Question

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

Explanation:

Step1: Recall horizontal transformation rule

For a function \(y = f(kx)\), if \(|k|\lt1\), the graph of \(y = f(x)\) is stretched horizontally. Here \(k=\frac{1}{7}\) (since the transformation is \(f(x)\to f(\frac{1}{7}x)\)).

Step2: Analyze the effect

Since \(\frac{1}{7}\lt1\), according to the rule for horizontal transformations of functions \(y = f(kx)\) (\(k\gt0\)), when \(k = \frac{1}{7}\), the graph of \(y = f(x)\) is stretched horizontally.

Answer:

stretches it horizontally