Function Equation Finder

To find the equation from a graph:

Method 1 (fitting): analyze the curve (by looking at it) in order to determine what type of function it is (rather linear, exponential, logarithmic, periodic etc.) and indicate some values in the table and dCode will find the function which comes closest to these points.

Method 2 (interpolation): from a finite number of points, there are formulas allowing to create a polynomial which passes exactly through these points (see Lagrange interpolation), indicate the values of certain points and dCode will calculate the passing polynomial by these points.

To derive the equation of a function from a table of values (or a curve), there are several mathematical methods.

Method 1: detect remarkable solutions, like remarkable identities, it is sometimes easy to find the equation by analyzing the values (by comparing two successive values or by identifying certain precise values).

Example: a function has for points (couples $ (x,y) $) the coordinates: $ (1,2) (2,4), (3,6), (4,8) $, the ordinates increase by 2 while the abscissas increase by 1, the solution is trivial: $ f (x) = 2x $

Method 2: use a interpolation function, more complicated, this method requires the use of mathematical algorithms that can find polynomials passing through any points. The most well known interpolations are Lagrangian interpolation, Newtonian interpolation and Neville interpolation.

NB: for a given set of points there is an infinity of solutions because there are infinite functions passing through certain points. dCode tries to propose the most simplified solutions possible, based on affine function or polynomial of low degree (degree 2 or 3).

To find the equation of a straight line, see the page: linear equation.