I'm trying to find a function that satisfies the following coordinates:
$$(1, 1)$$$$(2, 0.84)$$$$(4, 1.5)$$$$(31, 4.1)$$$$(44, 5)$$
The x parameters are always discrete and the function doesn't need to be exact but as close as possible although the first three coordinates are the most important ones.
The function is not asymptotic.
The growth for large numbers should be really slow and should be configurable if possible.
It supposed to look like this:
What is the best method for finding this function?
I've tried to play a bit with desmos but I don't have a specific way to approach this problem.
Without more information I can't find the best solution (need information about minimum value, behavior as the function approaches infinity, whether it is asymptotic or not), but your graph seems like it is not asymptomatic as $x\to\infty$, and it seems like the function
$$ f(x) = \frac{3x^{3/2}}{4\sqrt{x^2-1}} $$
Fits quite well.