Slideshare uses cookies to improve functionality and performance, and to provide you with relevant advertising. If you continue browsing the site, you agree to the use of cookies on this website. See our User Agreement and Privacy Policy.

Slideshare uses cookies to improve functionality and performance, and to provide you with relevant advertising. If you continue browsing the site, you agree to the use of cookies on this website. See our Privacy Policy and User Agreement for details.

Like this presentation? Why not share!

- Int Math 2 Section 6-1 1011 by Jimbo Lamb 878 views
- Int Math 2 Section 6-6 1011 by Jimbo Lamb 696 views
- Int Math 2 Section 6-9 1011 by Jimbo Lamb 667 views
- Int Math 2 Section 6-3 1011 by Jimbo Lamb 776 views
- Int Math 2 Section 6-1 by Jimbo Lamb 890 views
- Int Math 2 Section 6-8 1011 by Jimbo Lamb 769 views

743 views

Published on

Linear and Nonlinear Functions

Published in:
Education

No Downloads

Total views

743

On SlideShare

0

From Embeds

0

Number of Embeds

336

Shares

0

Downloads

3

Comments

0

Likes

1

No embeds

No notes for slide

- 1. SECTION 6-5 Linear and Nonlinear Functions
- 2. Essential QuestionsHow do you graph linear and nonlinear functions?How do you identify the domain and range of a function?Where you’ll see this: Machinery, travel, temperature
- 3. Vocabulary1. Function:2. Function Notation:3. Domain:4. Range:5. Continuous:6. Linear Function:7. Vertical-Line Test:
- 4. Vocabulary1. Function: A relationship where each x-value (independent variable) matches with only one y-value (dependent variable)2. Function Notation:3. Domain:4. Range:5. Continuous:6. Linear Function:7. Vertical-Line Test:
- 5. Vocabulary1. Function: A relationship where each x-value (independent variable) matches with only one y-value (dependent variable)2. Function Notation: f(x), reads “function of x”; tells us the independent variable is inside the parentheses; allows for working with multiple functions3. Domain:4. Range:5. Continuous:6. Linear Function:7. Vertical-Line Test:
- 6. Vocabulary1. Function: A relationship where each x-value (independent variable) matches with only one y-value (dependent variable)2. Function Notation: f(x), reads “function of x”; tells us the independent variable is inside the parentheses; allows for working with multiple functions3. Domain: Any possible value for the independent variable (usually x)4. Range:5. Continuous:6. Linear Function:7. Vertical-Line Test:
- 7. Vocabulary1. Function: A relationship where each x-value (independent variable) matches with only one y-value (dependent variable)2. Function Notation: f(x), reads “function of x”; tells us the independent variable is inside the parentheses; allows for working with multiple functions3. Domain: Any possible value for the independent variable (usually x)4. Range: Any possible value for the dependent variable (usually y)5. Continuous:6. Linear Function:7. Vertical-Line Test:
- 8. Vocabulary1. Function: A relationship where each x-value (independent variable) matches with only one y-value (dependent variable)2. Function Notation: f(x), reads “function of x”; tells us the independent variable is inside the parentheses; allows for working with multiple functions3. Domain: Any possible value for the independent variable (usually x)4. Range: Any possible value for the dependent variable (usually y)5. Continuous: A graph where all points are connected6. Linear Function:7. Vertical-Line Test:
- 9. Vocabulary1. Function: A relationship where each x-value (independent variable) matches with only one y-value (dependent variable)2. Function Notation: f(x), reads “function of x”; tells us the independent variable is inside the parentheses; allows for working with multiple functions3. Domain: Any possible value for the independent variable (usually x)4. Range: Any possible value for the dependent variable (usually y)5. Continuous: A graph where all points are connected6. Linear Function: A function that will give a straight line; any line other than a vertical line7. Vertical-Line Test:
- 10. Vocabulary1. Function: A relationship where each x-value (independent variable) matches with only one y-value (dependent variable)2. Function Notation: f(x), reads “function of x”; tells us the independent variable is inside the parentheses; allows for working with multiple functions3. Domain: Any possible value for the independent variable (usually x)4. Range: Any possible value for the dependent variable (usually y)5. Continuous: A graph where all points are connected6. Linear Function: A function that will give a straight line; any line other than a vertical line7. Vertical-Line Test: Tests whether a graph represents a function or not; can only touch a graph once
- 11. Example 1 To make coffee in a large coffee urn, one recipe calls for two spoonfuls for each cup plus 5 spoonfuls for the pot.a. Write a function where c is the number of cups of coffee being made and s is the total number of spoonfuls of coffee used.
- 12. Example 1 To make coffee in a large coffee urn, one recipe calls for two spoonfuls for each cup plus 5 spoonfuls for the pot.a. Write a function where c is the number of cups of coffee being made and s is the total number of spoonfuls of coffee used. Which is the independent variable?
- 13. Example 1 To make coffee in a large coffee urn, one recipe calls for two spoonfuls for each cup plus 5 spoonfuls for the pot. a. Write a function where c is the number of cups of coffee being made and s is the total number of spoonfuls of coffee used. Which is the independent variable?The number of cups determines how many spoonfuls, so c is independent
- 14. Example 1 To make coffee in a large coffee urn, one recipe calls for two spoonfuls for each cup plus 5 spoonfuls for the pot. a. Write a function where c is the number of cups of coffee being made and s is the total number of spoonfuls of coffee used. Which is the independent variable?The number of cups determines how many spoonfuls, so c is independent f(c) =
- 15. Example 1 To make coffee in a large coffee urn, one recipe calls for two spoonfuls for each cup plus 5 spoonfuls for the pot. a. Write a function where c is the number of cups of coffee being made and s is the total number of spoonfuls of coffee used. Which is the independent variable?The number of cups determines how many spoonfuls, so c is independent f(c) = 2c
- 16. Example 1 To make coffee in a large coffee urn, one recipe calls for two spoonfuls for each cup plus 5 spoonfuls for the pot. a. Write a function where c is the number of cups of coffee being made and s is the total number of spoonfuls of coffee used. Which is the independent variable?The number of cups determines how many spoonfuls, so c is independent f(c) = 2c + 5
- 17. Example 1 To make coffee in a large coffee urn, one recipe calls for two spoonfuls for each cup plus 5 spoonfuls for the pot. a. Write a function where c is the number of cups of coffee being made and s is the total number of spoonfuls of coffee used. Which is the independent variable?The number of cups determines how many spoonfuls, so c is independent f(c) = 2c + 5 s = 2c + 5
- 18. Example 1 To make coffee in a large coffee urn, one recipe calls for two spoonfuls for each cup plus 5 spoonfuls for the pot. a. Write a function where c is the number of cups of coffee being made and s is the total number of spoonfuls of coffee used. Which is the independent variable?The number of cups determines how many spoonfuls, so c is independent f(c) = 2c + 5 Function s = 2c + 5
- 19. Example 1 To make coffee in a large coffee urn, one recipe calls for two spoonfuls for each cup plus 5 spoonfuls for the pot. a. Write a function where c is the number of cups of coffee being made and s is the total number of spoonfuls of coffee used. Which is the independent variable?The number of cups determines how many spoonfuls, so c is independent f(c) = 2c + 5 Function s = 2c + 5 Equation
- 20. Example 1To make coffee in a large coffee urn, one recipe calls for two spoonfuls for each cup plus 5 spoonfuls for the pot. b. Make a table and graph the data.
