What is Range in Math? - Definition & Meaning

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  • 0:01 What Is a Function?
  • 0:42 Domain & Range
  • 0:57 Range
  • 1:20 Determining the Range
  • 3:10 Notation
  • 4:01 Lesson Summary
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Lesson Transcript
Instructor: Jennifer Beddoe

Jennifer has an MS in Chemistry and a BS in Biological Sciences.

The range of a function is the set of values that are produced by that function. This lesson will define and describe how to determine the range and will also give some examples.

What Is a Function?

A function defines a definite relationship between an input and an output. It can be compared to a machine that spits out different items depending on what was put into the machine. An example would be a fictional toy machine. The operator puts in a plastic block, and depending on the color of that block, a certain toy was created. So, if a red block was placed in the machine, it would create a car; a blue block was a plane; a yellow block made a dog. It was the same each time; never did the machine create a car from a yellow block.


In mathematics, functions are usually equations. They can be written as equations or shown as a graph.

Domain and Range

A function's input and output are called the domain and range of the function. The domain relates to the plastic blocks from the example above, and the range would be the toys that are created.

In this lesson, we are going to focus on the range.


The range of a function is the set of all possible values that can be produced by that function. Take for example, the function f(x) = x^2

No matter what value we substitute for x, f(x) will always be positive because any number multiplied to itself is positive.

Therefore, we would say that the range of this function is all positive numbers.

Determining the Range

There are three ways to determine the range of a function: from values, from graphing, and from the rules.

From the Values

A function can be written as a list of values

{(5,3), (2,7), (1,-3), (-2,9)}

The range of this simple function is the second number from each pair, or the list of output values. In this case they are 3, 7 -3, 9.

In the function example from earlier, f(x) = x^2, you also used values to determine the range. Although you might not have written them down, you took specific numbers and substituted them into the function to get an idea of what the result would be.

From Graphing

When you graph a function, the y-values signify the range of that function. You can often determine the range by looking at a graph.


You can see from this graph that the range of the function is between -1 and 1.

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