Vertical Line Test

Vertical Line Test

How to find out if the given graph is a function or not by using the vertical line test: how to test, examples, and their solutions.

How to Test

If every vertical line shows one output, then the graph passes the test. Then the graph is a function.

Recall a function means [one input], [one output].

The vertical line test is a test
to see if a graph is a function or not.

To do the test:

Make a vertical line on each point of the graph.
The vertical line means [one input], x.
(To make a vertical line,
you can use your pencil, ruler, etc.)

And see if each vertical line shows [one output], y.

If every vertical line shows one output,
then the graph passes the test.

Then the graph is a function.

If there's any vertical line that does not show one output, then the graph fails the test. So the graph is not a function.

If there's any vertical line
that does not show [one output],
(just like this case, showing two outputs,)
then the graph fails the test.

So the graph is not a function.

Example 1

Determine whether the given graph is a function. Graph: Five points

Starting from the left,
make a vertical line for every point,
and see if every vertical line passes
the vertical line test.

As you can see,
every vertical line shows one output.

So the graph passes the vertical line test.

Then the graph is a function.

Example 2

Determine whether the given graph is a function. Graph: Linear Function

Starting from the left,
do the vertical line test.

Every vertical line shows one output.

So the graph passes the vertical line test.

Then the graph is a function.

Example 3

Determine whether the given graph is a function. Graph: Absolute Value Function

The vertical line that is on the origin
passes the vertical line test.

But the other vertical lines show two outputs.

So the graph fails the vertical line test.

So this graph is not a function.

Example 4

Determine whether the given graph is a function. Graph: Quadratic function

Starting from the left,
do the vertical line test.

Every vertical line shows one output.
(It doesn't matter whether
the different vertical lines show the same output.)

Function - Example 3

So the graph passes the vertical line test.

Then the graph is a function.