State the value of a, k, c, and d for the following equation and describe the transformations that apply: f(x) = –1⁄4(x + 2)^3 – 7.?

1 Answer

  • Pope
    Lv 7
    4 years ago
    Favorite Answer

    You want us to do that without first defining a, k, c, or d?


    Your definitions answer your question, at least the first part. I am thinking you must mean this:

    Let p(x) = x³.

    f(x) = a[(x - d)/k]³ + c

    Begin with the graph of y = p(x).

    To get the graph of y = f(x), effect these transformations, in order, on the previous graph.

    Scale vertically, by factor a, with the x-axis invariant.

    Scale horizontally, by factor k, with the y-axis invariant.

    Translate by vector <d, c>.

    Actually, the order of the scalings does not matter, but the translation must be last. In your case, these are the transformations:

    Scale vertically, by factor -1/4, with the x-axis invariant.

    Scale horizontally, by factor 1, with the y-axis invariant. That is the identity transformation in this case, and may be omitted.

    Translate by vector <-2, -7>.

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