Longevity Writing a Relation and Finding Its Domain and Range Animal (Years) x y Bear 22.5 Cat 11 Cow 20.5 Deer 12.5 Dog 11 Elephant 35 Example 2 Table 2-4 gives five states in the United States and the corresponding number of representatives in the House of Representatives for a recent year. a. The data in the table define a relation. Write a list of ordered pairs for this relation. b. Write the domain and range. Answers 2. {(Bear, 22.5), (Cat, 11), (Cow, 20.5), (Deer, 12.5), (Dog, 11), (Elephant, 35)} 3. Domain: {Bear, Cat, Cow, Deer, Dog, Elephant}; range: {22.5, 11, 20.5, 12.5, 35} Number of Table 2-4 State Representatives x y Alabama 7 California 53 Colorado 7 Florida 25 Kansas 4 Solution: a. {(Alabama, 7), (California, 53), (Colorado, 7), (Florida, 25), (Kansas, 4)} b. Domain: {Alabama, California, Colorado, Florida, Kansas} Range: {7, 53, 25, 4} (Note: The element 7 is not listed twice.) Skill Practice The table depicts six types of animals and their average longevity. 2. Write the ordered pairs indicated by the relation in the table. 3. Find the domain and range of the relation. A relation may consist of a finite number of ordered pairs or an infinite number of ordered pairs. Furthermore, a relation may be defined by several different methods. • A relation may be defined as a set of ordered pairs. {(1, 2), (3, 4), (1, 4), (3, 4)} • A relation may be defined by a correspondence (Figure 2-28). The corresponding ordered pairs are {(1, 2), (1, 4), (3, 4), (3, 4)}. x y 1 3 3 2 4 4 Domain Range Figure 2-28 • A relation may be defined by a graph (Figure 2-29). The corresponding ordered pairs are {(1, 2), (3, 4), (1, 4), (3, 4)}. y x (3, 4) (1, 2) (3, 4) (1, 4) 54321 5 4 3 1 1 2 3 4 5 1 2 3 4 5 2 Figure 2-29 184 Chapter 2 Linear Equations in Two Variables and Functions
miller_intermediate_algebra_4e_ch1_3
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