I need the expression of a function that looks like the following:
The expression preferably needs to be simple e.g., comprised of as few elementary functions as possible. It doesn't matter what the function looks like for $x<0$, but as $x \rightarrow \infty$, the function should approach $0$. It seems like it could be a polynomial.
Also, the expression preferably should not be segmented, i.e., one expression for small $x$, another for large $x$, but be the same for all $x>0$.
To flip the function about the x-axis use f(-x). Therefore, for example, if the sigmoid is $$Y(t) = \frac{1}{1+exp(-t)}$$
the analytical expression for the reverse sigmoid is
$$Y(-t) = \frac{1}{1+exp(t)}$$