Need precal help! Fast! :(?

Question

Can someone help me explain or illustrate the graphs of y = a times f(x) and y = f(ax)? I need the answer a.s.a.p. Thanks!

Answer 1

For y = a*f(x), the function is multiplied by a; so the function operates only on x, not on a, and the result is multiplied by a.

For y = f(a*x), the variable is multiplied by a, so the function operates on both a and x.

A simple example of this is f(x) = sin x. In this case, a*sin x  will alter the amplitude of the sine wave, while sin a*x will alter the frequency of the sine wave.