Precalculus (10th Edition)

Published by Pearson
ISBN 10: 0-32197-907-9
ISBN 13: 978-0-32197-907-0

Chapter 6 - Trigonometric Functions - 6.4 Graphs of the Sine and Cosine Functions - 6.4 Assess Your Understanding - Page 409: 56

Answer

See graph. $(-\infty,\infty)$, $[1,2]$.

Work Step by Step

Step 1. See graph for $y=-\frac{1}{2}sin(\frac{\pi}{8}x)+\frac{3}{2}$ with key points or transform from $y=sin(x)$ (stretch horizontally by a factor of $\frac{8}{\pi}$, shrink vertically by a factor of $\frac{1}{2}$, reflect across the x-axis, then shift $\frac{3}{2}$ units up.) Step 2. Based on the graph, we can determine the domain as $(-\infty,\infty)$ range as $[1,2]$.
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