To transform the function [tex]f(x)= cos(x)[/tex] to have the amplitude of 3, we need to multiply the constant 3 to the function f(x), so we have [tex]y=3f(x)[/tex]
To transform the function [tex]f(x)=cos(x)[/tex] to have the midline [tex]y=-4[/tex] we need to subtract [tex]f(x)[/tex] by 4, so we have [tex]y=f(x)-4[/tex],
To transform the function [tex]f(x)=cos(x)[/tex] to have period of [tex] \frac{ \pi }{2} [/tex], we need to divide the original period [tex]2 \pi [/tex] by 4, so we have [tex]y=f(4x)[/tex]. Note that it is the [tex]4x[/tex] 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 [tex]y=3f(4x)-4[/tex] which is the last option
