What is the definition of a function?

A function is specifically defined as a relation in which every input corresponds to exactly one output. This means that for each element in the domain (the set of all possible inputs), there is a unique element in the codomain (the set of potential outputs). This property ensures that when an input is provided to the function, the resulting output is predictable and consistent.

The characteristic of uniqueness of outputs is crucial in distinguishing functions from other types of relations. For example, if an input leads to multiple outputs, it does not meet the criteria to be classified as a function.

This understanding highlights why the definition that articulates the relationship of each input having exactly one output is correct. It encapsulates the essence of what constitutes a function, fundamental to many concepts in mathematics, particularly in algebra and calculus.