I think I recall that there are methods for figuring out the original function behind a graph of a polynomial, and I know that there is not necessarily a 1-to-1 relationship between a graph and the functions that could produce that graph...
I'm looking into a problem where I have a bunch of point data from a graph [e.g. y = f(x)], and I'd like to distill that into the formula behind function f() that would produce that same graph (or a close approximation) over the same range of x values*.
I suspect that there is no general, mechanistic way of doing this, but since my knowledge of mathematics is very limited, I thought I'd ask here.
(*) Actually, I'd have an n-dimensional plot of points [gathered through a time-consuming process, such as experimentation], and in some/most/all cases, I could reduce the graph into a set of one or more mathematical formulae.