Which definition best describes a function?

The definition that best describes a function is that it is a relation in which each input has a unique output. This is a fundamental property of functions in mathematics. A function associates each element in the domain (the set of possible inputs) with exactly one element in the codomain (the set of possible outputs). This uniqueness of outputs is what distinguishes a function from other types of relations, where an input could potentially correspond to multiple outputs. The notion of a function ensures clarity and consistency in how we perform calculations or map values, which is essential in various mathematical applications.

For example, if we consider the function f(x) = x^2, for each input value of x, there is one specific output value obtained by squaring x. This relationship is crucial for understanding not just basic algebra, but also more complex concepts in calculus, statistics, and beyond.