y = f(x) into the form y = k f(x), with a scale factor 'k', parallel to the y-axis. Here,

  • If k > 1, then the graph stretches.
  • If 0 < k < 1, then the graph shrinks.

In this dilation, there will be changes only in the y-coordinates but there won't be any changes in the x-coordinates. Every old y-coordinate is multiplied by k to find the new y-coordinate. In the following graph, the original function y = x 3 is stretched vertically by a scale factor of 3 to give the transformed function graph y = 3x 3 . For example, the point (1, 1) (on the original graph) corresponds to (1, 3) on the new graph.

Vertical dilation of functions

Reflections of Functions

A reflection of a function is just the image of the curve with respect to either x-axis or y-axis. This occurs whenever we see the multiplication of a minus sign happening somewhere in the function. Here,

  • y = - f(x) is the reflection of y = f(x) with respect to the x-axis.
  • y = f(-x) is the reflection of y = f(x) with resepct to the y-axis.

Observe the graph below where the original graph y = (x + 2) 2 is reflected with respect to each of the x and y axes.

Reflections of Functions

Here, note that when the function is reflected

  • with respect to the x-axis, only the signs of the y-coordinates are changed and there is no change in x-coordinates.
  • with respect to the y-axis, only the signs of the x-coordinates are changed and there is no change in y-coordinates.

Function Transformation Rules

So far we have understood the types of transformations of functions and how do addition/subtraction/multiplication/division of a number and the multiplication of a minus sign would reflect a graph. Let us tabulate all function transformation rules together.

Are the above rules are confusing and difficult to remember? Let us see some important tips to remember these rules.

Tips and Tricks to Remember Function Transformations:

  • If some operation is inside the bracket, note that it is related to "horizontal" and in this case, things would happen reverse than what we think. For example, we may think f(x + 2) transforms f(x) to the right because it is + but it actually moves left by 2 units. In the same way, we may think f(3x) stretches f(x) but no, it shrinks f(x) by a scale factor of 1/3.
  • If some operation is outside the bracket, note that it is related to "vertical" and in this case, things would happen straight (not reverse). For example, f(x) + 2 moves f(x) "up" it is a "+" symbol there. In the same way, 3 f(x) stretches f(x) by a scale factor of 3 as 3 > 1.
  • If some number is being added / subtracted , then its related to "translation". For example, f(x + 2) is a horizontal translation and f(x) + 2 is a vertical translation.
  • If some number is being multiplied / divided , then its related to "dilation". For example, f(2x) is a horizontal dilation and 2 f(x) is a vertical dilation.
  • Just in case of reflection, it is just the opposite of the first and second tricks here. If the minus sign is inside the bracket, it is with respect to the y-axis and if the minus sign is outside the bracket, it is with respect to the x-axis.

Describing Function Transformations

We can use the above rules to describe any function transformation. For example, if the question is what is the effect of transformation g(x) = - 3f(x + 5) + 2 on y = f(x), then first observe the sequence of operations that had to be applied on f(x) to get g(x) and then use the above rules to define the transformations. Here, to get g(x) from f(x)

  • first f(x) changes into f(x + 5). i.e., horizontal translation by 5 units to the left.
  • Then it changes into 3 f(x + 5). i.e., vertical dilation by a scale factor of 3.
  • Then it changes into -3 f(x + 5). i.e., reflection about the x-axis.
  • Finally, it changes into -3 f(x + 5) + 2. i.e., vertical translation by 2 units up.

Thus, g(x) is obtained from f(x) by horizontal translation by 5 units to the left, vertical dilation by a scale factor of 3, reflection about the x-axis, and vertical translation by 2 units up. We can describe the transformations of functions by using the above tricks also. Give it a try now.

Graphing Transformations of Functions

Identifying the transformation by looking at the original and transformed graphs is easy because just by looking at the graph, we can say that the graph moves up by 2 units or left by 3 units, etc. But when a graph is given, graphing the function transformation is sometimes difficult. The following steps make graphing transformations so easier. Here, we are transforming the function y = f(x) to y = a f(b (x + c)) + d.

