Open the graphing tool. Move the slider for the equation y = kx3 to a position of your choice, where k ≠ 1. Next, move the slider of y = (kx)3 so the two graphs lie on top of one another. How do the values of k compare with one another in this situation? Why do you think that is?


For the functions to coincide, the value of k in y = (kx)3 must be smaller than in y = kx3. This is because the value of y changes more rapidly when k is cubed inside the parentheses. The behavior of the functions is similar since a vertical stretch is similar to a horizontal compression.