ƒ(x)=sin(x)

consider y = Asin(Bx + C)+D

A controls the amplitude (how high/low the function is)

B controls the # of complete wavelengths in a specified interval

C is the phase shift (left/right on the axis) -- (positive values will shift left)

D is the vertical shift (up/down) ex. +3 would move the whole function UP 3 units

In your case you want to stretch vertically -- that is the amplitude so A=4

And since you want to shift it 3 units right C = -3 (always the opposite of the direction you want to go)

Put it together...

g(x) = 4sin(x - 3)