  • Step 1: Note down some coordinates on the original curve that define its shape. i.e., we now know the old x and y coordinates .
  • Step 2: To find the new x-coordinate of each point just set "b (x + c) = old x-coordinate" and solve this for x.
  • Step 3: To find the new y-coordinate of each point, just apply all outside operations (of brackets) on the old y-coordinate. i.e., find ay + d to find each new y-coordinate where 'y' is the old y-coordinate.

We can understand these steps better by using the example below.

Example: The following graph represents f(x). Graph the function transformation y = 2 f(x/2) + 3.

Graphing Transformations of Functions

We can clearly see that (-3, 2), (-1, 2), (2, -1) and (6, 1) are defining the shape of the graph. Let us find the new x and y coordinates of each of these points.

Now, we will plot all old points and new points on the coordinate plane and observe the transformations.

Graph Transformations

☛ Related Topics:

  • Transformation Matrix
  • Linear Fractional Transformation

Function Transformations Examples

Example 1: Describe the transformations of quadratic function g(x) = x 2 + 4x + 5 by comparing it to its parent function f(x) = x 2 .

To identify the transformation of quadratic functions, we have to convert it into vertex form . Then we can write g(x) = x 2 + 4x + 5 can be written as g(x) = (x + 2) 2 + 1.

Now we will compare the original function f(x) = x 2 with g(x) = (x + 2) 2 + 1 and apply the function transformation rules.

  • x converted to x + 2 and it corresponds to the horizontal translation of 2 units to the left.
  • 1 is added to the function and it corresponds to the vertical translation of 1 unit upwards.

Answer: 2 units to left and 1 unit to up.

Example 2: State the combination of transformations applied on the function f(x) to obtain g(x): f(x) = -3x - 6 and g(x) = x + 2.

We have g(x) = x + 2 = -1/3 (-3x - 6) = -1/3 f(x)

Thus, the combinations of transformations applied on f(x) are:

  • Vertical dilation by a scale factor of 1/3 and
  • reflection with respect to the x-axis.

Answer: Vertical dilation and reflection.

Example 3: Write the function corresponding to the graph of g(x) that transformed from the graph f(x) by using the function transformation rules.

Function Transformations Example

Take f(x) as the original function and observe how it is moving/transforming to give g(x). Observe the vertex of both graphs to get an idea. It is very clear that

  • it moved 6 units to the left and so the function is f(x + 6).
  • it then reflected with respect to the x-axis, so the function is - f(x + 6).

Answer: g(x) = - f(x + 6).

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Practice Questions on Function Transformations

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FAQs on Function Transformations

What are transformations of functions.

The transformations of functions define how to graph a function is moving and how its shape is being changed. There are basically three types of function transformations: translation, dilation, and reflection.

How Do You Find the Function Transformations?

To find the function transformations we have to identify whether it is a translation, dilation, or reflection or sometimes it is a mixture of some/all the transformations. For a function y = f(x),

  • if a number is being added or subtracted inside the bracket then it is a horizontal translation . If the number is negative then the horizontal transformation is happening to the right side. If the number is positive then the horizontal transformation is happening to the left side.
  • If a number is being added or subtracted outside the bracket then it is a vertical translation. If the number is positive then the vertical translation is happening toward up. If the number is negative then the vertical translation is happening to the downside.
  • If a number is being multiplied or divided inside the brackets then it is horizontal dilation. If the number is > 1, then it is a horizontal shrink. If the number is between 0 and 1, then it is a horizontal stretch.
  • If a number is being multiplied or divided outside the brackets then it is vertical dilation. If the number is > 1, then it is a vertical stretch. If the number is between 0 and 1, then it is a vertical shrink.
  • If the function is multiplied by the minus sign inside the bracket, then it is a reflection with respect to the y-axis.
  • If the function is multiplied by the minus sign outside the bracket, then it is a reflection with respect to the x-axis.

