select the correct answer from each drop - down menu. which transformation causes the described change in…

Explanation:

Step1: Recall horizontal - compression rule

For a function $y = f(x)$ to $y=f(bx)$ where $b> 1$, it is a horizontal compression. For $y = \cos x$ to $y=\cos(3x)$, since $b = 3>1$, it is a horizontal compression.

Step2: Recall vertical - stretch rule

For a function $y = f(x)$ to $y = af(x)$ where $a>1$, it is a vertical stretch. For $y=\cos x$ to $y = 9\cos(x)$, since $a = 9>1$, it is a vertical stretch.

Step3: Recall horizontal - stretch rule

For a function $y = f(x)$ to $y=f(bx)$ where $0 < b<1$, it is a horizontal stretch. For $y=\cos x$ to $y=\cos(\frac{x}{5})$, since $b=\frac{1}{5}<1$, it is a horizontal stretch.

Step4: Recall vertical - compression rule

There is no option for vertical compression in the given list. The transformation $y=\cos(x + 2)$ is a horizontal shift (left - shift by 2 units) and not related to vertical or horizontal compression/stretch.

Answer:

The transformation $\cos(3x)$ results in a horizontal compression. The transformation $9\cos(x)$ results in a vertical stretch. The transformation $\cos(\frac{x}{5})$ results in a horizontal stretch. There is no transformation for vertical compression in the given list.