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Thread: 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 $\displaystyle k$ and $\displaystyle C$ to denote, but

    $\displaystyle f(x)=O(x)$

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

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

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

    But note $\displaystyle x_0$ and $\displaystyle M$ are not unique.

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

    RonL
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