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Represent Functions as Rules and Tables Warm Up Lesson

This lesson introduces the concept of representing functions as rules and tables. It covers topics such as determining if a number is a solution, finding the domain and range, and writing rules for functions.

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Represent Functions as Rules and Tables Warm Up Lesson

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

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

  3. ANSWER The domain is the set of inputs: 10, 12, 13, and17. The range is the set of outputs: 42.99, 51.59, 55.89,and 73.08. 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.

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

  5. Example 2 Tell whether the pairing is a function. a. The pairing is not a function because the input 0ispaired with both 2 and 3.

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

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

  8. Example 3 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.

  9. ANSWER 10 12 15 18 x 5 7 10 24 y = x – 5 range: 5, 7, 10, 13 and 24. 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.

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

  11. 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.

  12. Example 5 SOLUTION Write a verbal model. Then write a function rule. Let nrepresent the number of tickets purchased and Arepresent the amount spent (in dollars). A = 4  n 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.

  13. 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.

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

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

  16. y = 1.5x ANSWER 2. Write a rule for the function. Lesson Quiz

  17. 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. p = 8b; range: 40, 80, 120, 160, 200 ANSWER Lesson Quiz

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