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Math Help - The Growth of Functions

  1. #1
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    Exclamation The Growth of Functions

    I am a freshman taking discrete and its really hard i have a horrible teacher that doesnt offer study sessions can anyone explain to determine whether this function is O(x)
    f(x)= 3x+7 i have to find what is k and C
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  2. #2
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    Quote Originally Posted by lilheadbaby1
    I am a freshman taking discrete and its really hard i have a horrible teacher that doesnt offer study sessions can anyone explain to determine whether this function is O(x)
    f(x)= 3x+7 i have to find what is k and C
    Note sure what you want k and C to denote, but

    f(x)=O(x)

    means something like there exists an x_0 and M such that:

    |f(x)|<M|x|, \mbox{for all}\ x>x_0,

    In this case lets set x_0=1, and M=11, then the above condition is
    satisfied showing that f(x) is O(x).

    But note x_0 and M are not unique.

    Informally f(x)=O(x) means that |f(x)| grows no faster than
    some multiple of x.

    RonL
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