Horizontal line test

Definition

The horizontal line test is a method used to determine if a function is one-to-one (injective). If any horizontal line intersects the graph of the function at most once, then the function passes the test and is one-to-one.

5 Must Know Facts For Your Next Test

1. A function that passes the horizontal line test has an inverse function.
2. The horizontal line test can be applied to both linear and non-linear functions.
3. If a function fails the horizontal line test, it means there are at least two different x-values that produce the same y-value.
4. Functions that are strictly increasing or decreasing always pass the horizontal line test.
5. Polynomial functions of degree greater than one often fail the horizontal line test.

Review Questions

• What does it mean if a function passes the horizontal line test?
• How can you use the horizontal line test to determine if a function has an inverse?
• Why do strictly increasing or decreasing functions always pass the horizontal line test?

Related terms

One-to-One Function:

A function where each output value corresponds to exactly one input value.

Inverse Function:

A function that reverses another function, meaning if $f(x) = y$, then its inverse $f^{-1}(y) = x$.

Vertical Line Test:

A method used to determine if a curve is a graph of a function by checking that no vertical line intersects the curve more than once.