Concept

Range

The range of a function is the set of all y-values, called outputs, of the function. The range depends on both the domain and the function itself. For example, consider the following functions and their defined domains.

Function	Domain
f(x)=2x	All integers
g(x)=x^2	All real numbers
h(x)=4	All real numbers

The ranges of each function can be determined by analyzing the definition of each function along with the given domains.

Function	Domain	Analysis	Range
f(x) = 2x	All integers	The function takes any integer input and produces an output that is an even number, as each input is multiplied by 2.	All even numbers
g(x) = x^2	All real numbers	The function takes any real number input and produces an output that is a non-negative number, as each input is squared.	All non-negative numbers. That is, y≥ 0
h(x) = 4	All real numbers	The function takes any real number input and sends it to 4.	Only the number 4. That is, the range is {4}

The method used to determine the range of a function can vary depending on how that function is represented.

Graph in the coordinate plane, table of values, set of coordinate pairs, and mapping diagram

If more than one input have the same output, that output only needs to be written once in the range.