the amplitude of the graph is 2. the midline is y = 4. complete which function is graphed? y=-2cos(x)-4 y =…

Explanation:

Step1: Recall cosine - function form

The general form of a cosine function is $y = A\cos(Bx - C)+D$, where $A$ is the amplitude, $D$ is the mid - line value.

Step2: Use given amplitude and mid - line

We know that the amplitude $A = 2$ and the mid - line $y=D = 4$.

Step3: Analyze the sign of $A$

When $x = 0$, the graph is at its minimum value for a cosine - type function. For $y = A\cos(x)+D$, when $A<0$, $y = A\cos(x)+D$ starts at its minimum value when $x = 0$. Since $A=- 2$ will make the cosine function start at its minimum value at $x = 0$ (because $\cos(0)=1$ and $y=-2\times1 + 4=2$ which is the minimum value of the function based on the mid - line $y = 4$ and amplitude $2$).

Answer:

C. $y=-2\cos(x)+4$