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Graph the functions for one period. In each case, specify the amplitude, period, $x$ -intercepts, and interval(s) on which the function is increasing.

(a) $y=\cos 2 x$

(b) $y=2 \cos 2 x$

(a.) amplitude $=1,$ period $=\frac{2 \pi}{B}=\frac{2 \pi}{2}=\pi$

$x$ -intercepts $=\pi / 4,3 \pi / 4$

$x$ increases in $\left(\frac{\pi}{2}, \pi\right)$

(b.) amplitude $=2,$ period $=\frac{2 \pi}{2}=\pi$

$x$ -intercepts $=\frac{\pi}{4}, \frac{3 \pi}{4}$

$x$ increases in $(\pi / 2, \pi)$

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Numerade Educator

Oregon State University

Baylor University

Idaho State University

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