Fx sin x is compressed horizontally by a factor of 2 shift

F(x) = sin (x) is compressed horizontally by a factor of 2, shift horizontally 3 pi units to the right stretched vertically by a factor of 5, and move downward 2 units. The equation of the transformated function g(x) is (a) g (x) = 5 sin (2x - 3 pi) - 2 (b) g (x) = 2 sin (5x - 3 pi) + 2 (c) g (x) = 2 sin (3x + 5 pi) + 2 (d) g (x) = 5 sin (3x + pi) - 2 (e) g (x) = -5 sin (2x + 3 pi) - 2

Solution

y=sinx
compressed horizontally by a factor 2
so, y=sin2x
shift horizontallyto right by 3
so we get y=sin(2x-3)
if at this point we see we only have one option so option A is correct
vertical stretch will give us y=5sin(2x-3)
move down 2 units will be y=5sin(2x-3)-2