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: 47

Answer

odd

Work Step by Step

We know that if a function is odd, then $f(-x)=-f(x).$ We also know that if a function is even, then $f(-x)=f(x).$ Hence, we plug in $-x$ into $x$ to see what happens. \begin{align*} f(-x)&=\frac{-(-x)^3}{3(-x)^2-9}\\ &=\frac{x^3}{3x^2-9}\\ &=-\dfrac{-x^3}{3x^2-9}\\ &=-f(x) \end{align*} Therefore, the function is odd.
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