Calculus 8th Edition

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

Chapter 1 - Functions and Limits - 1.3 New Functions from Old Functions - 1.3 Exercises - Page 43: 30

Answer

Graph:

Work Step by Step

The most important features of the given graph are the x-intercepts and the maximum and minimum points. The graph of $y=1/f(x)$ has vertical asymptotes at the x-values where there are x-intercepts on the graph of $y=f(x)$. The maximum of 1 on the graph of $y=f(x)$ corresponds to a minimum of $1/1=1$ on $y=1/f(x)$. Similarly, the minimum on the graph of $y=f(x)$ corresponds to a maximum on the graph of $y=1/f(x)$. As the values of y get large (positively or negatively) on the graph of $y=f(x)$, the values of y get close to zero on the graph of $y=1/f(x)$. Graph:
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