How to Explain the Function Transformations?

To explain the function transformations we have to apply the rules of transformations of functions. For example, 3 f(x + 2) - 5 is obtained by applying the following function transformations on f(x):

  • horizontal translation by 2 units left.
  • Vertical dilation by a scale factor of 3.
  • Vertical translation by 5 units down.

What are the Rules of Transformations of Functions?

The rules of function transformations for each of the translation, dilation, and reflection:

  • Horizontal translation: it is of the form f(x + k) and it moves f(x) to k units left if k > 0 and k units right if k < 0. Vertical translation: it is of the form f(x) + k and it moves f(x) to k units up if k > 0 and k units down if k < 0.
  • Horizontal dilation : It is of the form f(kx) and it shrinks f(x) if k > 1 and stretches f(x) if 0 < k < 1. Vertical dilation: It is of the form k f(x) and it shrinks f(x) if 0 < k < 1 and stretches f(x) if k > 1.
  • Reflection with respect to the x-axis is of the form - f(x). Reflection with respect to the y-axis is of the form f(-x).

What are Different Types of Function Transformations?

There are mainly three types of function transformations.

  • Translation: it moves the graph of the original function to either left, right, up, or down.
  • Dilation: it either shrinks or stretches the graph of the original function horizontally or vertically.
  • Reflection: it reflects the graph of the original function ( in other words it creates the mirror image of the original function) with respect to x or y axes.

What is the Easiest Way of Remembering Function Transformations?

Here is the easiest way of remembering the function transformations. If something is happening inside the bracket then it corresponds to the horizontal transformations. If something is happening outside the brackets then it corresponds to the vertical transformations. If a minus sign is being multiplied either outside or inside the bracket then it corresponds to the reflection.

JS Tutorial

Js versions, js functions, js html dom, js browser bom, js web apis, js vs jquery, js graphics, js examples, js references, javascript functions.

A JavaScript function is a block of code designed to perform a particular task.

A JavaScript function is executed when "something" invokes it (calls it).

JavaScript Function Syntax

A JavaScript function is defined with the function keyword, followed by a name , followed by parentheses () .

Function names can contain letters, digits, underscores, and dollar signs (same rules as variables).

The parentheses may include parameter names separated by commas: ( parameter1, parameter2, ... )

The code to be executed, by the function, is placed inside curly brackets: {}

Function parameters are listed inside the parentheses () in the function definition.

Function arguments are the values received by the function when it is invoked.

Inside the function, the arguments (the parameters) behave as local variables.

Function Invocation

The code inside the function will execute when "something" invokes (calls) the function:

  • When an event occurs (when a user clicks a button)
  • When it is invoked (called) from JavaScript code
  • Automatically (self invoked)

You will learn a lot more about function invocation later in this tutorial.

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Function Return

When JavaScript reaches a return statement, the function will stop executing.

If the function was invoked from a statement, JavaScript will "return" to execute the code after the invoking statement.

Functions often compute a return value . The return value is "returned" back to the "caller":

Calculate the product of two numbers, and return the result:

Why Functions?

With functions you can reuse code

You can write code that can be used many times.

You can use the same code with different arguments, to produce different results.

The () Operator

The () operator invokes (calls) the function:

Convert Fahrenheit to Celsius:

Accessing a function with incorrect parameters can return an incorrect answer:

Accessing a function without () returns the function and not the function result:

As you see from the examples above, toCelsius refers to the function object, and toCelsius() refers to the function result.

Functions Used as Variable Values

Functions can be used the same way as you use variables, in all types of formulas, assignments, and calculations.

Instead of using a variable to store the return value of a function:

You can use the function directly, as a variable value:

You will learn a lot more about functions later in this tutorial.

Local Variables

Variables declared within a JavaScript function, become LOCAL to the function.

Local variables can only be accessed from within the function.

Since local variables are only recognized inside their functions, variables with the same name can be used in different functions.

Local variables are created when a function starts, and deleted when the function is completed.

