dCode is free and its tools are a valuable help in games, puzzles and problems to solve every day! You have a problem, an idea for a project, a specific need and dCode can not (yet) help you? You need custom development? Contact-me!

This page is using the new English version of dCode, please make comments !

Tool to check the parity of a function (even or odd functions): it defines its ability to verify symmetrical relations.

Answers to Questions

How to check if a function is even?

A function is even if the equality $$ f(x) = f(-x) $$ is true for all x from the domain of definition.

Consider \( f(x) = x^2 \) in \( \mathbb{R} \), then \( f(-x) = (-x)^2 = x^2 = f(x) \), so \( f(x) \) is even.

Graphically, this involves that opposed abscissae have the same ordinates, this means that the ordinate axis is an axis of symmetry of the curve representing f.

How to check if a function is odd?

A function is odd if the equality $$ f(x) = -f(-x) $$ is true for all x from the domain of definition.

Consider \( f(x) = x^3 \) in \( \mathbb{R} \), then \( -f(-x) = -(-x)^3 = x^3 = f(x) \), so \( f(x) \) is odd.

Graphically, this involves that opposed abscissae have opposed ordinates, this means that the origin (central point) (0,0) is a symmetry center of the curve representing f.

NB: if an odd function is defined in 0, then the curve passes at the origin: $$ f(0) = 0 $$

Ask a new question

Source code

dCode retains ownership of the source code of the script Even and Odd Function. Except explicit open source licence (free / freeware), any algorithm, applet, software (converter, solver, encryption / decryption, encoding / decoding, ciphering / deciphering, translator), or any snippet or function (convert, solve, decrypt, encrypt, decipher, cipher, decode, code, translate) written in PHP (or Java, C#, Python, Javascript, etc.) which dCode owns rights can be transferred after sales quote. So if you need to download the Even and Odd Function script for offline use, for you, your company or association, see you on contact page !

dCode uses cookies to customize the site content, analyze user behavior and adapt dCode to your use. Some data is stored and collected for advertising purposes and may be shared with our partners. OK