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4th Edition

James Stewart

Publisher: Cengage Learning

ISBN: 9781337687805

Chapter 1.1, Problem 6E

To determine

The curve is a graph of a function of *x*. If so, find the domain and range of the function.

Expert Solution

The curve is the graph of a function of *x*.

Vertical line test states that the curve in the *xy* coordinate plane is the graph of the function of *x* if and only if a vertical line intersects the curve at exactly one point.

Perform the vertical line test for the given graph.

Draw a vertical line such that it passes through the curve as shown below in Figure 1.

It is observed from Figure 1 that the vertical line intersects the curve exactly at one point. Therefore, the curve is the graph of a function of *x*.

Since, the domain of a function is the set of all possible *x* values of the graph, the domain of the function is

Since, the range of a function is the set of all possible *y* values of the graph, the range of the function is