Identifying Functions by the Domain and Range

Contributor: Ashley Nail. Lesson ID: 13634

What is a function? You may have learned about inputs and outputs, but what about domain and range? In this lesson, you will be able to recognize a function by looking at tables and graphs.


Algebra I, Functions

learning style
Auditory, Visual
personality style
Lion, Otter, Beaver, Golden Retriever
Grade Level
High School (9-12)
Lesson Type
Quick Query

Lesson Plan - Get It!

  • Could you look at a graph or an input-output table and be able to tell if you're looking at a function?
  • Did you know functions are the relationship between an input and an output?
  • But what happens when you have a set of inputs and a set of outputs?
  • Or a graph with ordered pairs?

Well, get ready to learn the basics of functions that will help you solve real-world problems and understand harder math concepts!

In order to identify and recognize functions, we need to understand the concept of domain and range. Then we can look at tables and graphs to find functions around us.

Domain and Range

A function is the relationship between the set of numbers in a domain to the set of numbers in a range.

Think of this as input and output.

The domain represents the set of all inputs for a function. The range represents the set of all possible outputs of a function.

figure 1

Let's imagine that x is a member of the domain.

x gets put into the function, f, and the output will be f(x).

In this example, let's say the rule of the function is x + 3

figure 2

Y then becomes a member of the range.

figure 3

Now, let's take the number 2 from our domain.

2 gets put into the same function f(x) = x + 3.

f(2) = 2 + 3

f(2) = 5

5 then becomes a member of the range, since it is the output of x + 3 and equals f(x).

figure 4

Following the same function rule, we can put each member of the domain into the function to find the output and complete the range.

figure 5

  • Do you see how each member of the domain correlates to exactly one member of the range?

This makes a true function.

If there were to be any repeating members in the domain, this would not be a function.

For example, look at this domain and range.

  • It is not a function...can you figure out why?

figure 6

According to this diagram, the 1 has an output of both 4 and 8. For any input into a function, you will only get one output. A member of the domain cannot be related to more than one member of the range.

figure 7

Therefore, this diagram does not represent a function.

Functions as Tables and Graphs

Functions and the relationships between the domain and range can also be represented in tables and graphs.

For example, look at the function table below:

figure 8

Every member of the domain has exactly one corresponding member of the range.

Now, look at examples of tables that DO NOT represent functions:

figure 9

  • Do you notice anything else different about the yellow table?

The value of 20 is listed twice in the domain; however, it only corresponds to -3 in the range, so that is not the reason the yellow table is not a function.

Now, let's look at graphs.

Remember that f(x) = y, which means ordered pairs represent the input-output.

(input, output)

(x, f(x))

(x, y)

Just like in the tables, every member of the domain correlates to exactly one member of the range.

In order to be a function, the x values cannot have more than one corresponding y value.

  • Are you ready to practice on your own?

Click NEXT to visit the Got It? section to try identifying functions!

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