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

Answer:

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

Explanation:

Step1: Recall horizontal - transformation rule

For $y = f(bx)$, if $b>1$, graph of $y = f(x)$ is horizontally compressed. For $y=\cos(x)$, $y = \cos(bx)$ with $b > 1$ gives horizontal compression.

Step2: Recall vertical - transformation rule

For $y = af(x)$, if $a>1$, graph of $y = f(x)$ is vertically stretched. For $y=\cos(x)$, $y = a\cos(x)$ with $a>1$ gives vertical stretch.

Step3: Recall horizontal - stretch rule

For $y = f(bx)$, if $0 < b<1$, graph of $y = f(x)$ is horizontally stretched. For $y=\cos(x)$, $y=\cos(bx)$ with $0 < b<1$ gives horizontal stretch.

Step4: Recall vertical - compression rule

For $y = af(x)$, if $0 < a<1$, graph of $y = f(x)$ is vertically compressed. For $y=\cos(x)$, $y = a\cos(x)$ with $0 < a<1$ gives vertical compression.