Essential Question:How can we solve and interpret absolute value inequalities to find the range of possible solutions?
Learning Target: Students will be able to solve absolute value inequalities and represent their solutions on a number line, understanding how the inequality affects the direction and type of solution set (e.g., union of intervals or a bounded interval).
Show your work for credit.
Day 1 10/9/24
Required
20 points
20
Question 1
1.
Solve, graph, and write the solutions to the following inequalities in interval notation.
Required
20 points
20
Question 2
2.
Solve, graph, and write the solutions to the following inequalities in interval notation.
Required
20 points
20
Question 3
3.
Solve, graph, and write the solutions to the following inequalities in interval notation.
Required
20 points
20
Question 4
4.
Solve, graph, and write the solutions to the following inequalities in interval notation.
Required
20 points
20
Question 5
5.
Solve, graph, and write the solutions to the following inequalities in interval notation.
Day 2 10/10/24
Spiral Review
Required
10 points
10
Question 6
6.
Reasoning: Explain why the absolute value equation |3x| + 8 = 5 has no solution.
Required
10 points
10
Question 7
7.
Compare and Contrast: Explain the similarities and differences in solving these inequalities |x - 1| ≤ 2 and |x - 1| ≥ 2.
Compare these two inequalities. (How are they alike?)
_______
Contrast these two inequalities. (How are they different?)
_______
Required
2 points
2
Question 8
8.
Is this an open or closed interval?
Required
2 points
2
Question 9
9.
Is this an open or closed interval?
Required
2 points
2
Question 10
10.
Is this an open or closed interval?
Required
2 points
2
Question 11
11.
Is this an open or closed interval?
Required
5 points
5
Question 12
12.
Use interval notation to describe the range of this function.
Required
5 points
5
Question 13
13.
Use interval notation to describe the domain of this function.
Required
5 points
5
Question 14
14.
Write the following in interval notation.
Required
5 points
5
Question 15
15.
Write the following in interval notatin.
Required
12 points
12
Question 16
16.
Match each inequality, absolute value, and interval notation with the correct graph. (Not every choice will be used)
x<-2 or x>2
|x|≤2
-2<x<2
|x|≥2
|x|>2
(-∞,-2)∪(2,∞)
-2≤x≤2
(-2,2)
|x|<2
Required
12 points
12
Question 17
17.
Match each inequality, absolute value, and interval notation with the correct graph. (Not every choice will be used)
x≤-4 or x≥4
x<-4 or x>4
|x|<4
|x|>4
(-3,13)
[-3,13]
-3≤x≤13
|x-5|<8
(-∞,-4)∪(4,∞)
Required
12 points
12
Question 18
18.
Match each inequality, absolute value, and interval notation with the correct graph. (Not every choice will be used)
3<x<5
(-∞,3)∪(5,∞)
(1,4]
x<3 or x>5
x<1 or x≥4
1<x≤4
1>x≤4
|x-4|>1
|x-2.5|<1.5
Required
8 points
8
Question 19
19.
Match each inequality, absolute value, and interval notation with the correct graph. (Not every choice will be used)
5<x≤9
x≤5 or x>9
(-∞,5)∪[9,∞)
(5,9]
(5,9)
x<5 or x≥9
(-∞,5]∪(9,∞)
More Solving Absolute Value Inequalities
Required
20 points
20
Question 20
20.
Solve and graph the inequality
Required
20 points
20
Question 21
21.
Solve and graph the inequality:
Required
20 points
20
Question 22
22.
Solve and graph the inequality:
Required
20 points
20
Question 23
23.
Solve and graph.
Required
20 points
20
Question 24
24.
Solve and graph the inequality:
Day 3 10/11/24
Spiral Review:
Graphing Linear Equations Using Slope-Intercept Form
Required
20 points
20
Question 25
25.
Directions: Complete each function table, then graph the function.
Required
20 points
20
Question 26
26.
Directions: Complete each function table, then graph the function.
Required
10 points
10
Question 27
27.
Watch the video and complete the notes of this section
Sprial Review: Slope
Required
5 points
5
Question 28
28.
Directions: Find the slope of each line. Write your answer in simplest form!
Required
5 points
5
Question 29
29.
Directions: Find the slope of each line. Write your answer in simplest form!
Required
5 points
5
Question 30
30.
Directions: Find the slope of each line. Write your answer in simplest form!
Main Idea: Linear Equations: Slope-Intercept Form
Required
20 points
20
Question 31
31.
Watch the video and complete the notes of this section.
Required
5 points
5
Question 32
32.
