Precalculus (6th Edition) Blitzer

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

Chapter 4 - Section 4.5 - Graphs of Sine and Cosine Functions - Exercise Set - Page 596: 70

Answer

Please see below.
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Work Step by Step

Please note that the absolute value for sine and cosine removes the lower half of the graph, which is below the $x$-axis, and flips it above. This results in two complete cycles, where there had been one. So, since the period of $2\sin \frac{\pi x }{2}$ is $\frac{2\pi }{\frac{\pi }{2}}=4$, the period of $y=- \left |2 \sin \frac{ \pi x}{2} \right |$ will become $\frac{4 }{2}=2$.
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