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 12: 28

Answer

The first part of the graph is $\frac{1}{x}$ between both asymptotes x=0 and y=0. The second part of the graph is the linear graph x from (0,0) on.
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Work Step by Step

$G(0) = \frac{1}{0}$, which is impossible. So x = 0 is an asymptote of $\frac{1}{x}$. The other asymptote of $\frac{1}{x}$ is y = 0, which is obtained by substituting a very big negative value of x. Thus the first part of the graph will be $\frac{1}{x}$ between both asymptotes x=0 and y=0. $G(0) = {0}$ $G(1) = {1}$ So the second part of the graph will be the linear graph x from (0,0) on.
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