Question

Please help :)
A. Explain the effect of c on the graph of y=f(x) for the function y=cf(x).
B. Explain the effect of c on the graph of y=f(x) for the function y=f(cx).

Answer 1

Also how y=(-3x)^2 is a transformation of the graph y=x^2 please :)

Answer 2

A. Amplitude increases. i.e. Graph moves away from the X-axis.

Answer 3

In situation A, c stretches the graph vertically. If c = 2 for example, the graph will be twice as tall. If c = 1/2, then the graph will be half as tall.

Answer 4

In situation B, c stretches the graph horizontally. It's a little weird, but if c = 2, for example, the graph will actually compress/shrink/be "half as long" <-- don't actually put "half as long" in your answer, it's just a way for you to imagine it. If c = 1/2, the graph will actually expand/grow/be "twice as long" <-- again, teachers won't like you to say "twice as long" put it helps get the picture in your own mind.

Answer 5

For your last question, notice that there is a "c" inside next to the x. This c = -3 and will stretch the graph horizontally. Since it is 3, it will compress/shrink the graph horizontally by a factor of three. Since it is also negative, it will flip the graph over the y-axis. I'll draw a picture so you can see what I mean.

Answer 6

Even better, let me draw the x^2 graph.

Answer 7

In this case the flip across the y-axis doesn't do anything because it is already a mirror image of itself.