Transcript Lesson 2.5
Absolute Value
Equations and
Inequalities
Lesson 2.5
Absolute Value Function
Whatever you put into the function
comes out positive
-3
+7
+3
+7
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Absolute Value Function
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
Note the graph of y = | x |
Table of values
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Absolute Value Equation
Let k be a positive number
Then
a x b k
means …
a x b k or a x b k
So we just solve two equations
Try it
3x 5 35
Solve analytically
Solve graphically
Absolute Value Inequalities
|a x + b | < k is equivalent to
-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!
|15 – x | < 7
Solve symbolically
|5x – 7 | > 2
Show graphical solution
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Application
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
Lesson 2.5
Page 154
Exercises 1 – 53 EOO
73, 75, 83
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