1. Explain/show how to find the amplitude of the function f(x)=-5 sin(x/3)-1.

1.  We have the form

y  = A sin (1/3 * x)  - 1

A  = the amplitude  =  l  -5 l  =   5

2. Midline

y = (High point + Low point) / 2

Low point  = -5sin (pi/2)  - 1=   -5 * ( 1 )  -1  =  -6

High point  = -5 (sin (3pi/2)  - 1 =  -5 * (-1) - 1  =  4

Midline =  y =  ( 4  + - 6)  / 2   =  -2  / 2  =  -1

3. Frequency =  1/ period  

Period  =  2pi  / B  =  2pi / (1/3)  =  6pi

So the frequency =  1/ (6pi)

4.

y  = -4sin x

This is  just the   graph  of   y =  4sin (x)   reflected across the x axis

The amplitude = 4

The midline =  0

High point  =  4

Low point = -4

Here's the graph