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: 23

Answer

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 $y=|\sqrt x-1|$ is $y=\sqrt x$ (Black dotted line graph in the image). Now, lets transform it a little and graph $y=\sqrt x-1$, which means shifting the graph downwards by 1 unit (Red line graph in the image) Finally, we graph $y=|\sqrt x-1|$, which means that we will reflect the portion of the graph below the $x$-axis about the $x$-axis (Blue line graph in the image).
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