I'm writing an app and I want to present some ratios normalized on a scale of 0 to 10. It's information like (number of issues resolved : number of issues remaining open).
My idea is to write a function, and a few of its inputs & outputs would be:
f(0) -> 0
f(0.1) -> 1.0
f(1) -> 5.0
f(10) -> 9.0
f(inf) -> 10.0
So, the input is a real number >= 0, and the output is a real between 0 and 10 inclusive.
So my immediate question is: Is there a well known formula that would create this kind of output? I got pretty close with some variations of y = a/(1 + be^(-kx)), but I'm mostly randomly guessing.
I'm interested in any way to solve this, as well as how to generate solutions for it.
Also: since I'm programming this, I could do this with a few functions which I alternatively invoke, depending on the input.
EDIT: Here's @A.S.'s solution, y=10*(x/(1+x)) which looks pretty much perfect:
This is my javascript implementation.