Ideally, the function f(x) would tend toward zero as x tends towards negative infinity, and f(x) would tend towards 1 as x tends towards infinity, all the while being monotonically increasing.
for example, I know that I could modify the inverse tangent function to achieve this, by doing something like:
f(x) = (InverseTan(x) + pi/2) / pi
I'm looking for other functions which satisfy the same criteria but are computationally cheap to calculate on a computer. It's been a decade since my last math course and I can't seem to recall any other functions that would do the trick.