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


See the image below

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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