# Want to understand Big O by graph [duplicate]

f(n) = 3n+3 ;
f(n) = O(n)

By definition :

$3n+3 \le c_1.n$

By dividing both side by n
$3+(3/n) \le c_1$
means we r getting constant range for $c_1$ for any $n$. Again it shows c's value must be greater than 3 at any cost.
e.g. if we take c's value 3.5 so n's value will be 6.
Now if we plot graph ( Bcoz I want to learn this concept by understanding graph )
$cg(n)$ graph goes below of $f(n)$ graph. I have taken following values for both functions :

f(n) : 3n+3
n  f(n)

1   6
2   9
3   12
-2  -3

for

g(n) = 3.5n
n   g(n)
1   3.5
2   7
3   10.5
-2  -7

If we plot graph by these values it doesn't bind $f(n)$ i.e. $3n+3$ above by the value of $g(n)$ i.e. $3.5\cdot n$
Can anyone explain me this concept by graph ?