- 21. Example 1To make coffee in a large coffee urn, one recipe calls for two spoonfuls for each cup plus 5 spoonfuls for the pot. b. Make a table and graph the data.c
- 22. Example 1To make coffee in a large coffee urn, one recipe calls for two spoonfuls for each cup plus 5 spoonfuls for the pot. b. Make a table and graph the data.c s
- 23. Example 1To make coffee in a large coffee urn, one recipe calls for two spoonfuls for each cup plus 5 spoonfuls for the pot. b. Make a table and graph the data.c s s = 2c + 5
- 24. Example 1To make coffee in a large coffee urn, one recipe calls for two spoonfuls for each cup plus 5 spoonfuls for the pot. b. Make a table and graph the data.c s s = 2c + 51
- 25. Example 1To make coffee in a large coffee urn, one recipe calls for two spoonfuls for each cup plus 5 spoonfuls for the pot. b. Make a table and graph the data.c s s = 2c + 51 7
- 26. Example 1To make coffee in a large coffee urn, one recipe calls for two spoonfuls for each cup plus 5 spoonfuls for the pot. b. Make a table and graph the data.c s s = 2c + 51 7 (1, 7)
- 27. Example 1To make coffee in a large coffee urn, one recipe calls for two spoonfuls for each cup plus 5 spoonfuls for the pot. b. Make a table and graph the data.c s s = 2c + 51 7 (1, 7)2
- 28. Example 1To make coffee in a large coffee urn, one recipe calls for two spoonfuls for each cup plus 5 spoonfuls for the pot. b. Make a table and graph the data.c s s = 2c + 51 7 (1, 7)2 9
- 29. Example 1To make coffee in a large coffee urn, one recipe calls for two spoonfuls for each cup plus 5 spoonfuls for the pot. b. Make a table and graph the data.c s s = 2c + 51 7 (1, 7)2 9 (2, 9)
- 30. Example 1To make coffee in a large coffee urn, one recipe calls for two spoonfuls for each cup plus 5 spoonfuls for the pot. b. Make a table and graph the data.c s s = 2c + 51 7 (1, 7)2 9 (2, 9)3
- 31. Example 1To make coffee in a large coffee urn, one recipe calls for two spoonfuls for each cup plus 5 spoonfuls for the pot. b. Make a table and graph the data.c s s = 2c + 51 7 (1, 7)2 9 (2, 9)3 11
- 32. Example 1To make coffee in a large coffee urn, one recipe calls for two spoonfuls for each cup plus 5 spoonfuls for the pot. b. Make a table and graph the data.c s s = 2c + 51 7 (1, 7)2 9 (2, 9)3 11 (3, 11)
- 33. Example 1To make coffee in a large coffee urn, one recipe calls for two spoonfuls for each cup plus 5 spoonfuls for the pot. b. Make a table and graph the data.c s s = 2c + 51 7 (1, 7)2 9 (2, 9)3 11 (3, 11)4
- 34. Example 1To make coffee in a large coffee urn, one recipe calls for two spoonfuls for each cup plus 5 spoonfuls for the pot. b. Make a table and graph the data.c s s = 2c + 51 7 (1, 7)2 9 (2, 9)3 11 (3, 11)4 13
- 35. Example 1To make coffee in a large coffee urn, one recipe calls for two spoonfuls for each cup plus 5 spoonfuls for the pot. b. Make a table and graph the data.c s s = 2c + 51 7 (1, 7)2 9 (2, 9)3 11 (3, 11)4 13 (4, 13)
- 36. Example 1To make coffee in a large coffee urn, one recipe calls for two spoonfuls for each cup plus 5 spoonfuls for the pot. b. Make a table and graph the data.c s s = 2c + 51 7 (1, 7)2 9 (2, 9)3 11 (3, 11)4 13 (4, 13)5
- 37. Example 1To make coffee in a large coffee urn, one recipe calls for two spoonfuls for each cup plus 5 spoonfuls for the pot. b. Make a table and graph the data.c s s = 2c + 51 7 (1, 7)2 9 (2, 9)3 11 (3, 11)4 13 (4, 13)5 15
- 38. Example 1To make coffee in a large coffee urn, one recipe calls for two spoonfuls for each cup plus 5 spoonfuls for the pot. b. Make a table and graph the data.c s s = 2c + 51 7 (1, 7)2 9 (2, 9)3 11 (3, 11)4 13 (4, 13)5 15 (5, 15)
- 39. Example 1To make coffee in a large coffee urn, one recipe calls for two spoonfuls for each cup plus 5 spoonfuls for the pot. b. Make a table and graph the data.c s s = 2c + 51 7 (1, 7)2 9 (2, 9)3 11 (3, 11)4 13 (4, 13)5 15 (5, 15)
- 40. Example 1To make coffee in a large coffee urn, one recipe calls for two spoonfuls for each cup plus 5 spoonfuls for the pot. b. Make a table and graph the data.c s s = 2c + 51 7 (1, 7)2 9 (2, 9)3 11 (3, 11)4 13 (4, 13)5 15 (5, 15)
