1. 5 Minute Check Complete in your notebook. Fill in with, or = to make the inequality true. 1. 302, 788 203,788 2. 892,341 892,431 Solve. 3. x + 44 = 90 4. 16m = 48

2. 5 Minute Check Fill in with, or = to make the inequality true. 1. 302, 788 203,788

3. 5 Minute Check Fill in with, or = to make the inequality true. 1. 302, 788 > 203,788

4. 5 Minute Check Fill in with, or = to make the inequality true. 2. 892,341 892,431

5. 5 Minute Check Fill in with, or = to make the inequality true. 2. 892,341 < 892,431

6. 5 Minute Check Solve. 3. x + 44 = 90

7. 5 Minute Check Solve. 3. x + 44 = 90 -44 = -44 x + 0 = 46

8. 5 Minute Check Solve. 4. 16m = 48

9. 5 Minute Check Solve. 4. 16m = 48 16m 48 16 = 16 m = 3

10. Thursday, Nov 20 Chapter 6.8.1/6.8.2 Function Tables & Function Rules

11. Function Tables Objective: Complete function tables and find function rules.

12. Function Tables A function is a relation that assigns exactly one output value to one input value.

13. Function Tables A function is a relation that assigns exactly one output value to one input value. Think of a function as an algebraic expression with one variable (x).

14. Function Tables A function rule describes the relationship between each input and output.

15. Function Tables A Function Rule is like a machine that has an input and an output. And the output is related somehow to the input.

16. Function Tables A table that contains an input, output and function rule is called a function table. function rule

17. Function Tables The input (x) values can be inserted into the function rule.

18. Function Tables The output (y) values can be inserted into the determined by simplifying function rule.

19. Function Tables Since the Function Rule is an expression that describes how the x value goes to the y value, it will only have an x variable.

20. Function Tables The input (x) value is also known as the independent variable. (The input value can be any number)

21. Function Tables The output (y) value is also known as the dependent variable. (The output value depends on the input value)

22. Function Tables Complete the function table. Do this on your own.

23. Function Tables Complete the function table.

24. Function Tables Sometimes the function table has the output values and the function rule, and the input values need to be determined. We can do this by applying the inverse operation of the function rule.

25. Function Tables Complete the function table. What is the inverse operation of the function rule?

26. Function Tables Complete the function table. What is the inverse operation of the function rule? Division. 2 5 7

27. Function Tables Complete the function table. We can complete the middle column by substituting the number in for the variable (x). 3(2) 3(5) 3(7) 2 5 7

28. Function Tables If there are two operations in the function rule, we apply the inverse operations in the reverse order of operations. i.e apply the inverse of subtraction, before the inverse of multiplication. 5 7

29. Function Tables Complete the function table. What operations do we have? 3(2) 3(5) 3(7) 2 5 7

30. Function Tables Complete the function table. 3(2) 3(5) 3(7) 2 5 7 (1 + 1) ÷ 2 = 1

31. Function Tables Complete the function table. 3(2) 3(5) 3(7) 2 5 7 1 2(1) - 1 (3 + 1) ÷ 2 = 2

32. Function Tables Complete the function table. 3(2) 3(5) 3(7) 2 5 7 1 2(1) - 1 2 2(2) - 1 (5 + 1) ÷ 2 = 3

33. Function Tables Complete the function table. 3(2) 3(5) 3(7) 2 5 7 1 2(1) - 1 2 2(2) - 1 3 2(3) - 1

34. Function Tables Complete the function table. Do this on your own. 3(2) 3(5) 3(7) 2 5 7 1 2(1) - 1 2 2(2) - 1 3 2(3) - 1

35. Function Tables Complete the function table. Do this on your own. 3(2) 3(5) 3(7) 2 5 7 1 2(1) - 1 2 2(2) - 1 3 2(3) - 1

36. Function Tables The Gomez family is traveling at a rate of 70 miles per hour. The function rule that represents this is 70x, where x is the number of hours. Make a table to find out how many hours they have driven at 140 miles, 280 miles and 350 miles. Do this on your own.

