b) The domain is {2, 0, 1, 4, 5}. The range is e6, 5, 9 2 , 3, 5 2 f . Ask yourself, “Does every fi rst coordinate correspond to exactly one second coordinate?” Yes. This relation is a function. c) The domain is {Omaha, Springfi eld, Houston}. The range is {Nebraska, Illinois, Missouri, Texas}. One of the elements in the domain, Springfi eld, corresponds to two elements in the range, Illinois and Missouri. Therefore, this relation is not a function. YOU TRY 1 Identify the domain and range of each relation, and determine whether each relation is a function. a) {(1, 3), (1, 1), (2, 3), (4, 7)} b) {(12, 6), (12, 6), (1, 13), (0, 0)} c) Daisy Tulip Dog Oak Flower Animal Tree We stated earlier that a relation is a function if each element of the domain corresponds to exactly one element of the range. If the ordered pairs of a relation are such that the fi rst coordinates represent x-values and the second coordinates represent y-values (the ordered pairs are in the form (x, y)), then we can think of the defi nition of a function in this way: Definition A relation is a function if each x-value corresponds to exactly one y-value. What does a function look like when it is graphed? Following are the graphs of the ordered pairs in the relations of Example 1a) and 1b). (6, 2) x y 6 (2, 0) (3, 1) 6 6 6 (6, 2) x y 6 6 6 (0, 5) 6 (4, 3) (2, 6) (1, ) 92 (5, ) 52 Example 1a) Example 1b) not a function is a function www.mhhe.com/messersmith SECTION 4.5 Introduction to Functions 199
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