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Identifying Functions &
Using the Vertical Line Test

Now that you've studied the three examples from our first functions lesson are you ready to try a few on your own?

Let's recap a few things that will help you identify whether the following relations are functions.

A relation is only a function if each input is only paired with one output. In other words - focus on your x coordinate (input). If you have 2 or more x coordinates that are the same - they must all have the same output or it is not a function.

If you are using the vertical line test, and your "line" touches the graph in more than one point, then it is not a function. Your vertical line must only touch the graph at one point.

Now that you have two strategies under your belt, let's give it a whirl.

Ok... let's try a few practice problems!

Practice Problems

Directions: For each problem below, determine if the relation is a function.

vertical line test practice problem

vertical line test practice

Directions: For the next two problems, determine whether the relations, written as ordered pairs, are functions. You can use the vertical line test if you choose to graph the ordered pairs.

Click here to print out graph paper.

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

4. {(-3, 1) (-1, -1) (3,0) (-2, -4)}

Ready to check your answers?

Answer Key

Problem 1

Yes, this graph represents a function. The vertical lines only pass through one point on the graph.

This graph represents a linear equation and all standard linear equations are functions.

vertical line test solutions

Problem 2

Yes, this graph represents a function. The vertical lines only pass through one point on the graph.

vertical line test

Problem 3

NO, this relation is NOT a function. The -5 is paired up with two different outputs.

vertical line test

If you graph the points on a grid, look what happens when you apply the vertical line test.

vertical line test graph

Graph courtesy of Rentcalculators.org free graphing tool.

Problem 4

{(-3, 1) (-1, -1) (3,0) (-2, -4)}

YES, this relation is a function. If we analyze the ordered pairs, we notice that each input is paired with one and only one output.

You can also graph the points if you are unsure and you will find that a vertical line only passes through one point on the graph. Take a look.

vertical line test

Graph courtesy of Rentcalculators.org free graphing tool.

Great Job! Next we will focus on function notation and evaluating functions.

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