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.
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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
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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}
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
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