Hi there!

I am having huge trouble understanding big-O-notation. I don't understand at all why the definition of big-O-notation mentions the constant C. Here is the definition from my book:

"Let f and g be functions. We say that f(x) is O(g(x)) if there are constants C and k such that:

|f(x)| ≤ C|g(x)|

whenever x > k"

I understand why absolute values are used and why x must be bigger than k, but I don't understand the purpose of the C-constant. If anyone could explain that in a simple way, if there is a simple way, I would be really greatfull.

Now, here is a problem from my book:

Show that f(x) = x^{2}+ 2x + 1 is O(x^{2})

Thanks so much to anyone who reads this!