Test Yourself With Exercises

Execute the function named myFunction .

Start the Exercise

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How do I convince the model to BOTH write a message and call a function?

I want the gpt4 (0125) model to BOTH write a message to the user and call a function. I tried every prompting technique I could think of, but it still only includes the message around 30% of the time - otherwise it returns the function call but no messages.

Any idea what I can do? The related part of the prompt is below:

When calling any of these functions, you ALWAYS also start by writing one sentence to the user about why you are using it. This helps you keep track of your reasoning, and helps the user follow along as you proceed. ALWAYS write additional explanation when using a tool or function. This is very important to me. You will be tipped extra if you do it. My grandmother will die if you don’t include explanations. I’m not kidding. She’s very old and frail. Please help me keep her alive.

Maybe try a one or two-shot example for the model to follow?

How can I do this in the system prompt for the chat api? I can’t really give it examples of function call responses, don’t know how openai represents them internally?

I would first try it ass a form of pseudocode. Basically give an example of a user input, a message to the user, then something like, “ <beep boop> now I’m calling this function with these parameters. <modem hiss> now I’m getting the results… Based on the previous function call the answer to your question is…”

Hmm, will try that, but I fear it will then just do the whole thing as a user message (with text saying “I’m calling function xxx”)… will report back!

And it very well might. You might need to preface the examples with an instruction to replace that but with actual function calls, but it’s worth a shot.

:slight_smile:

This is a good idea, and would probably work for a static message.

I didn’t suggest it because the OP’s original instruction was,

Which I assume will vary quite a bit, even for the same function call.

But, this is definitely an idea worthy of trying.

That’s plan B - just a lot harder to implement (and get to work with streaming responses) with our current framework/codebase, but if all else fails, it should indeed guarantee that we get the “thought” (as much as you can guarantee anything with LLMs)

Oh yes, streaming is more complex … Then there would be the double function call (2 functions) by forcing it to first call the thought function and then reinjecting…

I don’t think you are using this in the way it’s intended.

if you receive a function call you process that, then send the history window and the answer back to the llm to receive a further response which, if not another function call, might be something you then share with the user.

Yes, the goal here is that for multi-hop answers (e.g. the llm chooses a function call, I give it the results, then decides it needs to call another function before answering the user) I want to show progress to the user - otherwise they’re just staring at a blank screen for a long time until we get the final answer. It’s similar to what ChatGPT does with plugins (sometimes).

It also has the added benefit of serving as a “reasoning” step which is known to improve llm performance.

yeah, the delay on the bigger models is definitely an issue.

I don’t find this a problem with 3.5 though …

@OP - Did you recently start testing this? Your expected behaviour is what we experienced since going to to GPT4 Turbo. But the past few days we have seen a degradation, and beginning yesterday all function calling stopped working.

The model is now only “SIMULATING” function calls and hallucinating reaponses, instead of using calls. It’s very disturbing.

2 Options that you could try to achieve the desired behaviour are

a) Add a required function param like “message” that the model has to write. You can send the message param to the user as message and use the other params to call the actual function

b) Use Few Shot examples: Another post stated that you CAN actually send the called functions as example to a model by simply taking the function_calls array from a response where the model did what you want and appending that array in the example message where you want it to be. A 1-Shot History would then look something like this:

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Run » finance, how to write an employee expense policy.

An employee expense policy keeps team members aligned on spending for the company and provides a blueprint for getting reimbursed.

 A chef stands in a fully outfitted kitchen and looks down at a handwritten spreadsheet and a calculator. The chef is a man wearing a short white hat and white chef's uniform. He holds a pen in one hand and a piece of paper in the other.

A formal employee expense policy sets rules and terms for how team members should spend company money. This policy can help avoid confusion and budget mismanagement by detailing how your company deals with expenses related to your day-to-day work, as well as how employees can be reimbursed.

Successful employee expense policies cover three main topics : the expense categories that can be claimed against the company budget, steps for getting reimbursed, and the procedure that takes place if an expense is disputed. Here are some things to consider related to these categories that can help you make a user-friendly, transparent, and fair employee expense policy.

