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

Explanation:

Step1: Recall transformation rules

For $y = A\cos(Bx + C)+D$, horizontal compression/stretch is related to $B$ and vertical to $A$.

Step2: Identify horizontal compression

For $y=\cos x$, when $y = \cos(- 5x)$, since $|B|=5>1$, it causes horizontal compression.

Step3: Identify vertical stretch

For $y = A\cos x$, when $A = 9$ (i.e., $y=9\cos x$), $|A| = 9>1$ causes vertical stretch.

Step4: Identify horizontal stretch

For $y=\cos x$, there is no option given that correctly represents horizontal stretch in the form $y=\cos(Bx)$ with $0<|B|<1$.

Step5: Identify vertical compression

For $y = A\cos x$, when $A=\frac{1}{3}$ (i.e., $y = \frac{1}{3}\cos x$), $0<|A|<1$ causes vertical compression.

Answer:

The transformation $\cos(-5x)$ results in a horizontal compression. The transformation $9\cos(x)$ results in a vertical stretch. No correct option for horizontal stretch. The transformation $\frac{1}{3}\cos(x)$ results in a vertical compression.