Question

what does the transformation $f(x) \mapsto \frac{1}{9}f(x)$ do to the graph of $f(x)$?
shrinks it vertically
reflects it across the x-axis
reflects it across the y-axis
stretches it vertically

Explanation:

For a transformation of the form $a \cdot f(x)$ where $0 < |a| < 1$, each $y$-value of the original function $f(x)$ is multiplied by a factor smaller than 1, which compresses the graph toward the x-axis. Here, $a = \frac{1}{9}$, which is between 0 and 1, so it causes a vertical shrink.

Answer:

shrinks it vertically