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: 20

Answer

See the image below
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Work Step by Step

To graph the following function, we will first determine its parent function and then stretch the whole graph step by step. The parent function of $y=|x|-2$ is $y= x$ (Black dotted line graph in the image). Now, lets transform it a little and graph $y=|x|$, which means to reflect the portion of the graph below $x$-axis about the $x$-axis (Red line graph in the image) Finally, we graph $y=|x|-2$, which means that we have to shift the previous graph downwards by 2 units (Blue line graph in the image).
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