Tool to find the equation of a function from its points, its coordinates x, y=f(x) according to some interpolation methods and equation finder algorithms

Function Equation Finder - dCode

Tag(s) : Functions

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A Function Equation Finder is a tool designed to identify the mathematical equation that best represents a set of data points or the relationship between variables.

It uses various algorithms and methods (curve fitting, least squares regression analysis, etc.) to determine the underlying function.

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.

The accuracy of the results depends on several factors:

— The quality and quantity of input data (the more precise data, the better the result)

— The complexity of the relationship modeled (The equation model sought can greatly influence the quality of the equation)

— The algorithms and methods used (dCode does its best to use the most relevant algorithms)

dCode retains ownership of the "Function Equation Finder" source code. Except explicit open source licence (indicated Creative Commons / free), the "Function Equation Finder" algorithm, the applet or snippet (converter, solver, encryption / decryption, encoding / decoding, ciphering / deciphering, breaker, translator), or the "Function Equation Finder" functions (calculate, convert, solve, decrypt / encrypt, decipher / cipher, decode / encode, translate) written in any informatic language (Python, Java, PHP, C#, Javascript, Matlab, etc.) and all data download, script, or API access for "Function Equation Finder" are not public, same for offline use on PC, mobile, tablet, iPhone or Android app!

Reminder : dCode is free to use.

The copy-paste of the page "Function Equation Finder" or any of its results, is allowed (even for commercial purposes) as long as you credit dCode!

Exporting results as a .csv or .txt file is free by clicking on the *export* icon

Cite as source (bibliography):

*Function Equation Finder* on dCode.fr [online website], retrieved on 2024-10-05,

equation,coordinate,curve,point,interpolation,table

https://www.dcode.fr/function-equation-finder

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