Question

what does the transformation ( f(x)\to f(3x) ) do to the graph of ( f(x) )?
shrinks it horizontally
stretches it horizontally
stretches it vertically
shrinks it vertically

Explanation:

For a function \(y = f(x)\), when we have a transformation \(y = f(kx)\) (\(k> 1\)), it is a horizontal compression (shrink). Here \(k = 3>1\). The general rule is that if we replace \(x\) with \(kx\) in the function \(y=f(x)\), the graph of \(y = f(kx)\) is the graph of \(y = f(x)\) compressed horizontally by a factor of \(\frac{1}{k}\).

Answer:

shrinks it horizontally