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Also how y=(-3x)^2 is a transformation of the graph y=x^2 please :)
A. Amplitude increases. i.e. Graph moves away from the X-axis.
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.
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.
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.
Even better, let me draw the x^2 graph.
In this case the flip across the y-axis doesn't do anything because it is already a mirror image of itself. |dw:1437116265984:dw|
wait i don't get it so it doesn't flip? like not even on the x axis?
mhm... I was thinking you'd be confused by this particular special case. Here's a more general picture just to give you the idea for not so special functions.
so this one still flips on the y axis but not x?
That is correct. The general pattern is f(-cx) flips around the y-axis -c f(x) flips around the x-axis
So, another picture...
i get it now :) thank you so much!
Your welcome! Glad to help!