Get feedback from all your key functions

No matter if your business is 10 people or 100, it’s important to get input from different roles within the organization to learn more about their expenses. Sales, for instance, will have different costs than HR. What might be important for one role could look wasteful for another department.

Ideally, you’ll be able to define your expense policy in a way that’s equitable to every function’s needs. Likewise, your finance team can give you guidance on how much spending is too much. “Consider what [your employees] need to excel at their job, but also think about what they shouldn’t be able to buy,” wrote Spendesk .

Define your reimbursable expense categories

Start with a clear definition of what expenses you’re willing to reimburse as part of doing business. Establish clear, transparent rules for everyone to follow. For instance, every expense for which an employee is being reimbursed must have a direct business purpose. Employees must also provide proof of payment in the form of a receipt, invoice, or credit card statement.

Likewise, create spending categories that guide how you budget reimbursable expenses. “Clear expense categories simplify accounting, taxes, and financial reporting,” wrote Rho , a corporate card and expense management provider.

Common expense categories to include in your expense policy include:

  • Travel and travel-related expenses.
  • Meals and entertainment.
  • Transportation costs.
  • Accommodation.
  • Office expenses.
  • Communication.

Define each of these categories in depth as you write your policy to make sure employees know where to assign their reimbursement requests. It can also be helpful to include a list of expenses that aren’t eligible for reimbursement so there are no surprises in the future.

[Read more: A Small Business Guide to Employee Expense Reimbursement ]

A well-defined policy should pose guidelines for handling exceptions.

Justin Wolz, Head of Communications at Rho

Establish steps for getting reimbursed

Outline the process, required documentation, and any deadlines (e.g., reports must be in before the month end) that employees need to know to get reimbursed. Detail the key parties who need to approve the request, as well as how long an employee can expect to wait to receive payment. If a request is rejected, describe how someone can appeal the process.

On the finance side, describe the filing process for keeping receipts and reimbursement requests for compliance purposes. Local laws will dictate this section of your policy.

“Review any state and federal laws governing expense reporting and reimbursement. Make sure your policy aligns with these laws. Take a similar approach with tax laws, knowing that there are strict policies concerning which expenses can or can’t be deducted on your business tax return,” wrote NetSuite .

[Read more: 4 Helpful Tools for Managing Business Travel Expenses ]

Address how to handle expenses that aren’t covered

It’s nearly impossible to anticipate all the expenses that an employee will generate while working for your company. Include a section in your policy that covers any expenses that fall into a gray area or that aren’t addressed by the policy. “A well-defined policy should pose guidelines for handling exceptions. This could include expenditures like surprise medical expenses that aren't typically covered,” wrote Rho .

This section could be as simple as providing a point person to contact when a question comes up. This person could be your CFO, legal counsel, or you — the business owner. Whomever you choose, make sure they understand the philosophy behind your expense policy and can make a fair, transparent decision that aligns with your business values.

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CO—is committed to helping you start, run and grow your small business. Learn more about the benefits of small business membership in the U.S. Chamber of Commerce, here .

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IMAGES

  1. Function Notation

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  2. Writing a Function Rule with an Ordered Pairs Table with 1-Step Rules

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  4. How To Write a Linear Equation From a Function Table

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  5. What is Function Notation Formula? Examples

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  6. Writing A Function Rule Worksheet

    how to write a for function

VIDEO

  1. How to write function by using scientific calculator

  2. How to write function in standard form

  3. Types of Function

  4. 1.2 Representing Functions

  5. how to write a regular function and an arrow function in JavaScript #coding #javascript #shorts

  6. 3.1 Functions and Function Notation

COMMENTS

  1. Python "for" Loops (Definite Iteration)

    Python "for" Loops (Definite Iteration) by John Sturtz 20 Comments basics python Mark as Completed Share Share Email Table of Contents A Survey of Definite Iteration in Programming Numeric Range Loop Three-Expression Loop Collection-Based or Iterator-Based Loop The Python for Loop Iterables Iterators The Guts of the Python for Loop

