Funcion

Función, or función in Spanish, is a fundamental concept in mathematics and computer science describing a rule that assigns to each input exactly one output. In general usage, the term denotes a mapping from a domain to a codomain, where the input set is often called the domain and the output set the codomain. The standard notation expresses this as f: X → Y with f(x) = y, and the graph of the function consists of all ordered pairs (x, f(x)).

In mathematics, a function must assign a single output to every input in its domain. The image (or range) is the set of outputs that actually occur, while the domain is the set of inputs for which the rule is defined. Functions can be classified by properties such as injectivity (one-to-one), surjectivity (onto), and bijectivity (both). Examples include linear functions like f(x) = mx + b and the squaring function f(x) = x^2. The inverse of a function exists when the function is bijective, providing a rule that reverses the assignment.

In programming, a function is a reusable block of code that takes inputs, performs operations, and returns a value. Functions promote modularity and can be pure (no side effects) or impure (may affect external state). They are central to software design, with syntax and conventions varying across languages.

Etymology traces the term to the Latin functio, meaning performance or execution. In Spanish, the word is escrita as función with an acute accent; in English and many programming contexts, function is used without diacritics.

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