37. Function Tables The Gomez family is traveling at a rate of 70 miles per hour. The function rule that represents this is 70x, where x is the number of hours. Make a table to find out how many hours they have driven at 140 miles, 280 miles and 350 miles.

38. Function Tables The Gomez family is traveling at a rate of 70 miles per hour. The function rule that represents this is 70x, where x is the number of hours. Make a table to find out how many hours they have driven at 140 miles, 280 miles and 350 miles. Using the x and y values as ordered pairs a graph can be constructed.

39. Function Tables The Gomez family is traveling at a rate of 70 miles per hour. The function rule that represents this is 70x, where x is the number of hours. Make a table to find out how many hours they have driven at 140 miles, 280 miles and 350 miles.

40. Function Rules A sequence is a list of numbers in a specific order.

41. Function Rules Arithmetic sequences can be found by adding or subtracting the same number to the previous term. i.e. ; 2, 4, 6, 8, 10…….

42. Function Rules Geometric sequences can be found by multiplying or dividing the previous term by the same number. i.e. 1, 3, 9, 27……….

43. Function Rules We can determine if a sequence is arithmetic or geometric by finding the difference between terms.

44. Function Rules State whether the sequence is arithmetic or geometric, then find the next two terms in the sequence. 0.75, 1.75, 2.75, 3.75……

45. Function Rules State whether the sequence is arithmetic or geometric, then find the next two terms in the sequence. 0.75, 1.75, 2.75, 3.75…… 1 1 1 Since the difference between the terms is the same, it is arithmetic. The next term will be 1 + 3.75= 4.75 Then 1 + 4.75= 5.75

46. Function Rules State whether the sequence is arithmetic or geometric, then find the next two terms in the sequence. 1, 6, 36, 216……

47. Function Rules State whether the sequence is arithmetic or geometric, then find the next two terms in the sequence. 1, 6, 36, 216…… 5 30 180 Since the difference between the terms is increasing, it is geometric. The next term will be 6 x 216 = 1,296 Then 6 x 1296 = 7,776

48. Function Rules We can write a sequence on a function table with the value of the term being the output and the position of the number being the input. The position (n) is just the number of the term in order in the sequence. i.e. n = 8, mean the 8 th term of the sequence.

49. Function Rules Describe the pattern and state whether the sequence an arithmetic or geometric sequence. The position is just the number of term in the sequence.

50. Function Rules Describe the pattern and state whether the sequence an arithmetic or geometric sequence. How do we get from the position to the value of term?

51. Function Rules Describe the pattern and state whether the sequence an arithmetic or geometric sequence. Either position # - 4 or position # ÷ 3

52. Function Rules Describe the pattern and state whether the sequence an arithmetic or geometric sequence. Either position # - 4 or position # ÷ 3 Which one works for the 2 nd set of numbers?

53. Function Rules Describe the pattern and state whether the sequence an arithmetic or geometric sequence. The pattern is the position # - 4 Is this arithmetic or geometric?

54. Function Rules Describe the pattern and state whether the sequence an arithmetic or geometric sequence. The pattern is the position # - 4 It is arithmetic since it uses addition or subtraction.

55. Function Rules Describe the pattern and state whether the sequence an arithmetic or geometric sequence. Do this on your own.

56. Function Rules Describe the pattern and state whether the sequence an arithmetic or geometric sequence. The pattern is the position # ·5 It is geometric since it uses multiplication or division.

57. Function Rules Describe the pattern and state whether the sequence an arithmetic or geometric sequence. We can use n to represent the position, so the pattern can be described as 5n. 5n is the function rule for this table.

58. Function Rules Describe the pattern and state whether the sequence an arithmetic or geometric sequence. What would be the value for the 10 th term? (when n = 10)

59. Function Rules Describe the pattern and state whether the sequence an arithmetic or geometric sequence. What would be the value for the 10 th term? 5n, n = 10; 5·10 = 50

60. Function Rules Find the function rule and state whether the sequence an arithmetic or geometric sequence. Do this on your own.

