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4th Edition

James Stewart

Publisher: Cengage Learning

ISBN: 9781337687805

Chapter 1, Problem 3RCC

(a)

To determine

**To explain:** An even function; how to identify an even function by graph; three example of even function.

Expert Solution

**Even function:** A function *y*-axis is a reflection of the points in the positive *x*-axis. That is, if there exist a point (3, 4), then there also will be a point (−3, 4).

**How to identify an even function**: If a graph of the function is symmetric about the *y*-axis then the function is said to be an even function.

**Examples:**

Three possible even functions are

Graphs of the above three functions are shown below in Figure 1.

From Figure 1, it is observed that each graph is symmetric about the *y*-axis.

(b)

To determine

**To explain:** An odd function; how to identify an odd function by graph; three example of odd function.

Expert Solution

**Even function:** A function

**How to identify an even function**: If a graph of the function is symmetric about the origin then the function is said to be an odd function.

**Examples:**

Three possible even functions are

Graphs of the above three functions are shown below in Figure 2.

From Figure 2, it is observed that each graph is symmetric about the origin.