Question

Graph: f(x) = -3sin (x/2 - π/4)

Answer 1

This sine function has the form y = f(x) = a sin (bx + c), where |a| is the amplitude, b is the frequency, and c determines the phase shift.

The period of this sine curve is 2 pi/b, or (in this problem) 2 pi/(1/2).

The phase shift of this curve is -c/b, or -(pi/4)/(1/2).  Simplify this.

The amplitude is |-3|, or just 3.

Draw a set of coordinate axes.  Draw light horizontal lines through y=3 and y=-3.  These are the max and min. values of this sine function.

Plot the phase shift on your x-axis.

Your sine function will begin at (phase shift value, 0) and continue for one period.  Add the period to the phase shift value.  Draw a sine curve beginning and ending at these two x-values.

I encourage you to share your calculations and to sketch the graph described here.  Then I could give you more specific feedback on your work.  Good luck!