Question

what does the transformation ( f(x)\to\frac{1}{7}f(x) ) do to the graph of ( f(x) )?
stretches it horizontally
shrinks it vertically
shrinks it horizontally
stretches it vertically

Explanation:

For a function \( y = f(x) \), a transformation of the form \( y = a\cdot f(x) \) (where \( a>0 \)) is a vertical stretch or shrink. If \( 0 < a<1 \), it is a vertical shrink. Here \( a=\frac{1}{7}\) (since \( 0<\frac{1}{7}<1 \)), so the transformation \( f(x)\to\frac{1}{7}f(x) \) shrinks the graph of \( y = f(x) \) vertically.

Answer:

shrinks it vertically