What function looks like $\overbrace{}$? Here's my awesome drawing:

Basically it's a function that takes a high (or infinite) value at $0$, then falls off logarithmically for a while before falling off exponentially. 
It doesn't need to be symmetric, it would be ok if the negative $x$ values were 
reversed in sign or something like that. I really only care about $x\ge0$.
Edit: I would prefer if the function is not periodic.

How about $\frac{x^2-1}{x^2(x-2)(x+2)}$
