key term - 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

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.