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.
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.
Draw a horizontal line on each point. (one unique y)
Each point shows one x.
Then this graph is one-to-one.
(0, 0): one unique y, one x.
Other points: one
unique y, two x-s.
So this graph is not one-to-one.
If you draw a horizontal line like this,
there are two x-s.
So this function is not one-to-one.
Draw y = x2 (x ≥ 0)
Quadratic function: vertex form
For every y (horizontal line),
there's one x (red).
So this graph is one-to-one.