Answer
a) Amplitude is 5
period is 2$\pi$
Horizontal shift is -1/4
b) $y=5sin(2\pi(x+\frac{1}{4}))$
Work Step by Step
The amplitude is half the distance between the minimum and maximum values of the function. Since the minimum is $-5$ and the maximum is $5$, $\frac{5-(-5)}{2}=5$
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, $k=\frac{2\pi}{1}=2\pi$
Horizontal shift is the amount of units the function has displaced horizontally. Since the sine function starts at the origin, the function has displaced $-0.25$
