Precalculus (6th Edition)

Published by Pearson
ISBN 10: 013421742X
ISBN 13: 978-0-13421-742-0

Chapter 6 - The Circular Functions and Their Graphs - Quiz - Page 616: 9

Answer

amplitude $4$, period $\pi$, vertical translation $+3$ (up), and phase shift $-\frac{\pi}{4}$ (to the left).

Work Step by Step

Rewrite the function as $y=-4sin[2(x+\frac{\pi}{4})]+3$, we can identify the amplitude as $|A|=|-4|=4$, period as $p=\frac{2\pi}{2}=\pi$, vertical translation as $+3$ (positive means up), and phase shift as $-\frac{\pi}{4}$ (negative means to the left).
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