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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Function Equation Finder
Function Equation Search
Answers to Questions (FAQ)
What is a Function Equation Finder? (Definition)
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.
How to find the equation of a curve?
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.
How to find an equation from a set of 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).
How to find the equation of a line?
To find the equation of a straight line, see the page: linear equation.
How accurate are the results?
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)
Source code
dCode retains ownership of the "Function Equation Finder" source code. Any algorithm for the "Function Equation Finder" algorithm, applet or snippet or script (converter, solver, encryption / decryption, encoding / decoding, ciphering / deciphering, breaker, translator), or any "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.) or any database download or API access for "Function Equation Finder" or any other element are not public (except explicit open source licence like Creative Commons). Same with the download for offline use on PC, mobile, tablet, iPhone or Android app.
Reminder: dCode is an educational and teaching resource, accessible online for free and for everyone.
Cite dCode
The content of the page "Function Equation Finder" and its results may be freely copied and reused, including for commercial purposes, provided that dCode.fr is cited as the source.
Exporting the results is free and can be done simply by clicking on the export icons ⤓ (.csv or .txt format) or ⧉ (copy and paste).
To cite dCode.fr on another website, use the link:
In a scientific article or book, the recommended bibliographic citation is: Function Equation Finder on dCode.fr [online website], retrieved on 2025-04-15,
