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4th Edition

James Stewart

Publisher: Cengage Learning

ISBN: 9781337687805

Chapter 1.1, Problem 8E

To determine

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

Expert Solution

The curve is not a function of *x*.

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

Perform the vertical line test for the given graph.

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

From Figure 1, it is observed that the vertical line intersects the curve at two distinct points, which means it fails the vertical line test.

Therefore, the curve is not a graph of the function of *x*.