Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 5 - Section 5.3 - Trigonometric Graphs - 5.3 Exercises - Page 429: 30

Answer

The Amplitude is $ 3$ The Period is $ 2$ See graph below

Work Step by Step

For $y=a\sin c(x−h) + k$ $y =a \cos c(x−h) + k$, Amplitude: $|a|$, Period: $\frac{2\pi} {|c|}$, Given $y = -3 \sin (\pi x)$ The Amplitude is $|-3| = 3$ The Period is $\frac{2\pi}{|\pi|} = 2$ The transformations are as follows The blue graph represents the graph of $\sin x$ The red graph represents the graph of the given function that is reflected about the x-axis, compressed horizontally by a factor of $ \pi$ and stretched vertically by a factor of $3$ See graph below.
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