What does a function in mathematics do?

A function in mathematics is a specific relationship that associates each element in one set, known as the domain, with exactly one element in another set, referred to as the range. This means that for each input value (domain), there is a corresponding output value (range). This one-to-one association is a defining characteristic of functions, which can be represented in various forms, such as equations, graphs, or tables.

For example, if you consider the function f(x) = x + 2, every input of x from the domain leads to a unique output that we can calculate and identify in the range. This straight association showcases the fundamental nature of functions.

While other choices mention mathematical concepts, they do not accurately describe the core purpose of what a function is designed to do. Functions can indeed create geometric shapes when graphed, can be utilized in calculations that involve averages or ratios, but these aspects do not define the primary role of a function in mathematics. The ability to associate one set with another is what fundamentally characterizes a function.