Definition The domain of a relation is the set of all values of the independent variable (the fi rst coordinates in the set of ordered pairs). The range of a relation is the set of all values of the dependent variable (the second coordinates in the set of ordered pairs). The domain of the given relation is {1, 2, 2.5, 3}. The range of the relation is {60, 120, 150, 180}. The relation {(1, 60), (2, 120), (2.5, 150), (3, 180)} 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. Our previously stated defi nition of a function still holds. Remember that only special types of relations can be classified as functions. EXAMPLE 1 Identify the domain and range of each relation, and determine whether each relation is a function. a) {(2, 0), (3, 1), (6, 2), (6, 2)} b) e (2, 6), (0, 5), a1, 9 2 b, (4, 3), a5, 5 2 bf c) Omaha Springfield Houston Nebraska Illinois Missouri Texas Solution a) The domain is the set of fi rst coordinates, {2, 3, 6}. (We write the 6 in the set only once even though it appears in two ordered pairs.) The range is the set of second coordinates, {0, 1, 2, 2}. To determine whether or not this relation is a function ask yourself, “Does every fi rst coordinate correspond to exactly one second coordinate?” No. In the ordered pairs (6, 2) and (6, 2), the same fi rst coordinate, 6, corresponds to two different second coordinates, 2 and 2. Therefore, this relation is not a function. 198 CHAPTER 4 Linear Equations in Two Variables and Functions www.mhhe.com/messersmith
messersmith_power_intermediate_algebra_1e_ch4_7_10
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