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 210: 104

Answer

$f(x) =x^n$ is even when $n$ is either 0, 2, 4, 6, 8, 10 or any even numbers. Simarly, $f(x) =x^n$ is odd when $n$ is either 1, 3, 5, 7, 9, 11 or any odd numbers. Based on what was just previously mentioned, Even Functions were named like that because the exponent must be an even number. The same goes for Odd Functions: the exponent must be an odd number.

Work Step by Step

One can see that when the exponent is even, the function has a symmetry over the y-axis. And when the exponent is odd, the symmetry is about the origin.
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