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 $y = f(x)$, $y = a\cdot f(x)$ where $|a|> 1$ causes a vertical stretch.

Step2: Analyze given options

For $y=\cos x$, the function $y = - 5\cos(x)$ has $a=-5$ and $| - 5|=5>1$, so it results in a vertical stretch.

Step3: Recall horizontal - stretch rule

For a function $y = f(x)$, $y = f(bx)$ where $0 < |b|<1$ causes a horizontal stretch. For $y=\cos x$, if we consider $y=\cos\left(\frac{1}{3}x\right)$ (not in the options but for understanding the rule), for the given options $y=\cos(x + 4)$ is a horizontal shift, $y=\cos(-5x)=\cos(5x)$ is a horizontal compression ($|b| = 5>1$), and the correct form for horizontal stretch among the options is not present in a pure form but the concept is based on the coefficient of $x$ inside the cosine function.

Answer:

The transformation $-5\cos(x)$ results in a vertical stretch.