Precalculus (10th Edition)

Published by Pearson
ISBN 10: 0-32197-907-9
ISBN 13: 978-0-32197-907-0

Chapter 2 - Functions and Their Graphs - 2.3 Properties of Functions - 2.3 Assess Your Understanding - Page 79: 37



Work Step by Step

We know that if a function is odd, then $f(-x)=-f(x).$ We know that if a function is even, then $f(-x)=f(x).$ Hence we plug in $-x$ to see what happens. $f(-x)=4(-x)^3 \\f(-x)=4\cdot(-x^3) \\f(-x)=-4x^3 \\f(-x)=-f(x)$ Therefore the function is odd.
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