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Chapter 0: Problem 9

You are given the graph of a function \(f .\) Determine whether \(f\) is one-to- one.

Short Answer

Expert verified
To determine if the given function \(f\) is one-to-one, examine its graph and apply the horizontal line test. If no horizontal line intersects the graph more than once, then the function is one-to-one. Otherwise, it is not.

Step by step solution

01

Examine the graph

Examine the entire graph of the function, looking for any horizontal lines that cross the graph more than once.
02

Apply the horizontal line test

Draw different horizontal lines across the graph, at various heights. If any horizontal line intersects the graph more than once, the function is not one-to-one. If no horizontal line intersects the graph more than once, the function is one-to-one.
03

Conclude

Based on the outcome of the horizontal line test, determine if the function is one-to-one or not. If none of the horizontal lines intersected the graph more than once, then the function is one-to-one.

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Most popular questions from this chapter

Sketch the graph of the first function by plotting points if necessary. Then use transformation(s) to obtain the graph of the second function. \(y=x^{2}, \quad y=\left|x^{2}-1\right|\)

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