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

Explanation:

Step1: Recall horizontal - transformation rule

For the function $y = f(x)$, the transformation $y=f(bx)$ where $b> 1$ causes a horizontal compression. For $y = \cos x$, the transformation $y=\cos(bx)$ with $b > 1$ results in a horizontal compression.

Step2: Recall vertical - transformation rule

For the function $y = f(x)$, the transformation $y = af(x)$ where $a>1$ causes a vertical stretch. For $y=\cos x$, the transformation $y = a\cos x$ with $a > 1$ results in a vertical stretch.

Step3: Recall horizontal - stretch rule

For the function $y = f(x)$, the transformation $y=f(bx)$ where $0 < b<1$ causes a horizontal stretch. For $y=\cos x$, the transformation $y=\cos(bx)$ with $0 < b < 1$ results in a horizontal stretch.

Step4: Recall vertical - compression rule

For the function $y = f(x)$, the transformation $y=af(x)$ where $0 < a<1$ causes a vertical compression. For $y=\cos x$, the transformation $y = a\cos x$ with $0 < a < 1$ results in a vertical compression.

Answer:

1. $y=\cos(bx)$ where $b > 1$ results in a horizontal compression.
2. $y=a\cos x$ where $a > 1$ results in a vertical stretch.
3. $y=\cos(bx)$ where $0 < b < 1$ results in a horizontal stretch.
4. $y=a\cos x$ where $0 < a < 1$ results in a vertical compression.