Question

select the correct answer. the parent cosine function is shifted 5 units left, then vertically stretched by a factor of 4 and shifted up 2 units. which statement is true about the graph of the transformed function? a. the midline is y = 8. b. the midline is y = 2. c. the midline is y = 4. d. the midline is y = 5.

Explanation:

Step1: Recall parent cosine midline

The parent cosine function $y=\cos(x)$ has a midline of $y=0$.

Step2: Analyze vertical shift effect

Vertical shifts change the midline. A shift up 2 units adds 2 to the midline value.
Vertical stretches affect amplitude, not the midline, and horizontal shifts affect the x-values, not the midline.

Answer:

B. The midline is $y = 2$