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

Explanation:

Step1: Recall vertical - stretch rule

For a function $y = f(x)$, $y = a\cdot f(x)$ with $|a|>1$ causes a vertical stretch. So for $y=\cos x$, $y = - 5\cos(x)$ (since $| - 5|=5>1$) results in a vertical stretch.

Step2: Recall horizontal - stretch rule

For a function $y = f(x)$, $y=f(bx)$ with $0 < |b|<1$ causes a horizontal stretch. There is no such form in the given options with $0 < |b|<1$. But if we consider the general form, for horizontal stretch of $y = \cos x$, we can think conceptually.

Step3: Recall vertical - compression rule

For a function $y = f(x)$, $y=a\cdot f(x)$ with $0<|a|<1$ causes a vertical compression. For $y = \cos x$, $y=\frac{1}{3}\cos(x)$ (since $0<\frac{1}{3}<1$) results in a vertical compression.

Answer:

The transformation $-5\cos(x)$ results in a vertical stretch. The transformation $\frac{1}{3}\cos(x)$ results in a vertical compression.