What does the transformation f(x)↦

Question

1/5
f(x) do to the graph of f(x)?

stretches it horizontally
shrinks it vertically
shrinks it horizontally
stretches it vertically

Answer 1

The transformation \( f(x) \mapsto \frac{1}{5} f(x) \) affects the graph of \( f(x) \) by shrinking it vertically.

Here's why:

• The transformation involves multiplying the output of the function \( f(x) \) by \( \frac{1}{5} \).
• This means that for any input \( x \), the output (or \( y \)-value) will be one-fifth of what it was in the original function \( f(x) \).
• As a result, all points on the graph will be lower, leading to a vertical compression of the graph by a factor of 5.

Therefore, the correct answer is that it shrinks it vertically.