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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

Absolute Value Functions · 2017-04-20 · Nov 101:15 PM Absolute Value Functions MCC912.A.REI.2 Solve simple rational and radical equations in one variable, and give examples showing

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Page 1: Absolute Value Functions · 2017-04-20 · Nov 101:15 PM Absolute Value Functions MCC912.A.REI.2 Solve simple rational and radical equations in one variable, and give examples showing

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

Page 2: Absolute Value Functions · 2017-04-20 · Nov 101:15 PM Absolute Value Functions MCC912.A.REI.2 Solve simple rational and radical equations in one variable, and give examples showing

5 ­ Notes ­ Absolute Value Functions.notebook

2

April 20, 2017

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:

Page 3: Absolute Value Functions · 2017-04-20 · Nov 101:15 PM Absolute Value Functions MCC912.A.REI.2 Solve simple rational and radical equations in one variable, and give examples showing

5 ­ Notes ­ Absolute Value Functions.notebook

3

April 20, 2017

Mar 25­1:58 PM

Mar 25­1:57 PM

Defining an Absolute Value Function as a Piecewise Function

Page 4: Absolute Value Functions · 2017-04-20 · Nov 101:15 PM Absolute Value Functions MCC912.A.REI.2 Solve simple rational and radical equations in one variable, and give examples showing

5 ­ Notes ­ Absolute Value Functions.notebook

4

April 20, 2017

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

Page 5: Absolute Value Functions · 2017-04-20 · Nov 101:15 PM Absolute Value Functions MCC912.A.REI.2 Solve simple rational and radical equations in one variable, and give examples showing

5 ­ Notes ­ Absolute Value Functions.notebook

5

April 20, 2017

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:

Page 6: Absolute Value Functions · 2017-04-20 · Nov 101:15 PM Absolute Value Functions MCC912.A.REI.2 Solve simple rational and radical equations in one variable, and give examples showing

5 ­ Notes ­ Absolute Value Functions.notebook

6

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:

Page 7: Absolute Value Functions · 2017-04-20 · Nov 101:15 PM Absolute Value Functions MCC912.A.REI.2 Solve simple rational and radical equations in one variable, and give examples showing

5 ­ Notes ­ Absolute Value Functions.notebook

7

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. 

Page 8: Absolute Value Functions · 2017-04-20 · Nov 101:15 PM Absolute Value Functions MCC912.A.REI.2 Solve simple rational and radical equations in one variable, and give examples showing

5 ­ Notes ­ Absolute Value Functions.notebook

8

April 20, 2017

Apr 8 ­ 4:31 PM

1.

Nov 10­3:54 PM

2.

Page 9: Absolute Value Functions · 2017-04-20 · Nov 101:15 PM Absolute Value Functions MCC912.A.REI.2 Solve simple rational and radical equations in one variable, and give examples showing

5 ­ Notes ­ Absolute Value Functions.notebook

9

April 20, 2017

Dec 22 ­ 9:55 AM

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#, ∞)

Page 10: Absolute Value Functions · 2017-04-20 · Nov 101:15 PM Absolute Value Functions MCC912.A.REI.2 Solve simple rational and radical equations in one variable, and give examples showing

5 ­ Notes ­ Absolute Value Functions.notebook

10

April 20, 2017

Jan 9 ­ 12:58 PM

1.0

Jan 9 ­ 12:58 PM

0

2.

Page 11: Absolute Value Functions · 2017-04-20 · Nov 101:15 PM Absolute Value Functions MCC912.A.REI.2 Solve simple rational and radical equations in one variable, and give examples showing

5 ­ Notes ­ Absolute Value Functions.notebook

11

April 20, 2017

Nov 6­2:21 PM

03.

Dec 22 ­ 9:56 AM

0

4.

Page 12: Absolute Value Functions · 2017-04-20 · Nov 101:15 PM Absolute Value Functions MCC912.A.REI.2 Solve simple rational and radical equations in one variable, and give examples showing

5 ­ Notes ­ Absolute Value Functions.notebook

12

April 20, 2017

Jan 9 ­ 12:58 PM

5.0

Nov 10­4:58 PM