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Math Help - Functions

  1. #1
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    Functions

    Given f(x)=8x^3, sketch the graph of g(x) in detail, where g(x)=f(x - 1)+1


    Im unsure what to do!
    do you sub in f(x) or...??
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by scubasteve94 View Post
    Given f(x)=8x^3, sketch the graph of g(x) in detail, where g(x)=f(x - 1)+1


    Im unsure what to do!
    do you sub in f(x) or...??
    Since f\!\left(x\right)=8x^3, and g\!\left(x\right)=f\!\left(x-1\right)+1, this means that g\!\left(x\right)=8\left(x-1\right)^3+1.

    All that you're doing with f\!\left(x\right) is shifting it over one unit to the right (which is what f\!\left(x-1\right) represents) and then shifting it up one unit (which is what f\!\left(x-1\right)+1 represents).

    Does this make sense?
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  3. #3
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    Yes i think so but what does the 8 do??
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  4. #4
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by scubasteve94 View Post
    Yes i think so but what does the 8 do??
    You can think of it as a vertical stretch. It takes the values of the function x^3 and multiplies them by 8.
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  5. #5
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    so is it just the dilation factor??
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  6. #6
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by scubasteve94 View Post
    so is it just the dilation factor??
    Yes.
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  7. #7
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    Thank you very much
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