What Is Domain and Range Interval Notation?

By Staff WriterLast Updated Mar 29, 2020 11:42:02 PM ET

Interval notation is a method used to write the domain and range of a function. In interval notation, there are five basic symbols to be familiar with: open parentheses (), closed parentheses [], infinity (imagine an 8 sideways), negative infinity (an 8 sideways with a negative sign in front of it) and union (a symbol similar to an elongated U).


The open parentheses indicate that the value immediately to the parentheses' left or right is not included in the domain or range. A closed parentheses indicates that the value is included in the function's domain or range. The infinity signs, either positive or negative, indicate that the function does not have an upper or lower limit or both. The union sign indicates that there is a break in the functions domain and range.

An example of a function's domain in interval notation is (3,4]. Here, 3 is not included and is the function's lower limit, and 4 is included and is the functions upper limit. An example of a range with a union is [-3,2)U(5,9). In this function, -3 is included, as demonstrated by the use of the closed parenthesis, and 2 is not. Moreover, there is a break in the functions range, and the values between 2 and 5 are not included. Since the function has a range that includes the values between 5 and 9, a union sign must be used to tie the upper and lower limits while not including the values that do not fit the function.