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anonymous

  • one year ago

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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  1. anonymous
    • one year ago
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    Also how y=(-3x)^2 is a transformation of the graph y=x^2 please :)

  2. A_clan
    • one year ago
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    A. Amplitude increases. i.e. Graph moves away from the X-axis.

  3. jtvatsim
    • one year ago
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    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.

  4. jtvatsim
    • one year ago
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    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.

  5. jtvatsim
    • one year ago
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    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.

  6. jtvatsim
    • one year ago
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    Even better, let me draw the x^2 graph.

  7. jtvatsim
    • one year ago
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    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|

  8. anonymous
    • one year ago
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    wait i don't get it so it doesn't flip? like not even on the x axis?

  9. jtvatsim
    • one year ago
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    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.

  10. jtvatsim
    • one year ago
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    |dw:1437116444748:dw|

  11. anonymous
    • one year ago
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    so this one still flips on the y axis but not x?

  12. jtvatsim
    • one year ago
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    That is correct. The general pattern is f(-cx) flips around the y-axis -c f(x) flips around the x-axis

  13. jtvatsim
    • one year ago
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    So, another picture...

  14. jtvatsim
    • one year ago
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    |dw:1437116587371:dw|

  15. anonymous
    • one year ago
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    i get it now :) thank you so much!

  16. jtvatsim
    • one year ago
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    Your welcome! Glad to help!

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