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Math Help - function transformation

  1. #1
    Newbie
    Joined
    Sep 2005
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    5

    Exclamation please help

    would it be safe to conclude that the transformation f(x/m) and mf(x) produce graphs that are identical? explain ur answer
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  2. #2
    MHF Contributor
    Joined
    Apr 2005
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    Ummm, let us see.

    f(x/m), mf(x)
    I assume m is a constant.

    mf(x) is m"f(x), I assume also.

    f(x/m) and m*f(x) have identical graphs?

    Say, m=3
    And f(x/m) = f(x/3) = x^2 +2x + 6 ----(i)
    What would be f(x)?

    x = 3(x/3)
    How are we generate the f(x)?
    f(x) = (3x)^2 +2(3x) +6
    f(x) = 9x^2 +6x +6 -----------(ii)
    Check,
    If f(x) = 9x^2 +6x +6, what is f(x/3)?
    f(x/3) = 9(x/3)^2 +6(x/3) +6
    f(x/3) = 9[ x^2 / 9] +2x +6
    f(x/3) = x^2 +2x +6 -------same as (i).
    So (ii) is okay. f(x) = 9x^2 +6x +6 ---------***

    Now,
    f(x/m) = f(x/3) = x^2 +2x +6 ---------(i)
    mf(x) = m*f(x) = 3*f(x) = 3(9x^2 +6x +6) = 27x^2 +18x +18 ----(iii)

    Would (i) and (iii) have identical graphs?

    No. -----------answer.
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