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5 Notes Absolute Value Functions.notebook
1
April 20, 2017
Nov 101:15 PM
Absolute Value Functions
MCC912.A.REI.2 Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may
arise.
Nov 101:15 PM
Vocabulary
Absolute Value of x the distance from zero to a value of x on a number line. Denoted as x
5 Notes Absolute Value Functions.notebook
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Apr 1410:58 PM
What am I learning today?
How to solve and graph absolute value functions
How will I show that I learned it?
Graph absolute value functions and solve equations and inequalities
Nov 1210:50 AM
Parent Graphs and their Characteristics
Absolute Value
x y
Characteristics
Vertex: Axis of symmetry:
Domain: Range:
Max: Min:
Int of Inc: Int of Dec:
xintercept: yintercept:
end behavior:
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Defining an Absolute Value Function as a Piecewise Function
5 Notes Absolute Value Functions.notebook
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Nov 1211:09 AM
Standard Forms
For all types
a:______________
a >1: ___________
a <1: ___________
b:______________
1/b >1:__________
1/b <1: __________
h: _____________
k: _____________
Nov 1211:17 AM
Steps to graphing ALL graph types
1. Get the function in the correct form make sure that if there is a "b", it has been factored out.
2. Give the description of its transformations compared to the parent graph.
3. Write down the parent table.
4. Adjust parent table by multiplying "a" and "1/b"Reminder: "a" affects the range (yvalues)
"1/b" affects the domain (xvalues)
5. Adjust the new table by add/sub "h" and "k"Reminder: add/sub "h" to xvalues
add/sub "k" to yvalues
6. Plot your points and give the characteristics
5 Notes Absolute Value Functions.notebook
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Nov 1211:29 AM
Graph and give the requested characteristics
1.
x y x y
end behavior:
Nov 1211:29 AM
2.
x y x y
end behavior:
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April 20, 2017
Nov 1211:29 AM
3.
x y x y
end behavior:
Nov 1211:29 AM
4.
x y x y
end behavior:
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April 20, 2017
Nov 101:34 PM
Solving Absolute Value Equations
Absolute Value: The DISTANCE that a # is away from zero.
1. Isolate the absolute value grouping.
2. Determine is the equation is positive.
3. If split & create 2 new equations...
one pos# & one neg # then solve.
If then the answer is...
Apr 8 4:30 PM
Absolute value: The absolute ≠ -#
Reminder: Determine what x ≠ #. That # or range of numbers are where your extraneous solutions fall.
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2.
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Solving Absolute Value Inequalities
Dec 22 9:55 AM
Solving Absolute Value InequalitiesCreate the 2 equations and solve like before. Reminder: If positive, SPLIT If negative STOP Do NOT split! (special case)
POSITIVE Case NEGATIVE CaseTest value in between If x > #follows pattern T F T or F T F (∞,∞)
Equals PositiveShaded between 2 answers: If x < # (S#, L#) or [S#, L#] NO SOLUTION
Not shaded between:(∞, S#) U (L#, ∞)
or(∞, S#] U [L#, ∞)
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