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Math Help - Transformation Problem

  1. #1
    Junior Member BobBali's Avatar
    Joined
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    Transformation Problem

    Hello All,

    Having trouble with below question:

    The graph of:
    f(x) = x^3+3x^2-x+4
    is translated to its image g(x) by the vector \binom{-1}{3}
    Write the new equation of g(x) in the form :
    ax^3+bx^2+cx+d

    Ive tried using the GDC to graph f(x) and then translating points by the vector, but was wondering if there is an algebraic way of doing it without using the GDC? Thanks appreciate it.
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  2. #2
    MHF Contributor

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    Re: Transformation Problem

    The old x value is being replaced by x'= x- 1, so that x= x'+ 1, and the old y value is being replaced by y'= y+ 3, so that y= y'- 3:
    y'- 3= (x'+ 1)^3+ 3(x'+ 1)^2- (x'+ 1)+ 4. Multiply those out and then replace x' with x and y' with y.
    Thanks from BobBali
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  3. #3
    MHF Contributor
    skeeter's Avatar
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    Re: Transformation Problem

    g(x) = f(x+1) + 3
    Thanks from BobBali
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