Relations and Functions

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Relations and Functions ALGEBRA 1 LESSON 5-2 Find the domain and the range of the ordered pairs. age weight 14 120 12 110 18 126 14 125 16 124 domain: {12, 14, 16, 18} List the values in order. Do not repeat values. range: {110, 120, 124, 125, 126} 5-2

Relations and Functions ALGEBRA 1 LESSON 5-2 Determine whether each relation is a function. a. {(4, 3), (2, –1), (–3, –3), (2, 4)} The domain value 2 corresponds to two range values, –1 and 4. The relation is not a function. b. {(–4, 0), (2, 12), (–1, –3), (1, 5)} There is no value in the domain that corresponds to more than one value of the range. The relation is a function. 5-2

Relations and Functions ALGEBRA 1 LESSON 5-2 a. Evaluate ƒ(x) = –5x + 25 for x = –2. ƒ(x) = –5x + 25 ƒ(–2) = –5(–2) + 25 Substitute –2 for x. ƒ(–2) = 10 + 25 Simplify. ƒ(–2) = 35 b. Evaluate y = 4x2 + 2 for x = 3. y = 4x2 + 2 y = 4(3)2 + 2 Substitute 3 for x. y = 4(9) + 2 Simplify the powers first. y = 36 + 2 Simplify. y = 38 5-2

Relations and Functions ALGEBRA 1 LESSON 5-2 Evaluate the function rule ƒ(g) = –2g + 4 to find the range for the domain {–1, 3, 5}. ƒ(g) = –2g + 4 ƒ(–1) = –2(–1) + 4 ƒ(–1) = 2 + 4 ƒ(–1) = 6 ƒ(g) = –2g + 4 ƒ(3) = –2(3) + 4 ƒ(3) = –6 + 4 ƒ(3) = –2 ƒ(g) = –2g + 4 ƒ(5) = –2(5) + 4 ƒ(5) = –10 + 4 ƒ(5) = –6 The range is {–6, –2, 6}. 5-2

Relations and Functions ALGEBRA 1 LESSON 5-2 1. a. Find the domain and range of the ordered pairs (1, 3), (–4, 0), (3, 1), (0, 4), (2, 3). b. Use mapping to determine whether the relation is a function. domain: {–4, 0, 1, 2, 3} range: {0, 1, 3, 4} The relation is a function. 2. Find the range of the function ƒ(g) = 3g – 5 for the domain {–1.5, 2, 4}. {–9.5, 1, 7} 5-2