How do you graph #y=-4+2sin3x#?
We can consider transformations with this.
Firstly, consider the sketch of y = sinx
The function y = sin3x is a horizontal squash factor of 1/3
The function y = 2sin3x is a vertical stretch by a factor of 2
The function y = -4 + 2sin3x is a vertical translation of 4 units down
Red -> Blue -> Green
See the sketch below: