Transcript Lesson 2.5

Absolute Value
Equations and
Inequalities
Lesson 2.5
Absolute Value Function
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Whatever you put into the function
comes out positive
-3
+7
+3
+7
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Absolute Value Function
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Definition
 x if x  0
x  abs ( x)  
 x if x  0
Use the abs( )
function on your calculator
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Absolute Value Function
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Note the graph of y = | x |
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Table of values
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Absolute Value Equation
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Let k be a positive number
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Then
a x b  k
means …
a  x  b  k or a  x  b  k
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So we just solve two equations
Try it
3x  5  35
Solve analytically
Solve graphically
Absolute Value Inequalities
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|a x + b | < k is equivalent to
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-k<ax+b<k
- k < a x + b and a x + b < k
3x  5  7
7
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Absolute Value Inequalities
|a x + b | > k is equivalent to

a x + b < -k or a x + b > k
3x  5  7
7
)
)
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Try It Out!
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|15 – x | < 7
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Solve symbolically
|5x – 7 | > 2
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Show graphical solution
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Application
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Lou Scannon, the human cannon ball plans to
travel 180 feet and land squarely on a net with a
70 foot long safe zone.
What distances D can Lou travel and still land
safely on the net?
Use an absolute value inequality to describe the
restrictions on D
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Assignment
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Lesson 2.5
Page 154
Exercises 1 – 53 EOO
73, 75, 83
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