KATE'S MATH LESSONS
  • Home
  • LESSONS
    • Pre-Algebra
    • Algebra 1
    • Geometry
    • Algebra 2
  • About
  • Contact
  • Blog
  • Shop
  • Courses
  • Home
  • LESSONS
    • Pre-Algebra
    • Algebra 1
    • Geometry
    • Algebra 2
  • About
  • Contact
  • Blog
  • Shop
  • Courses

Different Ways of Representing Functions
(with Mappings, Ordered Pairs, Tables, and Graphs)

Accompanying Resources:
​Functions Bundle 
Intro to functions bundle of activities.  Printable and digital resources for in-class or distance learning.

What's a Function?

If you checked out the Intro to Functions lesson, you may remember that a function takes an input value and assigns an output value.  
You can think of a function like a vending machine. You give it an input value (the code you type in) and it gives an output value (chips, candy, etc). 
Think of a function as a vending machine. A function takes an input value and assigns it an output value.

Representing Functions with Mappings

One important rule to remember about a function is that it can only assign ONE output value to an input value.  The set of all input values is called the domain and the set of all output values is called the range.
There are several different ways to represent a function.  One way is to use a mapping diagram.  A mapping diagram uses arrows to show which input and output values are paired up.
Representing functions with mapping diagrams. The arrows show how the domain and range values are matched up.

In this example, the arrows tell you what you'll get when you enter a code into the vending machine.  There are two slots right next to each other that hold pretzels, so you can enter the code D3 or D4 to get a bag of pretzels.  If you enter the code C2, you'll get a bag of chips.

Remember, a function can only assign one output value to an input value. Here's an example of a mapping that does NOT represent a function:
Kate's Math Lessons
Welcome to Kate's Math Lessons!  

Teachers: make sure to check out the study guides and activities.

Picture
Not all mapping diagrams represent functions. A function can only assign ONE output value to each input value.

According to the mapping diagram above, if you entered the code C2 in the vending machine, it might drop either a bag of chips OR a water bottle.  There's something wrong with this machine!  In order to be a function, each input value can only be assigned to ONE output value. If you enter the code C2 and get a bag of chips, you should get a bag of chips the next time you enter C2. If you enter the same input value again later, you should get the same exact output value that you got the last time.

Let's look at a mapping diagram that uses numbers. Let's say our function takes an input value and multiplies it by 3.  We could enter a few different numbers as input values and make a mapping diagram to show the corresponding output values.
What's a mapping diagram?
This mapping diagram shows that if you enter the number 2, the function multiples it by 3 and gives 6 as the output value.  If you enter 5, you get 15 out.  If you enter in 10, you get 30 as the output value.

​

Representing Functions with Tables

You can also use tables to represent functions.  Instead of using two ovals with circles, a table organizes the input and output values with columns.  The input/domain values go first on the left as the x-values and the corresponding output/range values are listed second in the next column as the y-values.
Using a table to represent a function. The input values are listed on the left in the x column and the corresponding output values are listed in the second y column.

Remember, a function can only assign an input value to one output value.  If you see the same x-value with more than one y-value, the table does not represent a function.

Representing Functions with Ordered Pairs

Another option is to represent a function by writing it as a set of ordered pairs.  The input/domain values are always listed first in the ordered pair as the x-values and the output/range values are always listed second in the ordered pair as the y-values.
Using ordered pairs to represent functions. Input values are listed first as the x-coordinates and output values are listed second as the y-coordinates.
​
​We can use the same mapping diagram from earlier to represent the function with ordered pairs instead. The function can be written as a set of ordered pairs (notice the curly set brackets on the outside). Make sure to put the input values first as the x-coordinates and the corresponding output values second as the y-coordinates.
Representing functions using ordered pairs.

Remember, a function can only assign an input value to one output value.  If you see an x-value repeated in the set and it's been matched with a different y-value, it's not a function.

Representing Functions with Graphs

One additional way to represent a function is with a graph.  If you have a function that's represented as a set of ordered pairs, you can plot each ordered pair and use the graph to represent the function.  
Using a graph to represent a function.

​On a graph, a function could be just a set of ordered pairs or it can also be represented as a continuous line.  For example, the line y = 2x is a function, it takes an input value and multiplies it by 2 to get the output value.  The graph of a function doesn't have to be a straight line, a function can also be a curve.
Functions can be continuous lines or curves.

Video

Want to see some more examples? Check out the short video on functions below.


Practice

Can you answer some questions about functions on your own? Click the START button below to try a practice quiz.

Powered by Interact

Want to learn more about functions? Make sure to check out the lessons on function notation ​and the Vertical Line Test.
Want to try one of my digital math activities for free?  Click the link to grab the teacher version or student version.

Home

About

Privacy Policy

Lessons

Contact

Copyright © 2015 - 2021 Kate's Math Lessons