convex decreasing function with limit example

Question

I'm trying to find a function that is strictly decreasing function for $x\geq 0$ and has a positive limit, i.e. $lim_{x\rightarrow \infty}f(x)\in\mathbb{Z}^+$. I was thinking $$f(x)=\frac{a}{x^2+b}+c$$ for some positive constants $a,b,c$. However this is actually a concave-convex function. What are some great strategies when formulating a function? What are some examples that satisfy my conditions?