# Function

noun
• mathematics
a relationship between two sets, called the domain and the codomain, in which each element in the domain corresponds to exactly one element in the codomain.

## Description

A function is a mathematical relationship between two sets, called the domain and the codomain, in which each element in the domain corresponds to exactly one element in the codomain. The domain consists of the input values, and the codomain contains the possible output values. The actual set of output values that the function generates is called the range.

Functions are often represented by equations, graphs, or tables and can model real-world scenarios or abstract concepts. In an equation, a function can be denoted as , where represents the function, and represents the input variable. The output value of the function is denoted as or .

For example, the function represents a linear relationship between the input variable and the output variable . If , the output value would be .

## Related Terms

The domain of a function is the set of all possible input values for which the function is defined.

The range of a function is the set of all possible output values generated by the function for a given domain. It is a measure of how the output values of a function are distributed and can be used to analyze the behavior of the function and its applications in various contexts.

A graph is a visual representation of a function or a set of data in the Cartesian coordinate system. It helps in understanding the behavior of the function or the trend in the data. The horizontal axis is usually denoted as x-axis and the vertical axis as y-axis.