There are an infinite number of functions that pass through any set of points,

and there are many simple ways of finding some example of such a function,

but deciding which such function is preferable in a given application may not be an easy or well defined problem.

If the parameter values are another set of free variables, that could further multiply the number of potential functions that fit, which can potentially make the problem of finding some example of such a function easier, and can potentially make the problem of finding the preferred example of such a function more difficult.