Given the reciprocal function $\frac{a}{m \cdot x + b}$ where $a,m,b$ are constants. I'm trying to figure out how/if I can control the range that this produces. The application of this problem is generating a "score" based on a locations' proximity to me. So for example, in my problem I know the range of possible values is $0$-$100$ km, I need to build a score between $1.0$ and $3.0$ where a proximity of $0$ km (i.e., very close) would generate a score closer to $3.0$ and a distance of $100$ km (i.e., very far away) would generate a score closer to $1.0$.
I was previously using this successfully to produced a range of $0$-$1.0$, but it turned out that I need greater control over the range produced.
Any advice appreciated.