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Math Help - Simple graph question (conflicting solution)

  1. #1
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    Simple graph question (conflicting solution)

    Now, I have answered this question and it seems very simple. But the answer they give is different to mine, and i graphed to check, and it seems I am correct, but I want you guys to tell me what you think. Part c) is what I'm concerned with.

    a) The graph of g is obtained from the graph of the function f with rule f(x) = x^2 by a translation by +3 units parallel to the x-axis. Write down the rule for g.

    Now, i wrote (x-3)^2 which is correct.

    b) The graph of h is obtained from the graph of g by a translation by −1 unit parallel to the y-axis. Write down the rule for h.
    I wrote (x-3)^2-1

    c) The graph of k is obtained from the graph of h by a dilation by a scale factor of 0.5 from the y-axis. Write down the rule for k.

    I wrote 2(x-3)^2-1, but they say:
    (2x-3)^2-1. Now, how can that be correct since their version changes the turning point completely? It's basically a totally different graph, isn't it?

    So tell me what you think.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by scorpion007 View Post
    Now, I have answered this question and it seems very simple. But the answer they give is different to mine, and i graphed to check, and it seems I am correct, but I want you guys to tell me what you think. Part c) is what I'm concerned with.

    a) The graph of g is obtained from the graph of the function f with rule f(x) = x^2 by a translation by +3 units parallel to the x-axis. Write down the rule for g.

    Now, i wrote (x-3)^2 which is correct.

    b) The graph of h is obtained from the graph of g by a translation by −1 unit parallel to the y-axis. Write down the rule for h.
    I wrote (x-3)^2-1

    c) The graph of k is obtained from the graph of h by a dilation by a scale factor of 0.5 from the y-axis. Write down the rule for k.

    I wrote 2(x-3)^2-1, but they say:
    (2x-3)^2-1. Now, how can that be correct since their version changes the turning point completely? It's basically a totally different graph, isn't it?

    So tell me what you think.
    I think the given answer is correct. Let f_1(x) be the function
    you want to dilate. You want a new function f_2(x) such that:

    <br />
f_2(x)=f_1(2x)<br />

    Now let f_1(x)=(x-3)^2-1, then:

    <br />
f_2(x)=f_1(2x)=(2x-3)^2-1<br />

    RonL
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