what does the transformation ( f(x)\to fleft(\frac{1}{7}x\right) ) do to the graph of ( f(x) )?\nshrinks it…

what does the transformation ( f(x)\to fleft(\frac{1}{7}x\right) ) do to the graph of ( f(x) )?\nshrinks it horizontally\nshrinks it vertically\nstretches it vertically\nstretches it horizontally

what does the transformation ( f(x)\to fleft(\frac{1}{7}x\right) ) do to the graph of ( f(x) )?\nshrinks it horizontally\nshrinks it vertically\nstretches it vertically\nstretches it horizontally

Answer

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