3 Find the Domain and Range of a Relation from Its Graph EXAMPLE 3 In-Class Example 3 Identify the domain and range of each relation in In-Class Example 2. Answer: a) domain: (q, q); range: (q, q) b) domain: 4, 4; range: 4, 4 Identify the domain and range of each relation in Example 2. Solution a) The domain of this function is the set of x y 5 5 5 The range is the set of y-values on the graph. 5 The arrows on the graph indicate that the graph continues without bound. x-values on the graph. Since the graph continues indefi nitely in the x-direction, the domain is the set of all real numbers. The domain is (q, q). Since the arrows show that the graph continues indefi nitely in the y-direction, the range is the set of all real numbers or (q, q). b) The set of x-values on the graph includes all real The set of y-values on the graph includes all real x y 5 4 5 2 2 5 4 5 numbers from 2 to 2. The domain is 2, 2. numbers from 4 to 4. The range is 4, 4. Part (a) in Example 3 suggests the following point: Think about the graph of y b, where b is a real number. Is y b a function? Note A linear equation of the form y mx b is a function. Equations of the form x a are vertical lines with undefi ned slope and are not functions. YOU TRY 2 Use the vertical line test to determine whether each relation is also a function. Then, identify the domain and range. a) x y 5 5 5 5 b) x y 3 www.mhhe.com/messersmith SECTION 10.5 Introduction to Functions 643
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