1 6 Represent Functions as Rules and Tables

1. 6 Represent Functions as Rules and Tables Warm Up Lesson Presentation Lesson Quiz

1. 6 Warm-Up 1. Write an expression: 7 more than a number x. ANSWER x+7 2. Determine if 3 is a solution of 2 x – 4 = 2. ANSWER 2 = 2; 3 is a solution. 3. Gae spent $4 more than twice as much as Casey at a store. If Casey spent $6, how much did Gae spend? ANSWER $16

1. 6 Example 1 The input-output table shows the cost of various amounts of regular unleaded gas from the same pump. Identify the domain and range of the function. ANSWER The domain is the set of inputs: 10, 12, 13, range is the set of outputs: and 17. The 42. 99, 51. 59, 55. 89, and 73. 08.

1. 6 Guided Practice Identify the domain and range of the function. ANSWER domain: 0, 1, 2, and 4 range: 1, 2, and 5

1. 6 Example 2 Tell whether the pairing is a function. a. The pairing is not a function because the input 0 is paired with both 2 and 3.

1. 6 Example 2 b. The pairing is a function because each input is paired with exactly one output.

1. 6 Guided Practice Tell whether the pairing is a function. 2. ANSWER function 3. ANSWER not a function

1. 6 Example 3 The domain of the function y = 2 x is 0, 2, 5, 7, and 8. Make a table for the function, then identify the range of the function. SOLUTION The range of the function is 0, 4, 10, 14, and 16.

1. 6 4. Guided Practice Make a table for the function y = x – 5 with domain 10, 12, 15, 18, and 29. Then identify the range of the function. ANSWER x y=x– 5 10 12 15 18 5 7 10 24 range: 5, 7, 10, 13 and 24.

1. 6 Example 4 Write a rule for the function. SOLUTION Let x be the input, or independent variable, and let y be the output, or dependent variable. Notice that each output is 2 more than the corresponding input. So, a rule for the function is y = x + 2.

1. 6 Example 5 Concert Tickets You are buying concert tickets that cost $15 each. You can buy up to 6 tickets. Write the amount (in dollars) you spend as a function of the number of tickets you buy. Identify the independent and dependent variables. Then identify the domain and the range of the function.

1. 6 Example 5 SOLUTION Write a verbal model. Then write a function rule. Let n represent the number of tickets purchased and A represent the amount spent (in dollars). A = 4 � n So, the function rule is A = 15 n. The amount spent depends on the number of tickets bought, so n is the independent variable and A is the dependent variable.

1. 6 Example 5 Because you can buy up to 6 tickets, the domain of the function is 0, 1, 2, 3, 4, 5, and 6. Make a table to identify the range. The range of the function is 0, 15, 30, 45, 60, 75, and 90.

1. 6 5. Guided Practice Write a rule for the function. Identify the domain and the range. ANSWER y = 8 x; domain: 1, 2, 3, and 4; range: 8, 16, 24, and 32.

1. 6 Lesson Quiz 2 1. The domain of the function y = 3 x + 1 is 0, 3, 6 and 9. Make a table for the function. Identify the range of the function ANSWER range: 1, 3, 5, 7

1. 6 Lesson Quiz 2. Write a rule for the function. ANSWER y = 1. 5 x

1. 6 Lesson Quiz 3. Jasmine sells bracelets. Her profit on each bracelet is $8. Write a rule that shows her total profit p as a function of the number of bracelets b she sells. Write the range of the function if the domain is 5, 10, 15, 20, and 25. ANSWER p = 8 b; range: 40, 80, 120, 160, 200