If we compress the graph of [tex]y = sin x[/tex] vertically by 1/2, this gives us the equation [tex]y = \frac{1}{2} sin x[/tex]. Shifting this downward (vertically) by 3 units will mean that the expression must have 3 subtracted from it, leaving the final equation of g(x) to be:
[tex]g(x) = \frac{1}{2} sin x - 3[/tex]