- 41. Example 1To make coffee in a large coffee urn, one recipe calls for two spoonfuls for each cup plus 5 spoonfuls for the pot. b. Make a table and graph the data.c s s = 2c + 51 7 (1, 7)2 9 (2, 9)3 11 (3, 11)4 13 (4, 13)5 15 (5, 15) c
- 42. Example 1To make coffee in a large coffee urn, one recipe calls for two spoonfuls for each cup plus 5 spoonfuls for the pot. b. Make a table and graph the data.c s s = 2c + 5 s1 7 (1, 7)2 9 (2, 9)3 11 (3, 11)4 13 (4, 13)5 15 (5, 15) c
- 43. Example 1To make coffee in a large coffee urn, one recipe calls for two spoonfuls for each cup plus 5 spoonfuls for the pot. b. Make a table and graph the data.c s s = 2c + 5 s1 7 (1, 7)2 9 (2, 9)3 11 (3, 11)4 13 (4, 13)5 15 (5, 15) c
- 44. Example 1To make coffee in a large coffee urn, one recipe calls for two spoonfuls for each cup plus 5 spoonfuls for the pot. b. Make a table and graph the data.c s s = 2c + 5 s1 7 (1, 7)2 9 (2, 9)3 11 (3, 11)4 13 (4, 13)5 15 (5, 15) c
- 45. Example 1To make coffee in a large coffee urn, one recipe calls for two spoonfuls for each cup plus 5 spoonfuls for the pot. b. Make a table and graph the data.c s s = 2c + 5 s1 7 (1, 7)2 9 (2, 9)3 11 (3, 11)4 13 (4, 13)5 15 (5, 15) c
- 46. Example 1To make coffee in a large coffee urn, one recipe calls for two spoonfuls for each cup plus 5 spoonfuls for the pot. b. Make a table and graph the data.c s s = 2c + 5 s1 7 (1, 7)2 9 (2, 9)3 11 (3, 11)4 13 (4, 13)5 15 (5, 15) c
- 47. Example 1To make coffee in a large coffee urn, one recipe calls for two spoonfuls for each cup plus 5 spoonfuls for the pot. b. Make a table and graph the data.c s s = 2c + 5 s1 7 (1, 7)2 9 (2, 9)3 11 (3, 11)4 13 (4, 13)5 15 (5, 15) c
- 48. Example 1To make coffee in a large coffee urn, one recipe calls for two spoonfuls for each cup plus 5 spoonfuls for the pot. b. Make a table and graph the data.c s s = 2c + 5 s1 7 (1, 7)2 9 (2, 9)3 11 (3, 11)4 13 (4, 13)5 15 (5, 15) c
- 49. Example 1 To make coffee in a large coffee urn, one recipe calls for two spoonfuls for each cup plus 5 spoonfuls for the pot.c. An ofﬁce cafeteria has a coffee urn with the ability to make 16 to 35 cups. Determine the domain and range of the function as applied to this urn.
- 50. Example 1 To make coffee in a large coffee urn, one recipe calls for two spoonfuls for each cup plus 5 spoonfuls for the pot.c. An ofﬁce cafeteria has a coffee urn with the ability to make 16 to 35 cups. Determine the domain and range of the function as applied to this urn. Domain: {c : c = 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35}
- 51. Example 1 To make coffee in a large coffee urn, one recipe calls for two spoonfuls for each cup plus 5 spoonfuls for the pot.c. An ofﬁce cafeteria has a coffee urn with the ability to make 16 to 35 cups. Determine the domain and range of the function as applied to this urn. Domain: {c : c = 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35} Range: {s : s = 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59, 61, 63, 65, 67, 69, 71, 73, 75}
- 52. Example 2Graph the following relation, stating whether it is a function and listing the domain and range. y = x +1
- 53. Example 2Graph the following relation, stating whether it is a function and listing the domain and range. y = x +1
- 54. Example 2Graph the following relation, stating whether it is a function and listing the domain and range. y = x +1x
- 55. Example 2Graph the following relation, stating whether it is a function and listing the domain and range. y = x +1x y
- 56. Example 2Graph the following relation, stating whether it is a function and listing the domain and range. y = x +1x y-2
- 57. Example 2Graph the following relation, stating whether it is a function and listing the domain and range. y = x +1x y-2 1
- 58. Example 2Graph the following relation, stating whether it is a function and listing the domain and range. y = x +1x y-2 1 (-2, 1)
- 59. Example 2Graph the following relation, stating whether it is a function and listing the domain and range. y = x +1x y-2 1 (-2, 1)-1
- 60. Example 2Graph the following relation, stating whether it is a function and listing the domain and range. y = x +1x y-2 1 (-2, 1)-1 0
