Answer
(a) $\pi$
(b) $6$
(c) $[-3,9]$
(d) $(0,-3)$
(e) $-\frac{\pi}{4}$ (negative means shift to the left)
Work Step by Step
Given $y=3-6sin(2x+\frac{\pi}{2})=-6sin[2(x+\frac{\pi}{4})]+3$, we have:
(a) its period is $p=\frac{2\pi}{2}=\pi$
(b) the amplitude of its graph is $|A|=|-6|=6$
(c) its range is $[3-6, 3+6]$ or $[-3,9]$
(d) the y-intercept of its graph is $f(0)=3-6sin(\frac{\pi}{2})=-3$ or $(0,-3)$
(e) its phase shift is $-\frac{\pi}{4}$ (negative means shift to the left)
