Practice Horizontal Line Test in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

Quick Recap

The horizontal line test is a visual method to determine whether a function is one-to-one (injective). If every horizontal line intersects the function's graph at most once, the function passes the test and has an inverse function on its full domain.

A horizontal line that crosses the graph at two points means those two inputs produce the same output — the function is many-to-one and has no inverse without domain restriction.

Example 1

easy
Use the horizontal line test to determine whether f(x) = 2x + 5 is one-to-one.

Example 2

medium
Does f(x) = |x - 2| pass the horizontal line test? Explain algebraically.

Example 3

medium
Which of the following functions are one-to-one: (a) f(x) = x^3, (b) g(x) = x^3 - 3x, (c) h(x) = e^x?

Example 4

hard
Prove algebraically that f(x) = \frac{x}{x+1} (for x > -1) is one-to-one without graphing.
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