- 61. Example 2Graph the following relation, stating whether it is a function and listing the domain and range. y = x +1x y-2 1 (-2, 1)-1 0 (-1, 0)
- 62. Example 2Graph the following relation, stating whether it is a function and listing the domain and range. y = x +1x y-2 1 (-2, 1)-1 0 (-1, 0)0
- 63. Example 2Graph the following relation, stating whether it is a function and listing the domain and range. y = x +1x y-2 1 (-2, 1)-1 0 (-1, 0)0 1
- 64. Example 2Graph the following relation, stating whether it is a function and listing the domain and range. y = x +1x y-2 1 (-2, 1)-1 0 (-1, 0)0 1 (0, 1)
- 65. Example 2Graph the following relation, stating whether it is a function and listing the domain and range. y = x +1x y-2 1 (-2, 1)-1 0 (-1, 0)0 1 (0, 1)1
- 66. Example 2Graph the following relation, stating whether it is a function and listing the domain and range. y = x +1x y-2 1 (-2, 1)-1 0 (-1, 0)0 1 (0, 1)1 2
- 67. Example 2Graph the following relation, stating whether it is a function and listing the domain and range. y = x +1x y-2 1 (-2, 1)-1 0 (-1, 0)0 1 (0, 1)1 2 (1, 2)
- 68. Example 2Graph the following relation, stating whether it is a function and listing the domain and range. y = x +1x y-2 1 (-2, 1)-1 0 (-1, 0)0 1 (0, 1)1 2 (1, 2)2
- 69. Example 2Graph the following relation, stating whether it is a function and listing the domain and range. y = x +1x y-2 1 (-2, 1)-1 0 (-1, 0)0 1 (0, 1)1 2 (1, 2)2 3
- 70. Example 2Graph the following relation, stating whether it is a function and listing the domain and range. y = x +1x y-2 1 (-2, 1)-1 0 (-1, 0)0 1 (0, 1)1 2 (1, 2)2 3 (2, 3)
- 71. Example 2Graph the following relation, stating whether it is a function and listing the domain and range. y = x +1x y-2 1 (-2, 1)-1 0 (-1, 0)0 1 (0, 1)1 2 (1, 2)2 3 (2, 3)
- 72. Example 2Graph the following relation, stating whether it is a function and listing the domain and range. y = x +1x y-2 1 (-2, 1)-1 0 (-1, 0)0 1 (0, 1)1 2 (1, 2)2 3 (2, 3)
- 73. Example 2Graph the following relation, stating whether it is a function and listing the domain and range. y = x +1x y-2 1 (-2, 1)-1 0 (-1, 0)0 1 (0, 1)1 2 (1, 2)2 3 (2, 3)
- 74. Example 2Graph the following relation, stating whether it is a function and listing the domain and range. y = x +1x y-2 1 (-2, 1)-1 0 (-1, 0)0 1 (0, 1)1 2 (1, 2)2 3 (2, 3)
- 75. Example 2Graph the following relation, stating whether it is a function and listing the domain and range. y = x +1x y-2 1 (-2, 1)-1 0 (-1, 0)0 1 (0, 1)1 2 (1, 2)2 3 (2, 3)
- 76. Example 2Graph the following relation, stating whether it is a function and listing the domain and range. y = x +1x y-2 1 (-2, 1)-1 0 (-1, 0)0 1 (0, 1)1 2 (1, 2)2 3 (2, 3)
- 77. Example 2Graph the following relation, stating whether it is a function and listing the domain and range. y = x +1x y-2 1 (-2, 1)-1 0 (-1, 0)0 1 (0, 1)1 2 (1, 2)2 3 (2, 3)
- 78. Example 2Graph the following relation, stating whether it is a function and listing the domain and range. y = x +1
- 79. Example 2 Graph the following relation, stating whether it is a function and listing the domain and range. y = x +1Domain:
- 80. Example 2 Graph the following relation, stating whether it is a function and listing the domain and range. y = x +1Domain: {x : x is all real numbers}
- 81. Example 2 Graph the following relation, stating whether it is a function and listing the domain and range. y = x +1Domain: {x : x is all real numbers} Range:
- 82. Example 2 Graph the following relation, stating whether it is a function and listing the domain and range. y = x +1Domain: {x : x is all real numbers} Range: {y : y ≥ 0}
- 83. Problem Set
- 84. Problem Set p. 267 #1-23 odd"That is what learning is.You suddenly understand something youve understood all your life, but in a new way." - Doris Lessing

No public clipboards found for this slide

×
### Save the most important slides with Clipping

Clipping is a handy way to collect and organize the most important slides from a presentation. You can keep your great finds in clipboards organized around topics.

Be the first to comment