Question

consider the function $y = a\sin(bx)$, where $a > 0$ and $b > 0$. which change compresses the graph vertically?
decrease $b$.
increase $a$.
decrease $a$.
increase $b$.

Explanation:

Step1: Identify vertical scaling factor

For $y = a\sin(bx)$, $a$ is the amplitude (vertical scale factor).

Step2: Analyze vertical compression effect

Vertical compression reduces the amplitude. Since $a>0$, decreasing $a$ shrinks the graph vertically.

Step3: Rule out horizontal scaling

Changes to $b$ affect horizontal stretch/compression, not vertical.

Answer:

Decrease a.