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

### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

#### Solutions

Chapter 1.1, Problem 5E
To determine

## Whether 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 not a function of x.

### Explanation of Solution

Result used:

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

Calculation:

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 three distinct points.

So the given function fails the vertical line test.

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

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