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Math Help - Transformations

  1. #1
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    Transformations





    List the sequence of transformations that is necessary to obtain the graph of from

    How to do this question algebraically using and method.
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  2. #2
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    Hello, usagi_killer!

    f(x) \:=\:x^4-x
    [g(x) \:=\:16x^4 + 2x + 1

    List the sequence of transformations that is necessary to obtain the graph of g(x) from f(x).

    How to do this question algebraically using x' and y; method?
    I "eyeballed" the two functions . . .


    Start with: . f(x)\:=\:x^4 - x

    Replace x with \text{-}2x\!:\;\;f(\text{-}2x) \;=\;(\text{-}2x)^4 - (\text{-}2x) \;=\;16x^4 + 2x

    Add 1: . f(\text{-}2x) + 1 \;=\;16x^4 + 2x + 1

    . . Hence: . g(x) \;=\;f(\text{-}2x) + 1



    First, graph f(x).

    The sequence of transformations is:

    (1) Replace x with -x.
    . . .This reflects the graph of f(x) over the y-axis.

    (2) Replace x with 2x.
    . . .This contracts the graph to "half its width."

    (3) Add 1.
    . . .This raises the graph one unit.

    The result is the graph of g(x).

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  3. #3
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    Thank you!!!

    But is there no way of doing it with mapping method?

    Eg, if you had the graph y = x^2 and y = (x-1)^2

    then let (x',y') be the new x and y

    so y' = (x'-1)^2

    thus y = y' and x = x'-1

    so x' = x+1

    thus (x,y) is mapped onto (x+1,y)

    so the graph is moved 1 unit to the right.

    How can you do the same way here?
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