Thomas' Calculus 13th Edition

Published by Pearson
ISBN 10: 0-32187-896-5
ISBN 13: 978-0-32187-896-0

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


We match a with $h$, b with $f$, and c with $g$.

Work Step by Step

$x^4$ and $x^{10}$ can be expressed as $(x^2)^2$ and $(x^2)^5$, respectively. We know that $x^2\geq0$, so neither a nor c is $f$. We can see that after a certain point, $g$ becomes steeper than $h$, meaning that for the same $x$, $g$ will always have a larger $y$. Therefore: a. $y=x^4$ is $h$ b. $y=x^7$ is $f$ c. $y=x^{10}$ is $g$
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