SlideShare a Scribd company logo
Introduction: Products and Quotients of Functions
Definitions ,[object Object],[object Object],[object Object],[object Object]
Equations ,[object Object],[object Object],[object Object]
Investigation ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Investigation  (continued)
Investigation  (continued) 3.  Examine the pattern of symmetry of the function on the left side and right side of each identity in step 2.  Copy and complete the table. q(x) = x 4  (even) g(x) = x 2 (g(x)) 2  = q(x) g(x) = x 2  (even) f(x) = x (odd) f(x)f(x) = g(x) q(x) = x 4  (even) f(x) = x (odd) p(x) = x 3  (odd) f(x)p(x) = q(x) p(x) = x 3  (odd) f(x) = x (odd) g(x) = x 2  (even) f(x)g(x) = p(x) Symmetry of Product Function Symmetry of Factor Functions Identity
Investigation  (continued) ,[object Object],[object Object],[object Object],[object Object]
Investigation  (continued) f(x) = sin x h(x) = cos x  g(x) = x y(x) = x 2 v(x) = tan x w(x) = x 3 5.  Test your conjecture by exploring the graphs of various products of the following functions:
Quotient Graphs f(x) =  1  (odd) x g(x) =  1  (even) x 2 p(x) =  1  (odd) x 3 q(x) =  1  (even) x 4
Quotients of Functions  ,[object Object],[object Object],[object Object]
Purpose ,[object Object],[object Object]
Purpose  (continued.) ,[object Object]

More Related Content

What's hot

Inverse functions 13
Inverse functions 13Inverse functions 13
Inverse functions 13
Shaun Wilson
 
Parent Function Project
Parent Function ProjectParent Function Project
Parent Function Project
Joanne Rosa Crooks
 
Function Operations
Function OperationsFunction Operations
Function Operationsswartzje
 
2.4 operations on functions
2.4 operations on functions2.4 operations on functions
2.4 operations on functionshisema01
 
2.7 Piecewise Functions
2.7 Piecewise Functions2.7 Piecewise Functions
2.7 Piecewise Functionshisema01
 
Derivative investigation
Derivative investigationDerivative investigation
Derivative investigationjchartiersjsd
 
The Algebric Functions
The Algebric FunctionsThe Algebric Functions
The Algebric Functionsitutor
 
Inverse Functions
Inverse FunctionsInverse Functions
Inverse Functionsswartzje
 
Math - Operations on Functions, Kinds of Functions
Math - Operations on Functions, Kinds of FunctionsMath - Operations on Functions, Kinds of Functions
Math - Operations on Functions, Kinds of Functions
Chuckie Balbuena
 
Day 3a examples
Day 3a examplesDay 3a examples
Day 3a examplesjchartiersjsd
 
PCExam 1 study guide answers
PCExam 1 study guide answersPCExam 1 study guide answers
PCExam 1 study guide answersvhiggins1
 
Functions
FunctionsFunctions
Functions
JRMorano
 
Basics of functions continued
Basics of functions continuedBasics of functions continued
Basics of functions continuedcpirie0607
 
Day 4 examples u8f13
Day 4 examples u8f13Day 4 examples u8f13
Day 4 examples u8f13jchartiersjsd
 
Piecewise functions updated_2016
Piecewise functions updated_2016Piecewise functions updated_2016
Piecewise functions updated_2016
Benjamin Madrigal
 
Operations With Functions May 25 2009
Operations With Functions May 25 2009Operations With Functions May 25 2009
Operations With Functions May 25 2009ingroy
 
8.4 Rules For Linear Functions
8.4 Rules For Linear Functions8.4 Rules For Linear Functions
8.4 Rules For Linear Functions
Jessca Lundin
 
Piecewise function lesson 3
Piecewise function lesson 3Piecewise function lesson 3
Piecewise function lesson 3aksetter
 
Forms of Quadratics
Forms of QuadraticsForms of Quadratics
Forms of Quadratics
mrodolewicz
 

What's hot (20)

Inverse functions 13
Inverse functions 13Inverse functions 13
Inverse functions 13
 
Parent Function Project
Parent Function ProjectParent Function Project
Parent Function Project
 
Function Operations
Function OperationsFunction Operations
Function Operations
 
2.4 operations on functions
2.4 operations on functions2.4 operations on functions
2.4 operations on functions
 
