Section 2.5 Introduction to Relations 183 Introduction to Relations Section 2.5 1. Definition of a Relation In many naturally occurring phenomena, two variables may be linked by some other type of relationship.Table 2-3 shows a correspondence between the length of a woman’s femur and her height. (The femur is the large bone in the thigh attached to the knee and hip.) Concepts 1. Definition of a Relation 2. Domain and Range of a Relation 3. Applications Involving Relations Table 2-3 Length of Height Femur (cm) (in.) Ordered Pair x y 45.5 65.5 (45.5, 65.5) 48.2 68.0 (48.2, 68.0) 41.8 62.2 (41.8, 62.2) 46.0 66.0 (46.0, 66.0) 50.4 70.0 (50.4, 70.0) Each data point from Table 2-3 may be represented as an ordered pair. In this case, the first value represents the length of a woman’s femur and the second, the woman’s height. The set of ordered pairs {(45.5, 65.5), (48.2, 68.0), (41.8, 62.2), (46.0, 66.0), (50.4, 70.0)} defines a relation between femur length and height. 2. Domain and Range of a Relation Definition of a Relation in x and y A set of ordered pairs (x,y) is called a relation in x and y. Furthermore, • The set of first components in the ordered pairs is called the domain of the relation. • The set of second components in the ordered pairs is called the range of the relation. Finding the Domain and Range of a Relation Find the domain and range of the relation linking the length of a woman’s femur to her height {(45.5, 65.5), (48.2, 68.0), (41.8, 62.2), (46.0, 66.0), (50.4, 70.0)}. Solution: Domain: {45.5, 48.2, 41.8, 46.0, 50.4} Set of first components Range: {65.5, 68.0, 62.2, 66.0, 70.0} Set of second components Skill Practice Find the domain and range of the relation. 1. e 10, 02, 18, 42, a1 2 , 1b, 13, 42, 18, 02 f Example 1 The x and y components that constitute the ordered pairs in a relation do not need to be numerical.This is demonstrated in Example 2. Answer 1. Domain: e 0, 8, ; range: 50, 4, 16 1 2 , 3 f
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