Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

Chapter 1 - Section 1.2 - Mathematical Models: A Catalog of Essential Functions. - 1.2 Exercises: 3

Answer

$a)$ $y=h(x)$ $b)$ $y=f(x)$ $c)$ $y=g(x)$

Work Step by Step

$a)$ $y=x^{2}$ is an even function so it is symmetrical about the y-axis. This limits the possible graphs to $g(x)$ and $h(x)$. It has a lower power than c) so it is less flat near the origin and less steep when $|x|\geq1$. Therefore it must be $y=h(x)$. $b)$ $y=x^{5}$ is an odd function so it is symmetrical about the origin. The only graph possible is $y=f(x)$. $c)$ $y=x^{8}$ is an even function so it is symmetrical about the y-axis. This limits the possible graphs to $g(x)$ and $h(x)$. It has a higher power than a) so it is more flat near the origin and more steep when $|x|\geq1$. Therefore it must be $y=g(x)$.
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