Question

what does the transformation ( f(x)mapsto\frac{1}{9}f(x) ) do to the graph of ( f(x) )?<br>stretches it vertically<br>shrinks it horizontally<br>stretches it horizontally<br>shrinks it vertically

Explanation:

Step1: Recall vertical stretch/shrink rule

For a function \(y = af(x)\), if \(|a|> 1\), it is a vertical stretch; if \(0<|a|<1\), it is a vertical shrink.

Step2: Analyze the given transformation

In the transformation \(f(x)\mapsto\frac{1}{9}f(x)\), \(a = \frac{1}{9}\). Since \(0<\frac{1}{9}<1\), it is a vertical shrink.

Answer:

shrinks it vertically