Question

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

Answer 1

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

To transform the function $f(x)=cos(x)$ to have the midline $y=-4$ we need to subtract $f(x)$ by 4, so we have $y=f(x)-4$, 

To transform the function $f(x)=cos(x)$ to have period of $\frac{ \pi }{2}$, we need to divide the original period $2 \pi$ by 4, so we have $y=f(4x)$. Note that it is the $4x$ 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 $y=3f(4x)-4$ which is the last option

Answer 2

Answer:

D) f(x) 3 cos 4x-4 (I just took it)