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: 22

Answer

See the image below.

Work Step by Step

To graph the function, first we will determine its parent function and then apply the transformations to sketch it. The parent function for $y=\frac{1}{4}tan(x-\frac{\pi}{4})$ is $y=tanx$ (Black dotted line on the image). Now let's apply a transformation: $y=tan(x-\frac{\pi}{4})$, which means that we shift the parent graph to the right by $\frac{\pi}{4}$ unit (Red line graph on the image). Finally, let's apply the last transformation: $y=\frac{1}{4}tan(x-\frac{\pi}{4})$, which means shrinking the graph vertically by a factor of 4 (Green line graph on the image).
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