Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 1 - Functions and Limits - 1.2 Mathematical Models: A Catalog of Essential Functions - 1.2 Exercises: 3

Answer

(a) y = $x^{2}$ is graph $h$, the blue one (b) y = $x^{5}$ is graph $f$, the pink one (c) y = $x^{8}$ is graph $g$, the green one

Work Step by Step

y = $x^{2}$ is a power function (in this case parabola), which is an even function so $y\geq0$ for all $x$. But since y = $x^{8}$ is also a power even function, it must look similar to y = $x^{2}$ because they are both concave up. However, as y = $x^{8}$ has a higher degree, this means that for $x<1$ then $x^{8}1$, then $x^{8}>x^{2}$. This means that the graph y = $x^{8}$ will be under y = $x^{2}$ for $x<1$ and over y = $x^{2}$ for $x>1$. Hence y = $x^{2}$ is the blue curve and y = $x^{2}$ is the green curve. y = $x^{5}$ is easy to distinguish as the pink curve as its odd power means that for $x>0$, $y>0$ and for $x<0$, $y>0$
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