University Calculus: Early Transcendentals (3rd Edition)

Published by Pearson
ISBN 10: 0321999584
ISBN 13: 978-0-32199-958-0

Chapter 1 - Section 1.1 - Functions and Their Graphs - Exercises - Page 13: 65


$a.\:\:\:h$ $b.\:\:\:f$ $c.\:\:\:g$

Work Step by Step

Observe the given functions in terms of the $\:x\:$ power. We come to notice that the function $\:y=x^7\:$ is an odd function among the three. It is represented by $\:f(x).$ Although $\:g\:\:\mathrm{and}\:\:h\:$ are both even functions, $\:g\:$ is more flat around the origin $\:(0,0)\:$ and has a larger slope for bigger values of $\:x.$ Therefore, $\:g(x)=x^{10}\:$ (the function represented in yellow) and $\:h(x)=x^4$ (the function represented in blue).
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