# Thread: The Growth of Functions

1. ## 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

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