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.

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    $\begingroup$ The method you're looking for is called "fitting". $\endgroup$ – Bobson Dugnutt May 22 '17 at 22:52
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    $\begingroup$ Spreadsheets such as Excel are capable of finding the best polynomial fit to a data set. You specify the degree of the possible polynomial fit and it computes the coefficients optimized according to the "least squares" method. It can then plot the data along with the proposed fit. $\endgroup$ – John Wayland Bales May 22 '17 at 22:57

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