A function $f$ such that $f(x)$ increases from $0$ to $1$ when $x$ increases from $0$ to infinity? I am looking for a function f(x) with a value range of [0,1].
f(x) should increase from 0 to 1 while its parameter x increases from 0 to +infinity.
f(x) increases very fast when x is small, and then very slow and eventually approach 1 when x is infinity.
Here is a figure. The green curve is what I am looking for:

Thanks.
It would be great if I can adjust the slope of the increase. Although this is not a compulsory requirement.  

Try $f(x) = 1-e^{-x^2}$ , which will be 0 for x = 0 and approach 1 rapidly for big x.
