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1.7 Represent Functions as Rules and Tables

8-30-13. 1.7 Represent Functions as Rules and Tables. Warm-up:. 1 . Write an expression: 7 more than a number x. 2 . Determine if 3 is a solution of 2x – 4 =2. . Tom spent $4 more than twice as much as Casey at a store. If Casey spent $6, how much did Tom spend?.

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1.7 Represent Functions as Rules and Tables

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  1. 8-30-13 1.7 Represent Functions as Rules and Tables Warm-up: 1. Write an expression: 7 more than a number x. 2. Determine if 3 is a solution of 2x – 4 =2. Tom spent $4 more than twice as much as Casey at a store. If Casey spent $6, how much did Tom spend? Essential Question: How do you represent functions as rules and tables? 4. 5. 6. 7.

  2. A relation is a set of ordered pairs. The domain is the set of all x values in the relation domain = {-1,0,2,4,9} These are the x values written in a set from smallest to largest This is a relation {(2,3), (-1,5), (4,-2), (9,9), (0,-6)} {(2,3), (-1,5), (4,-2), (9,9), (0,-6)} {(2,3), (-1,5), (4,-2), (9,9), (0,-6)} These are the y values written in a set from smallest to largest range = {-6,-2,3,5,9} The rangeis the set of all y values in the relation

  3. Functions • A functionconsists of: • A set called the domaincontaining numbers called inputs, and a set called the range containing numbers called outputs. • A pairing of inputs with outputs such that each input is paired with exactly one output.

  4. 10 Input gallons 12 13 17 Output dollars 19.99 23.99 25.99 33.98 ANSWER The domain is the set of inputs: 10, 12, 13, range is the set of outputs: and17. The 19.99, 23.99, 25.99,and 33.98. EXAMPLE 1 Identify the domain and range of a function 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.

  5. ANSWER domain:0, 1, 2, and 4range:1, 2, and 5 for Example 1 GUIDED PRACTICE 1. Identify the domain and range of the function.

  6. EXAMPLE 2 Identify a function Tell whether the pairing is a function. a. The pairing is not a function because the input 0ispaired with both 2 and 3.

  7. Output Input 0 0 1 2 8 4 6 12 EXAMPLE 2 Identify a function b. The pairing is a function because each input is pairedwith exactly one output.

  8. 2. Input 3 6 9 12 Output 1 2 2 1 ANSWER function for Example 2 GUIDED PRACTICE Tell whether the pairing is a function.

  9. 3. Input 2 2 4 7 Output 0 1 2 3 ANSWER not a function for Example 2 GUIDED PRACTICE Tell whether the pairing is a function.

  10. Function Rules • A function may be represented using a rule that relates one variable to another. The input variable is called the independent variable. • The output variable is called the dependent variable because its value depends on the value of the input variable.

  11. x 0 2 5 7 8 y 7 8 = 2x 2 14 2 16 2 0 2 2 10 0 2 5 4 = = = = = EXAMPLE 3 Make a table for a function The domain of the function y = 2x 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.

  12. Input 0 4 6 10 1 6 Output 8 12 2 3 Let x be the input, or independent variable, and let y be the output, or dependent variable. Notice that each corresponding input. output is 2 more than the So, a + rule for the function isy x 2. = EXAMPLE 4 Write a function rule Write a rule for the function. SOLUTION

  13. EXAMPLE 5 Write a function rule for a real-world situation 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.

  14. Amount spent(dollars) Tickets purchased (tickets) Cost per ticket (dollars/ticket) • = 15 n A = EXAMPLE 5 Write a function rule for a real-world situation SOLUTION Write a verbal model. Then write a function rule. Let nrepresent the number of tickets purchased and Arepresent the amount spent (in dollars). So, the function rule is A =15n. The amount spent depends on the number of tickets bought, so nis the independent variable and Ais the dependent variable.

  15. Number of tickets, n 0 1 2 3 4 5 6 60 75 90 Amount (dollars), A 15 30 45 0 EXAMPLE 5 Write a function rule for a real-world situation 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.

  16. ANSWER range: 5, 7, 10, 13 and 24. for Examples 3,4 and 5 GUIDED PRACTICE 4. Make a table for the function y = x – 5 with domain 10, 12, 15, 18, and 29. Then identify the range of the function.

  17. Time (hours) 1 2 3 4 Pay (dollars) 8 16 24 32 ANSWER y = 8x; domain: 1, 2, 3, and 4; range: 8, 16, 24, and 32. for Examples 3,4 and 5 GUIDED PRACTICE 5. Write a rule for the function. Identify the domain and the range.

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