The Growth of Functions

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