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B. Domain and Range of Relations

The values by which a relation is defined are categorized into two groups: domain and range. The domain is the set of input values (the x-values) and the range is the set of output values (the y-values) that define a particular relation.

Domain
the set of all possible input values (x-values) of a relation

Range
the set of all possible output values (y-values) of a relation

Set
a collection of distinct objects, where each object is referred to as an element of the set


Refer to the following Example 1 relation of the speed of a snowboarder to explain the domain and range in words.

Example 1

A graph representing the speed of a snowboarder is shown. State the domain and range of the relation.

The domain of the relation represented in the graph is the set of time values for which the relation is defined. The relation is defined for all time values starting at 0 s and ending at 16 s. As such, the domain of the relation is from 0 s to 16 s.

The range of the same relation is the set of speed values for which the relation is defined. The relation is defined for all speed values starting at 0 m/s and ending at 55 m/s. As such, the range of the relation is from 0 m/s to 55 m/s.