Directions: Given the slope and y-intercept of the line, write the equation
in slope-intercept form.
Required
5 points
5
Question 33
33.
Directions: Given the slope and y-intercept of the line, write the equation
in slope-intercept form.
Required
5 points
5
Question 34
34.
Directions: Given the slope and y-intercept of the line, write the equation
in slope-intercept form.
Required
5 points
5
Question 35
35.
Directions: Given the slope and y-intercept of the line, write the equation
in slope-intercept form.
Required
15 points
15
Question 36
36.
Directions: Identify the slope and y-intercept of the line on the graph. Then, write the equation of the line in slope-intercept form.
m=_______
b=_______
Equation=_______
Required
15 points
15
Question 37
37.
Directions: Identify the slope and y-intercept of the line on the graph. Then, write the equation of the line in slope-intercept form.
m=_______
b=_______
Equation=_______
Required
15 points
15
Question 38
38.
Directions: Identify the slope and y-intercept of the line on the graph. Then, write the equation of the line in slope-intercept form.
m=_______
b=_______
Equation=_______
Required
15 points
15
Question 39
39.
Directions: Identify the slope and y-intercept of the line on the graph. Then, write the equation of the line in slope-intercept form.
m=_______
b=_______
Equation=_______
Required
15 points
15
Question 40
40.
Directions: Identify the slope and y-intercept of the line on the graph. Then, write the equation of the line in slope-intercept form.
m=_______
b=_______
Equation=_______
Required
10 points
10
Question 41
41.
Use the slope and y-intercept to graph this linear equation.
Click the graph tab.
Choose the correct graph type.
Click on the graph background to add a point. Add two points to create a graph. Drag a point or type in x and y coordinates to edit its position. Click on a point to delete it.
After you have plotted all graphs, click on x or y intercept tab to graph the intercepts.
Linearexpand_more
Required
10 points
10
Question 42
42.
Use the slope and y-intercept to graph this linear equation.
Click the graph tab.
Click on the graph background to add a point. Add two points to create a graph. Drag a point or type in x and y coordinates to edit its position. Click on a point to delete it.
Required
10 points
10
Question 43
43.
Use the slope and y-intercept to graph this linear equation.
Click the graph tab.
Click on the graph background to add a point. Add two points to create a graph. Drag a point or type in x and y coordinates to edit its position. Click on a point to delete it.
Required
10 points
10
Question 44
44.
Use the slope and y-intercept to graph this linear equation.
Click the graph tab.
Click on the graph background to add a point. Add two points to create a graph. Drag a point or type in x and y coordinates to edit its position. Click on a point to delete it.
Day 4 10/14/24
Graphing Absolute Value Functions
Required
10 points
10
Question 45
45.
Use a set of x values to graph the parent function y=|x|
Required
10 points
10
Question 46
46.
Use a set of x values to graph the function y=|x|+ 2
Required
10 points
10
Question 47
47.
Compare the graph y=|x|to y=|x|+ 2
How are they the same?
_______
How are they different?
_______
Required
10 points
10
Question 48
48.
Use a set of x values to graph the function y=|x - 2|
Required
10 points
10
Question 49
49.
Compare the graph y=|x| to y=|x - 2|
How are they the same?
_______
How are they different?
_______
Required
10 points
10
Question 50
50.
Make a prediction. What will the graph of y=|x - 2|+ 2 look like?
Required
10 points
10
Question 51
51.
Use a set of x values to graph the function y=|x - 2|+ 2
Day 5 10/15/24
Graphing Absolute Value part 2
Required
10 points
10
Question 52
52.
Notes: Critical Values of Absolute Value Functions
Required
20 points
20
Question 53
53.
1)What are the critical values of this absolute value function:
y=|x-1|+2
Opens (upward or downward)
_______
Axis of Symmetry
_______
Vertex
_______
Slope
_______
2) Use the critical values of this equation to graph it.
Required
8 points
8
Question 54
54.
What are the critical values of this absolute value function:
y=2|x+2|+2
Opens (upward or downward)
_______
Axis of Symmetry
_______
Vertex
_______
Slope
_______
2) Use the critical values of this equation to graph it.
Required
8 points
8
Question 55
55.
What are the critical values of this absolute value function:
Opens (upward or downward)
_______
Axis of Symmetry
_______
Vertex
_______
Slope
_______
2) Use the critical values of this equation to graph it.
Required
8 points
8
Question 56
56.
What are the critical values of this absolute value function:
Opens (upward or downward)
_______
Axis of Symmetry
_______
Vertex
_______
Slope
_______
2) Use the critical values of this equation to graph it.
