Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 2 - Section 2.6 - Transformations of Functions - 2.6 Exercises - Page 208: 86

Answer

The function is even.

Work Step by Step

$f(x)$ is even if $f(-x)=f(x).$ If so, it is symmetric relative to the y-axis. $f(x)$ is odd if $f(-x)=-f(x).$ If so, it is symmetric relative to the origin. ----- Replace x with $-x$ and check the result: $f(-x)=(-x)^{4}-4(-x)^{2}=x^{4}-4x^{2}=f(x),$ meaning that the function is even. Sketching the graph by taking some nonnegative values for x, $\left[\begin{array}{ccccc} x & 0 & 1 & 2 & 3\\ f(x) & 0 & -3 & 0 & 45 \end{array}\right]$ , we conclude that $(-1,-3), (-2,0),$ and $(-3,45)$ also belong to the graph
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