# Horizontal Line Test

How to use the horizontal line test to see if a function is one-to-one: how to, examples, and their solutions.

## One-to-One, How to Do

One-to-one means 'one x, one unique y'.

So if two x is mapped to the same y,
then it is not one-to-one.
(y is not unique.)

The horizontal line test is a way
to see if a graph satisfies that definition.

To do the test:
Draw a horizontal line on each point of the graph.
(one unique y)

See if there's only one x value for each point.
(one x)

If so, it is one-to-one.
If not, it's not one-to-one.

It's the horizontal version of the vertical line test.

## Example 1

Draw a horizontal line on each point. (one unique y)

Each point shows one x.

Then this graph is one-to-one.

## Example 2

(0, 0): one unique y, one x.

Other points: one unique y, two x-s.

So this graph is not one-to-one.

## Example 3

If you draw a horizontal line like this,
(one unique y)
there are two x-s.

So this function is not one-to-one.

## Example 4

Draw y = x2 (x ≥ 0)