Required
8 points
8
Question 57
57.
What are the critical values of this absolute value function:
Opens (upward or downward)
_______
Axis of Symmetry
_______
Vertex
_______
Slope
_______
2) Use the critical values of this equation to graph it.
Day 6 10/16/24
More Graphing Absolute Value
Required
8 points
8
Question 58
58.
How is the absolute function below different than the parent function y=|x|:
y=|x-1|+2
Opens (Upward or Downward) _______
Horizontal Shift (write none if there is none) _______
Vertical Shift (write none if there is none) _______
Stretched (0<|a|<1), Compressed (|a|>1), or None _______.
Required
8 points
8
Question 59
59.
How is the absolute function below different than the parent function y=|x|:
y=2|x+6|-2
Opens (Upward or Downward) _______
Horizontal Shift (write none if there is none) _______
Vertical Shift (write none if there is none) _______
Stretched (0<|a|<1), Compressed (|a|>1), or None _______.
Required
8 points
8
Question 60
60.
How is the absolute function below different than the parent function y=|x|:
y=-3|x-4|-9
Opens (Upward or Downward) _______
Horizontal Shift (write none if there is none) _______
Vertical Shift (write none if there is none) _______
Stretched (0<|a|<1), Compressed (|a|>1), or None _______.
Required
8 points
8
Question 61
61.
How is the absolute function below different than the parent function y=|x|:
y=1/2|x+3|+1
Opens (Upward or Downward) _______
Horizontal Shift (write none if there is none) _______
Vertical Shift (write none if there is none) _______
Stretched (0<|a|<1), Compressed (|a|>1), or None _______.
Required
8 points
8
Question 62
62.
How is the absolute function below different than the parent function y=|x|:
y=-1/3|x-5|-5
Opens (Upward or Downward) _______
Horizontal Shift (write none if there is none) _______
Vertical Shift (write none if there is none) _______
Stretched (0<|a|<1), Compressed (|a|>1), or None _______.
Required
8 points
8
Question 63
63.
How is the absolute function below different than the parent function y=|x|:
y=.5|x-8|+3
Opens (Upward or Downward) _______
Horizontal Shift (write none if there is none) _______
Vertical Shift (write none if there is none) _______
Stretched (0<|a|<1), Compressed (|a|>1), or None _______.
Spiral Review
Required
5 points
5
Question 64
64.
Simplify each radical
Required
5 points
5
Question 65
65.
Simplify each radical
Required
5 points
5
Question 66
66.
Simplify this expression. Your answer should not have negative exponents.
Required
5 points
5
Question 67
67.
Simplify this expression. Your answer should not have negative exponents.
Required
5 points
5
Question 68
68.
Simplify this expression. Your answer should not have negative exponents.
Required
10 points
10
Question 69
69.
Find the Product of these polynomials.
Required
10 points
10
Question 70
70.
Find the Product of these polynomials.
Required
10 points
10
Question 71
71.
Find the Product
Required
10 points
10
Question 72
72.
Find the Product:
Day 7 10/18/24
Real World Applications
Required
20 points
20
Question 73
73.
Sam is sitting in a boat on a lake. She can get burned by the sunlight that hits her directly and by sunlight that reflects off the water. Sunlight reflects off the water at the point (2, 0) and hits Sam at the point (3.5, 3). Write and graph the function that shows the path of the sunlight.
1) Graph the function
2) Write the function that shows the path of the sunlight.
_______
Required
20 points
20
Question 74
74.
A rainstorm begins as a drizzle, builds up to a heavy rain, and then drops back to a drizzle. The rate r (in inches per hour) at which it rains is given by the function r = −0.5 ⎜t − 1⎟ + 0.5, where t is the time (in hours). Graph the function. Determine for how long it rains and when it rains the hardest.
Opens (upward or downward)
_______
Axis of Symmetry
_______
Vertex
_______
Slope
_______
2) Use the critical values of this equation to graph it.
3) Determine for how long it rains
_______
and when it rains the hardest.
_______
Required
20 points
20
Question 75
75.
While playing pool, a player tries to shoot the eight ball into the corner pocket as shown. Imagine that a coordinate plane is placed over the pool table. The eight ball is at (5, 5/4) and the pocket they are aiming for is at (10, 5). The player is going to bank the ball off the side at (6, 0).
2) Write an equation for the path of the ball.
3) Did the player make the shot? How do you know?
_______
Required
10 points
10
Question 76
76.
Explain the Error Explain why the graph shown is not the graph of y = ⎜x + 3⎟ + 2. What is the correct equation shown in the graph?