Reversed graph plotting algorithm Consider a real-valued polynomial function of one variable. Knowing the "rules" function dictates we can plot the graph of that function with a given accuracy. 
Question: is the reversed process possible?
 A: Given the "rule-based" part of your comment, if you demand perfect accuracy, the answer is no.  Just take any curve that goes through $(0,y)$ at an indefinable real number.  If you accept some error in both directions, you can use an interpolating polynomial of high enough degree.
A: Is this what you're looking for?
http://www.arachnoid.com/sage/polynomial.html
https://en.wikipedia.org/wiki/Polynomial_regression
A: I assume that, beside the graph, you have a table with some values $(x,f(x))$. In some cases, say equispaced $x$ points, building a finite difference table should allow to guess the degree of the polynomial and, subsequently, to compute the coefficients by interpolation. If you know that the data is produced by a polynomial, then iterative regressions (or interpolations) with different polynomial specifications must ultimately estimate the right coefficients giving null error up to roundoff.
More generally, symbolic regression may help, see http://www.ams.org/notices/201306/rnoti-p713.pdf for an interesting description of a software that can guess the symbolic form of your function. You can specify the search space to include only "+" and "*" (sum and product), effectively reducing the search to polynomials. 
The software can be downloaded at http://formulize.nutonian.com/ and a serious treatment appeared on Science, http://www.sciencemag.org/content/324/5923/81.abstract 
