Domain, Codomain, and Range of a Function

Functions and Their Components

• A function describes a relationship between input and output values.
• The domain is the set of x-values to be evaluated by a function.
• The codomain is the set of all possible y-values that could result from the evaluation of the function.
• Unless otherwise stated, the codomain of a function is assumed to be all real numbers.

Range and Function Types

• The range is the set of y-values that actually result from the evaluation of the function.
• The range is contained within the codomain.
• A function is one-to-one if each element of its range is paired with exactly one element of the domain.
• A function is onto if its codomain is the same as its range.