# The Growth of Functions

• Feb 12th 2006, 06:53 PM
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
• Feb 12th 2006, 11:09 PM
CaptainBlack
Quote:

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