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Math Help - Transformation of graph

  1. #1
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    Transformation of graph

    A graph with the equation y=f(x) undergoes, in succession, the following transformations:

    A: A translation of 1 unit in the direction of the positive x-axis.
    B: A scaling parallel to the x-axis by a scale factor \frac{1}{2}
    C: A reflection in the y-axis.

    The equation of the resulting curve is y=\frac{2}{2x^2+2x+1}

    Determine the equation y=f(x)



    What I did:

    -f(\frac{1}{2}x-1) =\frac{2}{2x^2+2x+1}
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  2. #2
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    Let f_1(x), f_2(x) and f_3(x) be the results of transformations after the step A, B and C, respectively. Thus, f_3(x) = 2/(2x^2+2x+1). Then f_1(x) = f(x-1), f_2(x)=f_1(2x)=f(2x-1) and f_3(x)=f_2(-x)=f(-2x-1), not -f(\frac{1}{2}x-1).

    One way to find f(x) is assume that it has the form 2/(Ax^2+Bx+C). Then A(-2x-1)^2+B(-2x-1)+C=2x^2+2x+1. By equating the corresponding coefficients, you can find A, B, and C.

    Another, perhaps, more reliable, way is to apply the inverse transformations to f_3(x).
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