I'm building a game that requires a bit of mathematical magic, and I'm not a math major, so I'm not entirely sure where I should be beginning as someone with a basic knowledge of limits and such.
I'm looking for a formula that goes to a specific limit: $$\lim_{x\to\infty}f(x) = B$$ where B is some specific number, non infinity, but also: $$\lim_{x\to0}f(x) = A$$ where A is another specific number, non infinity. In other words, the range of the formula goes from A-B. This range could be, say, 0-1, or 0.5-3, or any other range where A<B.
In more specific example, I'm trying to do something where the formula as I input values increasing from 0, it goes in the range something like 0.95 to 1, but never hitting 1. I'm going to have to reuse this curve in multiple areas, so understanding the generic formula here is something I'd like to hope to do more than just a specific case. For the purposes of this question, I'm only really interested in the area 0-infinity; I'm not going to be plugging in negative numbers to this, so whatever they do doesn't really matter.