61. Function Rules Find the function rule and state whether the sequence an arithmetic or geometric sequence. The function rule is 8n, and it is geometric.

62. Function Rules Find the function rule and state whether the sequence an arithmetic or geometric sequence. The function rule is 8n, and it is geometric. What is the value for the 8 th term?

63. Function Rules Find the function rule and state whether the sequence an arithmetic or geometric sequence. The function rule is 8n, and it is geometric. What is the value for the 8 th term? 8n, n = 8; 8·8 = 64

64. Function Rules Find the function rule and determine the value for the 10 th term. Do this on your own.

65. Function Rules Find the function rule and determine the value for the 10 th term. n + 4 n = 10, 10 + 4 = 14

66. Function Rules Find the function rule and determine the value for the 12 th term. Do this on your own.

67. Function Rules Find the function rule and determine the value for the 12 th term. 3n n = 12, 3 · 12 = 36

68. Function Rules Find the function rule and determine the value for the 10 th term. Do this on your own.

69. Function Rules Find the function rule and determine the value for the 10 th term. 6n, n = 10, 6 · 10 = 60

70. Function Rules Find the function rule and determine the value for the 15 th term. Do this on your own.

71. Function Rules Find the function rule and determine the value for the 15 th term. n + 2, n = 15, 15 + 2 = 17

72. Function Rules Find the function rule and determine the value for the 9 th term. Do this on your own.

73. Function Rules Find the function rule and determine the value for the 9 th term. 2n, n = 9, 2 · 9 = 18

74. Function Rules The table at the right shows the fee for overdue books at a library, based on the number of weeks the book is overdue. Write a function rule to find the fee for a book that is x weeks overdue. Do this on your own.

75. Function Rules The table at the right shows the fee for overdue books at a library, based on the number of weeks the book is overdue. Write a function rule to find the fee for a book that is x weeks overdue. Notice the fee values increase by 2, this means it is multiplied by 2. (but that is not all the function rule) increase

76. Function Rules The table at the right shows the fee for overdue books at a library, based on the number of weeks the book is overdue. Write a function rule to find the fee for a book that is x weeks overdue. 2x + 1

77. Function Rules The table shows the number of necklaces that Ari can make, based on the number of hours she works. Write a function rule to find the number of necklaces she can make in x hours. Do this on your own.

78. Function Rules The table shows the number of necklaces that Ari can make, based on the number of hours she works. Write a function rule to find the number of necklaces she can make in x hours. 2x + 3

79. Function Tables Isaiah is buying jelly beans. In bulk, they cost $3 per pound, and a candy dish costs $2. The function rule, 3x + 2 where x is the number of pounds, can be used to find the total cost of x pounds of jelly beans and 1 dish. Make a table that shows the total cost of buying 2, 3, and 4 pounds of jelly beans and 1 dish. Do this on your own.

80. Function Tables Isaiah is buying jelly beans. In bulk, they cost $3 per pound, and a candy dish costs $2. The function rule, 3x + 2 where x is the number of pounds, can be used to find the total cost of x pounds of jelly beans and 1 dish. Make a table that shows the total cost of buying 2, 3, and 4 pounds of jelly beans and 1 dish..

81. Function Rules Find the function rule and determine the value for the 10 th term.

82. Function Rules Find the function rule and determine the value for the 10 th term. n²; n = 10; 10² = 100

83. Function Tables u Explain how to find the input given the function rule and output.

84. Function Tables u Explain how to find the input given the function rule and output. To find the input, work backwards by performing the reverse of the operation.

85. Function Tables Agenda Notes Homework – Homework Practice 6.8.1 – Questions 1, 2, 5 & 8 Homework Practice 6.8.2- All Questions Due Friday, Nov 21 Mid-Chapter 6.8 Quiz – Tuesday, Nov 25