Domain Definition

noun
  • mathematics
    the set of all possible input values for which the function is defined.

Explanation

The domain of a function is the set of all possible input values for which the function is defined. For example, the domain of the function is all non-negative real numbers, because the square root is not defined for negative numbers in the real number system.

Domain of square root function.

The domain of a function is often represented using interval notation or set notation. For instance, the domain of the function can be represented as or .

Related Terms

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.

An interval is a set of real numbers that lies between two given numbers. The two numbers that define the interval are often called the endpoints. Intervals can be open (not including the endpoints), closed (including the endpoints), or a mix of both.

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.