Vertical Line Test

How to do the vertical line test to see if a graph is a function: 3 examples and their solutions.

Vertical Line Test

Pass

A vertical line test is a way
to see if a graph is a function.
(= to see if a graph shows [one x, one y])

For every point of the graph,
draw a vertical line (= one x).

If the vertical line and the graph
intersect at one point (= one y),
the graph passes the test.

Fail

If the vertical line and the graph
intersect at more than one point
(= not one y),

the graph fails the test.

Example 1

Solution

From the left side of the graph,
think of a vertical line.
Move the vertical line to the right side.
And see if the vertical line and the graph
intersect at [one point].

As you can see,
the line and the graph intersect at one point.

So this graph passes the vertical line test.

So this graph is a function.

Example 2

Solution

Do the vertical line test.

If the vertical line is on the origin,
the line and the graph intersect at one point.

So, at this point,
the graph passes the test.

But if the vertical line is moved to the right,
the line and the graph intersect at two points:
not at one point.

So this graph fails the vertical line test.

So this graph is not a function.

Example 3

Solution

Do the vertical line test.

Move the vertical line from the left to the right.
And see if the vertical line and the graph intersect at [one point].

The line and the graph intersect at one point.
So this graph passes the vertical line test.

So this graph is a function.