What does the transformation f(x)↦f

Question

1/8
x do to the graph of f(x)?

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

Answer 1

The transformation \( f(x) \mapsto f\left(\frac{1}{8} x\right) \) stretches the graph of \( f(x) \) horizontally.

This is because substituting \( x \) with \( \frac{1}{8} x \) means that for every \( x \) in the original function, the value of the function is taken at a point that is 8 times further away from the y-axis. Thus, it expands the graph horizontally by a factor of 8.

So the correct answer is: stretches it horizontally.