Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 4 - Section 4.6 - Graphs of Other Trigonometric Functions - Exercise Set - Page 610: 54

Answer

See graph and explanations.
1583876164

Work Step by Step

Step 1. Given $g(x)=-2tan(x)$ and $h(x)=2x-\frac{\pi}{2}$, we have $y=(g\circ h)(x)=-2tan(2x-\frac{\pi}{2})$ Step 2. Start from $y=tan(x)$ (purple), we can obtain $y=tan(2x)$ (green) by shrinking horizontally with a factor of 2. Step 3. Start from $y=tan(2x)$, shift the curve horizontally $\frac{\pi}{4}$ to the right, stretch vertically by a factor of 2 and then reflect around the x-axis to get the red curve for $y=(g\circ h)(x)=-2tan(2x-\frac{\pi}{2})$
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