Is this an open or closed interval?
Is this an open or closed interval?
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.
Solve, graph, and write the solutions to the following inequalities in interval notation.
Solve, graph, and write the solutions to the following inequalities in interval notation.
Solve, graph, and write the solutions to the following inequalities in interval notation.
Reasoning: Explain why the absolute value equation |3x| + 8 = 5 has no solution.
Is this an open or closed interval?
Is this an open or closed interval?
Is this an open or closed interval?
Is this an open or closed interval?
Use interval notation to describe the range of this function.
Use interval notation to describe the domain of this function.
Write the following in interval notation.
Write the following in interval notatin.
Match each inequality, absolute value, and interval notation with the correct graph. (Not every choice will be used)
(-∞,-2)∪(2,∞)
(-2,2)
-2≤x≤2
|x|≥2
|x|>2
|x|≤2
-2<x<2
x<-2 or x>2
|x|<2
Match each inequality, absolute value, and interval notation with the correct graph. (Not every choice will be used)
x<-4 or x>4
-3≤x≤13
|x|<4
|x|>4
[-3,13]
|x-5|<8
(-3,13)
(-∞,-4)∪(4,∞)
x≤-4 or x≥4
Match each inequality, absolute value, and interval notation with the correct graph. (Not every choice will be used)
1>x≤4
(-∞,3)∪(5,∞)
|x-2.5|<1.5
(1,4]
x<1 or x≥4
1<x≤4
x<3 or x>5
3<x<5
|x-4|>1
Match each inequality, absolute value, and interval notation with the correct graph. (Not every choice will be used)
(5,9)
(-∞,5)∪[9,∞)
(5,9]
(-∞,5]∪(9,∞)
x<5 or x≥9
x≤5 or x>9
5<x≤9
Solve and graph the inequality
Solve and graph the inequality:
Solve and graph the inequality:
Solve and graph.
Solve and graph the inequality:
Use a set of x values to graph the parent function y=|x|
Use a set of x values to graph the function y=|x|+ 2
Use a set of x values to graph the function y=|x - 2|
Make a prediction. What will the graph of y=|x - 2|+ 2 look like?
Use a set of x values to graph the function y=|x - 2|+ 2
Notes: Critical Values of Absolute Value Functions
Simplify each radical
Simplify each radical
Simplify this expression. Your answer should not have negative exponents.
Simplify this expression. Your answer should not have negative exponents.
Simplify this expression. Your answer should not have negative exponents.
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?
