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- anonymous

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).

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- anonymous

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- anonymous

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

- A_clan

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

- jtvatsim

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.

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- jtvatsim

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.

- jtvatsim

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.

- jtvatsim

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

- jtvatsim

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|

- anonymous

wait i don't get it
so it doesn't flip? like not even on the x axis?

- jtvatsim

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.

- jtvatsim

|dw:1437116444748:dw|

- anonymous

so this one still flips on the y axis but not x?

- jtvatsim

That is correct. The general pattern is
f(-cx) flips around the y-axis
-c f(x) flips around the x-axis

- jtvatsim

So, another picture...

- jtvatsim

|dw:1437116587371:dw|

- anonymous

i get it now :) thank you so much!

- jtvatsim

Your welcome! Glad to help!

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