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.  

Here are two simple functions with slope $k$ at $x=0$, for some $k>0$:
$$f(x) = 1-e^{-kx}$$
and
$$g(x) = \frac{2}{\pi}\arctan\left(\frac{\pi}{2}kx\right)$$
The first of these approaches $1$ more quickly than the second.
