How is a function defined in mathematical terms?

A function in mathematical terms is defined as a relation that assigns exactly one output for every input. This means that for each element in the domain (the set of possible inputs), there is a single corresponding element in the codomain (the set of possible outputs).

This definition ensures that the relationship between the input and output is consistent and predictable, which is crucial for many mathematical operations and applications. For example, if you consider a function that takes a number as input and doubles it, each input number will always result in one specific output (the doubled value), satisfying the definition of a function.

The concept of having 'exactly one output for every input' prevents ambiguity and allows us to use functions in various mathematical contexts, such as equations, graphs, and real-world applications, where each input needs to lead to a unique result.