SlideShare une entreprise Scribd logo
1  sur  3
Télécharger pour lire hors ligne
Exercise #11
Graphing Absolute Value


Recall        x


Definition:




Example
Write f ( x)      x 2 as a piece-wise function.




The graph of f ( x) is:
                             y




                                              x




Example
Graph f ( x)      2x 1
                             y




                                              x
Example
Graph f ( x)   x2 1
                       y




                           x




Example
Graph f ( x) 3 x 2 4
                       y




                           x




Example
Graph f ( x)   cos x
                       y




                           x
Example
Graph f ( x) 2 x 3 1
                           y




                                              x




Piece-Wise Graphs




                   x 2            x<0
                       2
      Ex. f ( x)   x       when   0   x   2
                       x          x>3


                                  y




                                                  x

Contenu connexe

Tendances

Reciprocals Oct 13th
Reciprocals Oct 13thReciprocals Oct 13th
Reciprocals Oct 13thingroy
 
Quadratic Function by Taylor & Asia
Quadratic Function by Taylor & Asia Quadratic Function by Taylor & Asia
Quadratic Function by Taylor & Asia Hope Scott
 
Lesson 5: Functions and surfaces
Lesson 5: Functions and surfacesLesson 5: Functions and surfaces
Lesson 5: Functions and surfacesMatthew Leingang
 
5 4 function notation
5 4 function notation5 4 function notation
5 4 function notationhisema01
 
Summary of Integration Methods
Summary of Integration MethodsSummary of Integration Methods
Summary of Integration MethodsSilvius
 
Exponential and logarithmic functions
Exponential and logarithmic functionsExponential and logarithmic functions
Exponential and logarithmic functionsNjabulo Nkabinde
 
プログラミングHaskell 13章 問題7
プログラミングHaskell 13章 問題7プログラミングHaskell 13章 問題7
プログラミングHaskell 13章 問題7Kiwamu Okabe
 
Lesson 3 Nov 16 09
Lesson 3 Nov 16 09Lesson 3 Nov 16 09
Lesson 3 Nov 16 09ingroy
 
January 7, 2014 function notation
January 7, 2014  function notationJanuary 7, 2014  function notation
January 7, 2014 function notationkhyps13
 
X2 T04 03 cuve sketching - addition, subtraction, multiplication and division
X2 T04 03 cuve sketching - addition, subtraction,  multiplication and divisionX2 T04 03 cuve sketching - addition, subtraction,  multiplication and division
X2 T04 03 cuve sketching - addition, subtraction, multiplication and divisionNigel Simmons
 

Tendances (20)

Reciprocals Oct 13th
Reciprocals Oct 13thReciprocals Oct 13th
Reciprocals Oct 13th
 
Exponential functions (1)
Exponential functions (1)Exponential functions (1)
Exponential functions (1)
 
Quadratic Function by Taylor & Asia
Quadratic Function by Taylor & Asia Quadratic Function by Taylor & Asia
Quadratic Function by Taylor & Asia
 
Day 5 examples
Day 5 examplesDay 5 examples
Day 5 examples
 
Exponential functions
Exponential functionsExponential functions
Exponential functions
 
Day 3a examples
Day 3a examplesDay 3a examples
Day 3a examples
 
Fungsi kuadrat
Fungsi kuadratFungsi kuadrat
Fungsi kuadrat
 
Lesson 5: Functions and surfaces
Lesson 5: Functions and surfacesLesson 5: Functions and surfaces
Lesson 5: Functions and surfaces
 
Limits2
Limits2Limits2
Limits2
 
5 4 function notation
5 4 function notation5 4 function notation
5 4 function notation
 
Summary of Integration Methods
Summary of Integration MethodsSummary of Integration Methods
Summary of Integration Methods
 
Exponential and logarithmic functions
Exponential and logarithmic functionsExponential and logarithmic functions
Exponential and logarithmic functions
 
プログラミングHaskell 13章 問題7
プログラミングHaskell 13章 問題7プログラミングHaskell 13章 問題7
プログラミングHaskell 13章 問題7
 
Functionworksheet1
Functionworksheet1Functionworksheet1
Functionworksheet1
 
Day 4 examples
Day 4 examplesDay 4 examples
Day 4 examples
 
Day 3 examples
Day 3 examplesDay 3 examples
Day 3 examples
 
Day 1 examples
Day 1 examplesDay 1 examples
Day 1 examples
 
Lesson 3 Nov 16 09
Lesson 3 Nov 16 09Lesson 3 Nov 16 09
Lesson 3 Nov 16 09
 
January 7, 2014 function notation
January 7, 2014  function notationJanuary 7, 2014  function notation
January 7, 2014 function notation
 
X2 T04 03 cuve sketching - addition, subtraction, multiplication and division
X2 T04 03 cuve sketching - addition, subtraction,  multiplication and divisionX2 T04 03 cuve sketching - addition, subtraction,  multiplication and division
X2 T04 03 cuve sketching - addition, subtraction, multiplication and division
 

