Main Idea: Compound Inequalities
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10
Solve and graph the compound inequality for the given variable.
Ɛhia
10
Solve and graph the compound inequality for the given variable.
Vocabulary Review: Mark each statement as True or False.
True
False
The answer to the absolute value of 8 is -8.
The absolute value of -8 is -8, since -8 is 8 units from 0 on the number line.
The absolute value of -8 is 8, since -8 is 8 units from 0 on the number line.
According to the definition of absolute value, if |r|= 3, then r = 3 or r = -3.
The definition of absolute value is...
Solve this absolute Value equation:
|-2x+5|= 7
+ Case
- Case
Solve and graph the compound inequality for the given variable.
Solve and graph the compound inequality for the given variable.
Solve and graph the inequality
Solve and graph the inequality:
+ case
- case
How is the absolute function below different than the parent function y=|x|:
y=-4|x-3|+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
The number of boats B a boat dealer sells in each month of the year from March to December can be modeled by the function 𝐵 = −15|𝑡 − 5| +120 where t is the time in months and t = 1 represents January.
1)Complete the table of values and then graph the function.
2) What is the maximum number of sales in one month?
3) In what month is the maximum reached?
4) What is the minimum number of sales in one month?
5) In what month is the minimum reached?
Put the interval notations and graphs in the right category.
[3,5)
[3.5]
(3,5]
(3,5)
(-∞,-9)
[5,∞)
Open Interval
Closed Interval
Both
Describe the domain of this function.
In interval notation:
As an inequality:
Use these symbols if you can not find them ≥ ≤ ∞
Describe the range of this function.
In interval notation:
As an inequality:
Use these symbols if you can not find them ≥ ≤ ∞
Describe the domain of this function.
In interval notation:
As an inequality:
Use these symbols if you can not find them ≥ ≤ ∞
Describe the range of this function.
In interval notation:
As an inequality:
Use these symbols if you can not find them ≥ ≤ ∞
What intervals of x is the function f(x) increasing?
For what interval of x is the function f(x) decreasing?
For what interval of x is the function f(x) negative?
Name an interval of x is the function f(x) positive?
Write the following in interval notation. Use the little side keyboard to find infinity if you need it and type your answer.
Write the following in interval notation.
What is the domain of the function?
What is the range of the function?
Use the graph to create a function with the following features:
1) As x gets smaller; the function approaches negative infinity. x→ - ∞; f(x)→ -∞
2) As x gets larger; the function approaches negative infinity. x→ ∞; f(x)→ -∞
3) The graph of the function passes through the x-axis at -2.
4) The graph of the function passes though the y-axis at y=4
Find the absolute value of this expression:
Find the absolute value of this expression:
Solve this absolute Value equation:
|3x+6|=15
+ Case
- Case
Solve this absolute Value equation:
2|4x+6|=36
+ Case
- Case
Solve this absolute Value equation:
+ Case
- Case
Solve this absolute Value equation:
4|n - 2| – 3 = 25
+ Case
- Case
Solve and graph the inequality:
+ case
- case
Solve and graph.
+ case
- case
How is the absolute function below different than the parent function y=|x|:
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
1) What are the critical values of this absolute value function:
y=|x-3|+4
Opens (upward or downward)
Axis of Symmetry
Vertex
Slope
2) Use the critical values of this equation to graph it.
What are the critical values of this absolute value function:
y=2|x+4|- 2
Opens (upward or downward)
Axis of Symmetry
Vertex
Slope
2) Use the critical values of this equation to graph it.
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.