2.7 Piecewise Functions
2.7 Piecewise Functions2.7 Piecewise Functions
2.7 Piecewise Functions
 
Derivative investigation
Derivative investigationDerivative investigation
Derivative investigation
 
The Algebric Functions
The Algebric FunctionsThe Algebric Functions
The Algebric Functions
 
Inverse functions (2)
Inverse functions (2)Inverse functions (2)
Inverse functions (2)
 
Inverse Functions
Inverse FunctionsInverse Functions
Inverse Functions
 
Math - Operations on Functions, Kinds of Functions
Math - Operations on Functions, Kinds of FunctionsMath - Operations on Functions, Kinds of Functions
Math - Operations on Functions, Kinds of Functions
 
Day 3a examples
Day 3a examplesDay 3a examples
Day 3a examples
 
PCExam 1 study guide answers
PCExam 1 study guide answersPCExam 1 study guide answers
PCExam 1 study guide answers
 
Functions
FunctionsFunctions
Functions
 
Basics of functions continued
Basics of functions continuedBasics of functions continued
Basics of functions continued
 
Day 4 examples u8f13
Day 4 examples u8f13Day 4 examples u8f13
Day 4 examples u8f13
 
Piecewise functions updated_2016
Piecewise functions updated_2016Piecewise functions updated_2016
Piecewise functions updated_2016
 
Operations With Functions May 25 2009
Operations With Functions May 25 2009Operations With Functions May 25 2009
Operations With Functions May 25 2009
 
8.4 Rules For Linear Functions
8.4 Rules For Linear Functions8.4 Rules For Linear Functions
8.4 Rules For Linear Functions
 
Piecewise function lesson 3
Piecewise function lesson 3Piecewise function lesson 3
Piecewise function lesson 3
 
Forms of Quadratics
Forms of QuadraticsForms of Quadratics
Forms of Quadratics
 

Viewers also liked

Trig identities
Trig identitiesTrig identities
Trig identitiestschmucker
 
Trig Identities Calc I
Trig Identities Calc ITrig Identities Calc I
Trig Identities Calc Itschmucker
 
Trigonometric identities simplify
Trigonometric identities simplifyTrigonometric identities simplify
Trigonometric identities simplifyJessica Garcia
 
Quotient groups-Group theory
Quotient groups-Group theoryQuotient groups-Group theory
Quotient groups-Group theory
Ayush Agrawal
 
Analytic Trigonometry
Analytic TrigonometryAnalytic Trigonometry
Analytic Trigonometry
Kristen T
 
Trigonometric Identities.
Trigonometric Identities. Trigonometric Identities.
Trigonometric Identities.
jhey2
 

Viewers also liked (6)

Trig identities
Trig identitiesTrig identities
Trig identities
 
Trig Identities Calc I
Trig Identities Calc ITrig Identities Calc I
Trig Identities Calc I
 
Trigonometric identities simplify
Trigonometric identities simplifyTrigonometric identities simplify
Trigonometric identities simplify
 
Quotient groups-Group theory
Quotient groups-Group theoryQuotient groups-Group theory
Quotient groups-Group theory
 
Analytic Trigonometry
Analytic TrigonometryAnalytic Trigonometry
Analytic Trigonometry
 
Trigonometric Identities.
Trigonometric Identities. Trigonometric Identities.
Trigonometric Identities.
 

Similar to Products And Quotients

Chapter 1 (math 1)
Chapter 1 (math 1)Chapter 1 (math 1)
Chapter 1 (math 1)
Amr Mohamed
 
Functions
FunctionsFunctions
Functions
Motlalepula Mokhele
 
Module 2 quadratic functions
Module 2   quadratic functionsModule 2   quadratic functions
Module 2 quadratic functions
dionesioable
 
exponen dan logaritma
exponen dan logaritmaexponen dan logaritma
exponen dan logaritma
Hanifa Zulfitri
 
Grph quad fncts
Grph quad fnctsGrph quad fncts
Grph quad fncts
Edrian Gustin Camacho
 
Algebra 1
Algebra 1Algebra 1
Algebra 1
April Smith
 
Module 1 quadratic functions
Module 1   quadratic functionsModule 1   quadratic functions
Module 1 quadratic functions
dionesioable
 
Ch 3 lessons
Ch  3 lessons Ch  3 lessons
Ch 3 lessons
mikewilmes
 
Review
ReviewReview
Functions for Grade 10
Functions for Grade 10Functions for Grade 10
Functions for Grade 10Boipelo Radebe
 
