Horizontal line test

Definition

The horizontal line test is a method to determine if a function has an inverse that is also a function. A function passes the test if and only if no horizontal line intersects its graph more than once.

5 Must Know Facts For Your Next Test

1. A function must pass the horizontal line test to have an inverse that is also a function.
2. If any horizontal line intersects the graph of the function at more than one point, the function fails the test.
3. The horizontal line test can be applied visually on a graph or analytically using algebraic methods.
4. Passing the horizontal line test implies that the function is one-to-one (injective).
5. A common example of functions failing this test includes quadratic functions like $f(x) = x^2$.

Review Questions

• What does it mean for a function to pass the horizontal line test?
• Why is passing the horizontal line test crucial for determining if a function has an inverse?
• Can a quadratic function such as $f(x) = x^2$ pass the horizontal line test? Why or why not?

Related terms

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

One-to-One Function: A function where each output value corresponds to exactly one input value, ensuring no repeated outputs.

Vertical Line Test: A method to determine if a graph represents a function by checking that no vertical line intersects the graph more than once.