1 Define and Identify Relation, Function, Domain, and Range If we form a set of ordered pairs from the ones listed on the previous page, we get a relation: {(10, 95.00), (15, 142.50), (22, 209.00), (30, 285.00)} Definition A relation is any set of ordered pairs. Definition The domain of a relation is the set of all values of the fi rst coordinates in the set of ordered pairs. The range of a relation is the set of all values of the second coordinates in the set of ordered pairs. The domain of the given relation is {10, 15, 22, 30}. The range of the relation is {95.00, 142.50, 209.00, 285.00}. The relation {(10, 95.00), (15, 142.50), (22, 209.00), (30, 285.00)} is also a function because every fi rst coordinate corresponds to exactly one second coordinate. A function is a very important concept in mathematics. Definition A function is a special type of relation. If each element of the domain corresponds to exactly one element of the range, then the relation is a function. Relations and functions can be represented in another way—as a correspondence or a mapping from one set, the domain, to another, the range. In this representation, the domain is the set of all values in the fi rst set, and the range is the set of all values in the second set. EXAMPLE 1 In-Class Example 1 Identify the domain and range of each relation, and determine whether each relation is a function. a) {(4, 1), (2, 1), (1, 5), (2, 8), (6, 11)} b) {(9, 3), (3, 1), (0, 0), (6, 2)} c) Mexico Italy Canada Spanish Italian English French Identify the domain and range of each relation, and determine whether each relation is a function. a) {(3, 2), (4, 0), (5, 3), (5, 3)} b) e (4, 1), (2, 0), (0, 1), a3, 5 2 b, (4, 3) f c) hicago e or San iego ears ets iants hargers 640 CHAPTER 10 Quadratic Equations www.mhhe.com/messersmith
messersmith_power_introductory_algebra_1e_ch4_7_10
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