Chapter 6 - Trigonometric Functions - 6.4 Graphs of the Sine and Cosine Functions - 6.4 Assess Your Understanding - Page 408: 30

$\text{(G)}$

Work Step by Step

The amplitude and period can be calculated as, if $y=A\cos(wx)$: Amplitude=$|A|$ period: $T=\frac{2\pi}{w}$ In this function, $y=-2\cos(\frac{\pi}{2}x)$ Amplitude=$|-2|=2$ Period: $T=\frac{2\pi}{\frac{\pi}{2}}=4$ Also, the cosine function does not have a y-intercept at the origin, $y=-2$. The graph that has the same characteristics is $\text{(G)}$.

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