Calculus: Early Transcendentals 8th Edition

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

Chapter 1 - Review - Exercises - Page 70: 14

Answer

Refer to the blue graph below.
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Work Step by Step

The parent function of $y=\ln{(x+1)}$ is $y=\ln{x}$. Note that in $y=\ln{x}$, when $x$ is replaced by $x+1$, the function becomes $y=\ln{(x+1)}$ This means that with $y=f(x)=\ln{x}$ as the parent function, the given function is equivalent to $y=f(x+1)$ RECALL: The graph of $y=f(x+c)$ involves a horizontal shift of $c$ units to the left of the parent function $y=f(x)$. Thus, to graph the given function, perform the following steps: (1) Graph the parent function $y=\ln{x}$. Refer to the black graph below. (2) Shift the graph of $y=\ln{x}$ one unit to the left to to obain the graph of $y=\ln{(x+1)}$. Refer to the blue graph below.
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