Answer
a) Amplitude is 4
period is 4$\pi$/3
Horizontal shift is -1/2
b) $y=4sin(\frac{4\pi}{3}(x+\frac{1}{2}))$
Work Step by Step
The amplitude is half the distance between the minimum and maximum values of the function. Since the minimum is $-4$ and the maximum is $4$, $\frac{4-(-4)}{2}=4$
The period is the interval needed to complete one cycle, and it is given by $k=\frac{2\pi}{b}$, where $k$ is the period and $b$ is the horizontal length of a function when it completes one cycle. Since the length, in this case, is 1.5, $k=\frac{2\pi}{1.5}=\frac{4\pi}{3}$
Horizontal shift is the amount of units the function has displaced horizontally. Since the sine function starts at the origin, the function has displaced $-0.5$
