Understanding Functions in Mathematics

In mathematics, a function is a relationship between two sets where each element from the first set, called the domain, is related to exactly one element in the second set, known as the codomain. A function processes an input and produces an output determined by its rule. Formally, a function f from set A to set B is written as f: A → B. Key components include the domain (all possible inputs), codomain (all possible outputs), and the rule that assigns each input to one output. Examples include a linear function f(x) = 2x + 3 and a square function f(x) = x², both showcasing how inputs are transformed into outputs.