En vedette (20)

Lesson 17
Lesson 17Lesson 17
Lesson 17
 
Lesson 30 35
Lesson 30   35Lesson 30   35
Lesson 30 35
 
Review key for test #3
Review key for test #3Review key for test #3
Review key for test #3
 
Lesson 10
Lesson 10Lesson 10
Lesson 10
 
Review key test 4
Review key test 4Review key test 4
Review key test 4
 
Lesson 40
Lesson 40Lesson 40
Lesson 40
 
Exercise #16 notes
Exercise #16 notesExercise #16 notes
Exercise #16 notes
 
Pythagoras examples
Pythagoras examplesPythagoras examples
Pythagoras examples
 
Exponents
ExponentsExponents
Exponents
 
Number systems
Number systemsNumber systems
Number systems
 
Absolute values
Absolute valuesAbsolute values
Absolute values
 
Equvalent fractions
Equvalent fractionsEquvalent fractions
Equvalent fractions
 
Exponents day 4
Exponents day 4Exponents day 4
Exponents day 4
 
Circle review key
Circle review keyCircle review key
Circle review key
 
Lesson 54
Lesson 54Lesson 54
Lesson 54
 
What is a spreadsheet
What is a spreadsheetWhat is a spreadsheet
What is a spreadsheet
 
Operations with rational numbers
Operations with rational numbersOperations with rational numbers
Operations with rational numbers
 
Rational numbers
Rational numbersRational numbers
Rational numbers
 
Enseignements des audits DV et VCB - Laurent Beaussoubre
Enseignements des audits DV et VCB - Laurent BeaussoubreEnseignements des audits DV et VCB - Laurent Beaussoubre
Enseignements des audits DV et VCB - Laurent Beaussoubre
 
Accueil numerique atout france
Accueil numerique atout franceAccueil numerique atout france
Accueil numerique atout france
 

Similaire à Exercise #11 notes

Algebra 2 Unit 5 Lesson 2
Algebra 2 Unit 5 Lesson 2Algebra 2 Unit 5 Lesson 2
Algebra 2 Unit 5 Lesson 2Kate Nowak
 
Limits and derivatives
Limits and derivativesLimits and derivatives
Limits and derivativessahil9100
 
2.2 Polynomial Function Notes
2.2 Polynomial Function Notes2.2 Polynomial Function Notes
2.2 Polynomial Function Noteslgemgnani
 
X2 T07 03 addition, subtraction, multiplication & division (2011)
X2 T07 03 addition, subtraction,  multiplication & division (2011)X2 T07 03 addition, subtraction,  multiplication & division (2011)
X2 T07 03 addition, subtraction, multiplication & division (2011)Nigel Simmons
 
X2 t07 03 addition, subtraction, multiplication & division (2012)
X2 t07 03 addition, subtraction,  multiplication & division (2012)X2 t07 03 addition, subtraction,  multiplication & division (2012)
X2 t07 03 addition, subtraction, multiplication & division (2012)Nigel Simmons
 
Partial Differentiation & Application
Partial Differentiation & Application Partial Differentiation & Application
Partial Differentiation & Application Yana Qlah
 
Concept map function
Concept map functionConcept map function
Concept map functionzabidah awang
 
Antiderivatives nako sa calculus official
Antiderivatives nako sa calculus officialAntiderivatives nako sa calculus official
Antiderivatives nako sa calculus officialZerick Lucernas
 
Cea0001 ppt project
Cea0001 ppt projectCea0001 ppt project
Cea0001 ppt projectcea0001
 
Lesson 15: Inverse Functions and Logarithms
Lesson 15: Inverse Functions and LogarithmsLesson 15: Inverse Functions and Logarithms
Lesson 15: Inverse Functions and LogarithmsMatthew Leingang
 
Lesson 21: Curve Sketching (slides)
Lesson 21: Curve Sketching (slides)Lesson 21: Curve Sketching (slides)
Lesson 21: Curve Sketching (slides)Mel Anthony Pepito
 
Lesson 21: Curve Sketching (slides)
Lesson 21: Curve Sketching (slides)Lesson 21: Curve Sketching (slides)
Lesson 21: Curve Sketching (slides)Matthew Leingang
 
Lesson 15: Inverse Functions and Logarithms
Lesson 15: Inverse Functions and LogarithmsLesson 15: Inverse Functions and Logarithms
Lesson 15: Inverse Functions and LogarithmsMatthew Leingang
 

Similaire à Exercise #11 notes (20)

Chapter 3
Chapter 3Chapter 3
Chapter 3
 
Algebra 2 Unit 5 Lesson 2
Algebra 2 Unit 5 Lesson 2Algebra 2 Unit 5 Lesson 2
Algebra 2 Unit 5 Lesson 2
 
Limits and derivatives
Limits and derivativesLimits and derivatives
Limits and derivatives
 
