which of the following would best represent a cosine function with an amplitude of 3, a period of pi/2 , and a midline at y = –4? (1 point)f(x) = –4 cos 4x + 3

f(x) = 3 cos(x – pi/2 ) – 4

f(x) = 4 cos(x – pi/2 ) + 3

f(x) = 3 cos 4x – 4

To transform the function  to have the amplitude of 3, we need to multiply the constant 3 to the function f(x), so we have 

To transform the function  to have the midline  we need to subtract  by 4, so we have , 

To transform the function  to have period of , we need to divide the original period  by 4, so we have . Note that it is the  gives the effect of dividing the points on x-axes by 4 and the period is read on x-axes

Hence, the full transformation is given  which is the last option