Calculus 10th Edition

Published by Brooks Cole
ISBN 10: 1-28505-709-0
ISBN 13: 978-1-28505-709-5

Chapter P - P.3 - Functions and Their Graphs - Exercises: 79

Answer

This is an even function. The zeroes are -2, 0, and 2.

Work Step by Step

To find whether a function is even or odd, plug in -x and evaluate the result. $f(-x)=(-x)^2(4-(-x)^2)$ $f(-x)=x^2(4-x^2)$ Because the result is the same as $f(x)$, this is an even function. To find the zeroes, use the zero product property. $x^2=0$ $x=0$ $4-x^2=0$ $x^2=4$ $x=2,-2$
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