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Chapter 5: Q. 103 (page 271)

Explain why the horizontal-line test can be used to identify one-to-one functions from a graph.

Short Answer

Expert verified

Horizontal-line test states that if every horizontal line intersects the graph of a function f in at most one point, then f is one-to-one. That's why the horizontal test can be used to identify one-to-one functions from a graph.

Step by step solution

01

Step 1. Given Information

We have to explain why the horizontal-line test can be used to identify one-to-one functions from a graph.

02

Step 2. Explanation

Horizontal-line test states that if every horizontal line intersects the graph of a function f in at most one point, then f is one-to-one.

Let's take an example by letting the function f(x)=x3, as we can depict from the following graph that the graph of the function passes the horizontal line by at most one point. Hence it is a one-to-one function.

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