4.1.2 Relations and Functions Key Objectives • Show multiple representations of relations • Find the domain and range of relations. • Determine whether relations are functions. Key Terms • A relation is a set of ordered pairs.
• The domain is the set of all possible x -values (inputs) of a relation or function. • The range is the set of all possible y -values (outputs) of a relation or function. • A function is a relation where each x -value is associated with a single y -value. Example 1 Showing Multiple Representations of Relations In Example 1, Prof. Burger represents a relation (a list of ordered pairs) as a table, a mapping diagram, and a graph. Recall that in an ordered pair ( x , y ) the first value is the x -value (or x -coordinate), and the second value is the y -value (or y -coordinate). To represent the relation as a table, make a table with 2 columns. Write x as the first column’s header, and write y as the second column’s header. Then list the x -value from each ordered pair under x , and list the y -value from each ordered pair under y . Note that each row in the table represents one of the ordered pairs in the relation. To represent the relation as a mapping diagram, make a vertical list of the x -values from the ordered pairs, and then do the same with the y -values. Then, draw an arrow from each x -value to its corresponding y - value. To represent the relation as a graph, plot each ordered pair as a point on a coordinate plane.
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