Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 1 - Functions and Limits - 1.1 Four Ways to Represent a Function - 1.1 Exercises - Page 22: 69


$g(x)$ is even and $f(x)$ is odd.

Work Step by Step

The graph of g is symmetric across the y-axis meaning that the half of the function that is on one side of the y-axis is reflected on the other side of the y-axis. This graph of g visually depicts the definition of an even function ($f(x) = f(-x)$). Therefore g is an even function. The graph of f is symmetric about the origin where if you rotate the graph by $180^{o}$ around the origin, it would be the same as before the rotation. This is the visual depiction of the definition of an odd function ($-f(x) = f(-x)$). Therefore the function is an odd function.
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