2.2 Polynomial Function Notes
2.2 Polynomial Function Notes2.2 Polynomial Function Notes
2.2 Polynomial Function Notes
 
Functions
FunctionsFunctions
Functions
 
X2 T07 03 addition, subtraction, multiplication & division (2011)
X2 T07 03 addition, subtraction,  multiplication & division (2011)X2 T07 03 addition, subtraction,  multiplication & division (2011)
X2 T07 03 addition, subtraction, multiplication & division (2011)
 
125 5.4
125 5.4125 5.4
125 5.4
 
X2 t07 03 addition, subtraction, multiplication & division (2012)
X2 t07 03 addition, subtraction,  multiplication & division (2012)X2 t07 03 addition, subtraction,  multiplication & division (2012)
X2 t07 03 addition, subtraction, multiplication & division (2012)
 
Limits
LimitsLimits
Limits
 
Partial Differentiation & Application
Partial Differentiation & Application Partial Differentiation & Application
Partial Differentiation & Application
 
Concept map function
Concept map functionConcept map function
Concept map function
 
gfg
gfggfg
gfg
 
Antiderivatives nako sa calculus official
Antiderivatives nako sa calculus officialAntiderivatives nako sa calculus official
Antiderivatives nako sa calculus official
 
Cea0001 ppt project
Cea0001 ppt projectCea0001 ppt project
Cea0001 ppt project
 
Lesson 15: Inverse Functions and Logarithms
Lesson 15: Inverse Functions and LogarithmsLesson 15: Inverse Functions and Logarithms
Lesson 15: Inverse Functions and Logarithms
 
F.Komposisi
F.KomposisiF.Komposisi
F.Komposisi
 
Lesson 51
Lesson 51Lesson 51
Lesson 51
 
Lesson 21: Curve Sketching (slides)
Lesson 21: Curve Sketching (slides)Lesson 21: Curve Sketching (slides)
Lesson 21: Curve Sketching (slides)
 
Lesson 21: Curve Sketching (slides)
Lesson 21: Curve Sketching (slides)Lesson 21: Curve Sketching (slides)
Lesson 21: Curve Sketching (slides)
 
Lesson 15: Inverse Functions and Logarithms
Lesson 15: Inverse Functions and LogarithmsLesson 15: Inverse Functions and Logarithms
Lesson 15: Inverse Functions and Logarithms
 

Plus de Kelly Scallion

Plus de Kelly Scallion (20)

May 2011 schedule
May 2011 scheduleMay 2011 schedule
May 2011 schedule
 
Exercise #23
Exercise #23Exercise #23
Exercise #23
 
Exercise #21
Exercise #21Exercise #21
Exercise #21
 
Exercise #21
Exercise #21Exercise #21
Exercise #21
 
Exercise #22
Exercise #22Exercise #22
Exercise #22
 
Lesson 19 last two examples worked out
Lesson 19 last two examples worked outLesson 19 last two examples worked out
Lesson 19 last two examples worked out
 
Exercise #19
Exercise #19Exercise #19
Exercise #19
 
Exercise #18 notes
Exercise #18 notesExercise #18 notes
Exercise #18 notes
 
Exercise #17 notes
Exercise #17 notesExercise #17 notes
Exercise #17 notes
 
Exercise #13 notes ~ graphing
Exercise #13 notes ~ graphingExercise #13 notes ~ graphing
Exercise #13 notes ~ graphing
 
Exercise #13 notes ~ equations
Exercise #13 notes ~ equationsExercise #13 notes ~ equations
Exercise #13 notes ~ equations
 
Exercise #15 notes
Exercise #15 notesExercise #15 notes
Exercise #15 notes
 
Exercise #14 notes
Exercise #14 notesExercise #14 notes
Exercise #14 notes
 
Exercise #9 notes
Exercise #9 notesExercise #9 notes
Exercise #9 notes
 
Exercise #7 notes
Exercise #7 notesExercise #7 notes
Exercise #7 notes
 
Statement and demand assignment
Statement and demand assignmentStatement and demand assignment
Statement and demand assignment
 
Statement and demand notes
Statement and demand notesStatement and demand notes
Statement and demand notes
 
Statement and demand forms
Statement and demand formsStatement and demand forms
Statement and demand forms
 
Exercise #6 notes
Exercise #6 notesExercise #6 notes
Exercise #6 notes
 
Circle properties summary
Circle properties summaryCircle properties summary
Circle properties summary
 

Exercise #11 notes

  • 1. Exercise #11 Graphing Absolute Value Recall x Definition: Example Write f ( x) x 2 as a piece-wise function. The graph of f ( x) is: y x Example Graph f ( x) 2x 1 y x
  • 2. Example Graph f ( x) x2 1 y x Example Graph f ( x) 3 x 2 4 y x Example Graph f ( x) cos x y x
  • 3. Example Graph f ( x) 2 x 3 1 y x Piece-Wise Graphs x 2 x<0 2 Ex. f ( x) x when 0 x 2 x x>3 y x