  2. Python For Loops

    Loop through the letters in the word "banana": for x in "banana": print(x) Try it Yourself » The break Statement With the break statement we can stop the loop before it has looped through all the items: Example Exit the loop when x is "banana": fruits = ["apple", "banana", "cherry"] for x in fruits: print(x) if x == "banana": break

  3. Python for Loop (With Examples)

    for Loop with Python range () In Python, the range () function returns a sequence of numbers. For example, values = range (4) Here, range (4) returns a sequence of 0, 1, 2 ,and 3. Since the range () function returns a sequence of numbers, we can iterate over it using a for loop. For example,

  4. How to Write a For Loop in Python

    Let's go over the syntax of the for loop: It starts with the for keyword, followed by a value name that we assign to the item of the sequence ( country in this case). Then, the in keyword is followed by the name of the sequence that we want to iterate. The initializer section ends with ": ".

  5. python

    Ask Question Asked 1 year, 10 months ago Modified 1 year, 10 months ago Viewed 287 times -2 I'm new to python and I want to convert a loop "for" into a function. My loop I created enables me to multiply all the number of a list and print the result. This is my loop: a= [1,2,3,4,9] y=1 for x in a: y=y*x print (y)

  6. Python For Loops

    geeks Python For Loop in Python Dictionary This code uses a for loop to iterate over a dictionary and print each key-value pair on a new line. The loop assigns each key to the variable i and uses string formatting to print the key and its corresponding value. Python print("Dictionary Iteration") d = dict() d ['xyz'] = 123 d ['abc'] = 345

  7. for

    Syntax js for (initialization; condition; afterthought) statement initialization Optional An expression (including assignment expressions) or variable declaration evaluated once before the loop begins. Typically used to initialize a counter variable.

  8. C for Loop (With Examples)

    Example 1: for loop // Print numbers from 1 to 10 #include <stdio.h> int main() { int i; for (i = 1; i < 11; ++i) { printf("%d ", i); } return 0; } Run Code Output 1 2 3 4 5 6 7 8 9 10 i is initialized to 1. The test expression i < 11 is evaluated. Since 1 less than 11 is true, the body of for loop is executed.

  9. JavaScript for Loop

    The for statement creates a loop with 3 optional expressions: for ( expression 1; expression 2; expression 3) { // code block to be executed } Expression 1 is executed (one time) before the execution of the code block. Expression 2 defines the condition for executing the code block.

  10. for loop to repeat specified number of times

    To programmatically exit the loop, use a break statement. To skip the rest of the instructions in the loop and begin the next iteration, use a continue statement.. Avoid assigning a value to the index variable within the loop statements. The for statement overrides any changes made to index within the loop.. To iterate over the values of a single column vector, first transpose it to create a ...

  11. Functions

    Algebra 1 Unit 8: Functions 2,200 possible mastery points Mastered Proficient Familiar Attempted Not started Quiz Unit test About this unit A function is like a machine that takes an input and gives an output. Let's explore how we can graph, analyze, and create different types of functions. Evaluating functions Learn What is a function?

  12. Javascript: Creating Functions in a For Loop

    3 Answers Sorted by: 42 The second method is a little clearer if you use a parameter name that does not mask the loop variable name: funArr [funArr.length] = (function (val) { return function () { return val; }}) (i); The problem with your current code is that each function is a closure and they all reference the same variable i.

  13. Python Using a For loop inside a function

    It knows how to create a student by prompting for input, and how to calculate an overall grade from the marks. marks are entered using a list comprehension; something like. result = [func (x) for x in lst] which is an easier-to-read equivalent of. result = [] for x in lst: result.append (func (x))

  14. What is a function? (video)

    What is a function? Google Classroom About Transcript Functions assign a single output for each of their inputs. In this video, we see examples of various kinds of functions. Created by Sal Khan. Questions Tips & Thanks Want to join the conversation? Sort by: Top Voted Hannah 11 years ago at 7:26 why is y a square root of three? why not 3 squared?

