1. 1.7 Represent Functions as Rules and Tables Essential Question: How do you represent functions as rules and tables? 8-26-15 Warm-up: 1. Write an expression: 7 more than a number x. 2. Determine if 3 is a solution of 2x – 4 =2. 3.Tom spent $4 more than twice as much as Casey at a store. If Casey spent $6, how much did Tom spend? 4.4. 5. 6.7.7. SCCCR Standards 8.F.1 Explore the concept of functions a-e.

2. A relation is a set of ordered pairs. {(2,3), (-1,5), (4,-2), (9,9), (0,-6)} This is a relation The domain is the set of all x values in the relation {(2,3), (-1,5), (4,-2), (9,9), (0,-6)} The range is the set of all y values in the relation {(2,3), (-1,5), (4,-2), (9,9), (0,-6)} domain = {-1,0,2,4,9} These are the x values written in a set from smallest to largest range = {-6,-2,3,5,9} These are the y values written in a set from smallest to largest Essential Question: How do you represent functions as rules and tables?

3. Functions A function consists of: A set called the domain containing 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. SCCCR Standards 8.F.1 Explore the concept of functions a-e.

4. Identify the domain and range of a function 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 19.99, 23.99, 25.99, and 33.98. The domain is the set of inputs: 10, 12, 13, and 17. The range is the set of outputs: 10 Input gallons Output dollars 121317 19.9923.9925.9933.98 Essential Question: How do you represent functions as rules and tables?

5. GUIDED PRACTICE for Example 1 1. Identify the domain and range of the function. Input 0124 Output 5221 domain: 0, 1, 2, and 4 range: 1, 2, and 5 ANSWER Essential Question: How do you represent functions as rules and tables? SCCCR Standards 8.F.1 Explore the concept of functions a-e.

6. Tell whether the pairing is a function. Identify a function EXAMPLE 2 a. a. The pairing is not a function because the input 0 is paired with both 2 and 3. Essential Question: How do you represent functions as rules and tables? SCCCR Standards 8.F.1 Explore the concept of functions a-e.

7. b.b. Identify a function EXAMPLE 2 Output Input 2 1 0 0 4 8 6 12 The pairing is a function because each input is paired with exactly one output. Essential Question: How do you represent functions as rules and tables? SCCCR Standards 8.F.1 Explore the concept of functions a-e.

8. GUIDED PRACTICE for Example 2 Tell whether the pairing is a function. 1221 Output 12963 Input 2. ANSWER function Essential Question: How do you represent functions as rules and tables? SCCCR Standards 8.F.1 Explore the concept of functions a-e.

9. GUIDED PRACTICE for Example 2 Tell whether the pairing is a function. 3210 Output 7422 Input 3. ANSWER not a function Essential Question: How do you represent functions as rules and tables? SCCCR Standards 8.F.1 Explore the concept of functions a-e.

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. Essential Question: How do you represent functions as rules and tables? SCCCR Standards 8.F.1 Explore the concept of functions a-e.

11. The range of the function is 0, 4, 10, 14, and 16. Make a table for a function 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. x y 25 7 0 8 = 2x 2 2 = 4 2 5 = 10 2 7 = 142 8 = 16 2 0 = 0 SOLUTION Essential Question: How do you represent functions as rules and tables? SCCCR Standards 8.F.1 Explore the concept of functions a-e.

12. Write a function rule EXAMPLE 4 Write a rule for the function. Input Output 2 1 6 12 3 4 8 6010 SOLUTION and let y or dependent variable. Notice that eachbe the output, Let x be the input, or independent variable, output is 2 more than the corresponding input. So, a rule for the function is y = x + 2. Essential Question: How do you represent functions as rules and tables? SCCCR Standards 8.F.1 Explore the concept of functions a-e.

13. Write a function rule for a real-world situation 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. Essential Question: How do you represent functions as rules and tables? SCCCR Standards 8.F.1 Explore the concept of functions a-e.

14. Write a function rule for a real-world situation EXAMPLE 5 SOLUTION So, the function rule is A = 15n. The amount spent depends on the number of tickets bought, so n is the independent variable and A is the dependent variable. 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 15 n = Amount spent (dollars) Cost per ticket (dollars/ticket) Tickets purchased (tickets) = Essential Question: How do you represent functions as rules and tables? SCCCR Standards 8.F.1 Explore the concept of functions a-e.

15. Write a function rule for a real-world situation 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. Amount (dollars), A 0132 654 0 154530 756090 Number of tickets, n The range of the function is 0, 15, 30, 45, 60, 75, and 90. Essential Question: How do you represent functions as rules and tables? SCCCR Standards 8.F.1 Explore the concept of functions a-e.

16. GUIDED PRACTICE for Examples 3,4 and 5 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. range: 5, 7, 10, 13 and 24. ANSWER Essential Question: How do you represent functions as rules and tables? SCCCR Standards 8.F.1 Explore the concept of functions a-e.

17. GUIDED PRACTICE for Examples 3,4 and 5 5. Write a rule for the function. Identify the domain and the range. Pay (dollars) 1243 8163224 Time (hours) y = 8x ; domain: 1, 2, 3, and 4 ; range: 8, 16, 24, and 32. ANSWER Essential Question: How do you represent functions as rules and tables? SCCCR Standards 8.F.1 Explore the concept of functions a-e.

18. Classwork/Homework 1.7 Exercises Pages 44-46 1-29 all Essential Question: How do you represent functions as rules and tables? SCCCR Standards 8.F.1 Explore the concept of functions a-e.