Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

Published by Pearson
ISBN 10: 0-32193-104-1
ISBN 13: 978-0-32193-104-7

Chapter 1 - Functions and Their Graphs - Chapter Review - Review Exercises - Page 114: 20


The function is neither even nor odd.

Work Step by Step

Remember that when a function is odd, then $g(−x)=−g(x)$ and when a function is even, then $g(−x)=g(x)$. Thus, in order to find out whether the function is even, odd, or neither, we will find $g(-x)$ . We are given: $g(x)=1-x+x^3$ Thus we have: $g(-x)=1-(-x)+(-x)^3\\=1+x-x^3$ This shows that the function is neither even nor odd.
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