Problem 109 - Precalculus Essentials

Question

What is a relation? Describe what is meant by its domain and its range.

Step-by-Step Solution

Answer

A relation is a set of ordered pairs and shows the relationship between the components of the pairs. The domain is the set of all 'x' values in the pairs while the range is the set of all 'y' values in those pairs.

Step 1: Definition of Relation

A relation in mathematics can be defined as a set of ordered pairs \((x, y)\). This means anytime you have a set of pairs where the 'x' value from one pair matches the 'x' value from another pair, and the 'y' value from one pair matches the 'y' value from another pair, you have a relation. This ordered pair \((x, y)\) usually indicates that there is some relationship between 'x' and 'y', hence the term 'relation'.

Step 2: Explaining Domain

The domain of a relation is the set of all 'x' values or inputs of the ordered pairs. In simpler terms, it can be defined as the set of all possible values that the independent variable, usually 'x', can take within the given context. For instance, if a relation consists of the ordered pairs \((2, 3)\), \((5, 6)\), and \((4, 7)\), the domain would be the set \{2, 5, 4\}.

Step 3: Explaining Range

The range of a relation is the set of all 'y' values or outputs of the ordered pairs. It's the set of all potential values that the dependent variable, often 'y', can take within the provided context. For example, if a relation comprises the ordered pairs \((2, 3)\), \((5, 6)\), and \((4, 7)\), the range would be the set \{3, 6, 7\}.