  15. 1.1: Four Ways to Represent a Function

    The tabular form for function P seems ideally suited to this function, more so than writing it in paragraph or function form. How To: Given a function represented by a table, identify specific output and input values. 1. Find the given input in the row (or column) of input values. 2. Identify the corresponding output value paired with that ...

  16. How to Make FOR Loop in Excel Using Formula (3 Examples)

    Steps to Solve the Above Problem: Here, I will use OR, OFFSET, MAX, MIN, and ROW functions as Excel Formula to create a FOR Loop. Firstly, your job is to open a new workbook and input the above values one by one into the worksheet [start from cell C5 ]. Secondly, select the whole range [from cell C5:C34 ].

  17. Functions Calculator

    Free functions calculator - explore function domain, range, intercepts, extreme points and asymptotes step-by-step

  18. for

    The for statement is used to repeat a block of statements enclosed in curly braces. An increment counter is usually used to increment and terminate the loop. The for statement is useful for any repetitive operation, and is often used in combination with arrays to operate on collections of data/pins. Syntax

  19. Python Functions

    Python Functions is a block of statements that return the specific task. The idea is to put some commonly or repeatedly done tasks together and make a function so that instead of writing the same code again and again for different inputs, we can do the function calls to reuse code contained in it over and over again.

  20. How to Use a For-Loop in R (with 18 Code Examples)

    The basic syntax of a for-loop in R is the following: for (variable in sequence) { expression } Here, sequence is a collection of objects (e.g., a vector) over which the for-loop iterates, variable is an item of that collection at each iteration, and expression in the body of the loop is a set of operations computed for each item.

  21. Python Program to Swap Two Elements in a List [4 Methods]

    In this Python tutorial, I will demonstrate how to write a Python Program to swap two elements in a list. Here, we will cover different methods to swap two elements in a list in Python, such as using comma assignment, temporary variables, pop() function, and enumerate() function. To better understand the problem, let's consider an example.

  22. How to Write Functions in R (with 18 Code Examples)

    The syntax is as follows: function_name <- function (parameters) { function body } Above, the main components of an R function are: function name, function parameters, and function body. Let's take a look at each of them separately. Function Name

  23. How to Use TAKE in Excel to Extract Data

    Excel's TAKE function is mostly used to extract the first or last few rows or columns from your table. The formula you'll need to use is: =TAKE(X,Y,Z) where X is the table name, Y is the number of rows to extract, and Z is the number of columns to extract. Simply place a "-" in front of Y or Z to change that part of the formula from the first ...

  24. Functions Transformations

    Example 3: Write the function corresponding to the graph of g(x) that transformed from the graph f(x) by using the function transformation rules. Solution: Take f(x) as the original function and observe how it is moving/transforming to give g(x). Observe the vertex of both graphs to get an idea. It is very clear that

  25. JavaScript Functions

    Function arguments are the values received by the function when it is invoked. Inside the function, the arguments (the parameters) behave as local variables. ... With functions you can reuse code. You can write code that can be used many times. You can use the same code with different arguments, to produce different results. The Operator.

  26. How do I convince the model to BOTH write a message and call a function?

    When calling any of these functions, you ALWAYS also start by writing one sentence to the user about why you are using it. This helps you keep track of your reasoning, and helps the user follow along as you proceed. ALWAYS write additional explanation when using a tool or function. This is very important to me. You will be tipped extra if you ...

  27. How to Write an Employee Expense Policy

    Before writing your expense policy, make sure to get input from employees in various roles so you have a sense of what resources are needed for each part of your business. ... Get feedback from all your key functions. No matter if your business is 10 people or 100, it's important to get input from different roles within the organization to ...

  28. Business Analyst Job Description (With Examples)

    How To Write a Business Analyst Job Description ... The above job description for a Technical Business Analyst relates to software analysis and includes several of the key functions of a business ...