Module1 exponential functions
Module1  exponential functionsModule1  exponential functions
Module1 exponential functions
dionesioable
 
Algebra 2 Section 5-1
Algebra 2 Section 5-1Algebra 2 Section 5-1
Algebra 2 Section 5-1
Jimbo Lamb
 
Module 3 exponential and logarithmic functions
Module 3   exponential and logarithmic functionsModule 3   exponential and logarithmic functions
Module 3 exponential and logarithmic functions
dionesioable
 
Higher formal homeworks unit 1
Higher formal homeworks   unit 1Higher formal homeworks   unit 1
Higher formal homeworks unit 1
sjamaths
 
Mathematics 9 Quadratic Functions (Module 2)
Mathematics 9 Quadratic Functions (Module 2)Mathematics 9 Quadratic Functions (Module 2)
Mathematics 9 Quadratic Functions (Module 2)
Juan Miguel Palero
 
How to graph Functions
How to graph FunctionsHow to graph Functions
How to graph Functionscoolhanddav
 
4 4 graphingfx
4 4 graphingfx4 4 graphingfx
4 4 graphingfxcoolhanddav
 
Integration_of_Rational_Functions_by_Partial_Fraction.ppt
Integration_of_Rational_Functions_by_Partial_Fraction.pptIntegration_of_Rational_Functions_by_Partial_Fraction.ppt
Integration_of_Rational_Functions_by_Partial_Fraction.ppt
silva765736
 
Mathematics 9 Quadratic Functions (Module 1)
Mathematics 9 Quadratic Functions (Module 1)Mathematics 9 Quadratic Functions (Module 1)
Mathematics 9 Quadratic Functions (Module 1)
Juan Miguel Palero
 

Similar to Products And Quotients (20)

Chapter 1 (math 1)
Chapter 1 (math 1)Chapter 1 (math 1)
Chapter 1 (math 1)
 
Functions
FunctionsFunctions
Functions
 
Module 2 quadratic functions
Module 2   quadratic functionsModule 2   quadratic functions
Module 2 quadratic functions
 
exponen dan logaritma
exponen dan logaritmaexponen dan logaritma
exponen dan logaritma
 
Grph quad fncts
Grph quad fnctsGrph quad fncts
Grph quad fncts
 
Algebra 1
Algebra 1Algebra 1
Algebra 1
 
Module 1 quadratic functions
Module 1   quadratic functionsModule 1   quadratic functions
Module 1 quadratic functions
 
Ch 3 lessons
Ch  3 lessons Ch  3 lessons
Ch 3 lessons
 
Review
ReviewReview
Review
 
Functions for Grade 10
Functions for Grade 10Functions for Grade 10
Functions for Grade 10
 
Module1 exponential functions
Module1  exponential functionsModule1  exponential functions
Module1 exponential functions
 
Algebra 2 Section 5-1
Algebra 2 Section 5-1Algebra 2 Section 5-1
Algebra 2 Section 5-1
 
Module 3 exponential and logarithmic functions
Module 3   exponential and logarithmic functionsModule 3   exponential and logarithmic functions
Module 3 exponential and logarithmic functions
 
Higher formal homeworks unit 1
Higher formal homeworks   unit 1Higher formal homeworks   unit 1
Higher formal homeworks unit 1
 
Mathematics 9 Quadratic Functions (Module 2)
Mathematics 9 Quadratic Functions (Module 2)Mathematics 9 Quadratic Functions (Module 2)
Mathematics 9 Quadratic Functions (Module 2)
 
Quadratic functions
Quadratic functionsQuadratic functions
Quadratic functions
 
How to graph Functions
How to graph FunctionsHow to graph Functions
How to graph Functions
 
4 4 graphingfx
4 4 graphingfx4 4 graphingfx
4 4 graphingfx
 
Integration_of_Rational_Functions_by_Partial_Fraction.ppt
Integration_of_Rational_Functions_by_Partial_Fraction.pptIntegration_of_Rational_Functions_by_Partial_Fraction.ppt
Integration_of_Rational_Functions_by_Partial_Fraction.ppt
 
Mathematics 9 Quadratic Functions (Module 1)
Mathematics 9 Quadratic Functions (Module 1)Mathematics 9 Quadratic Functions (Module 1)
Mathematics 9 Quadratic Functions (Module 1)
 

Recently uploaded

Generating a custom Ruby SDK for your web service or Rails API using Smithy
Generating a custom Ruby SDK for your web service or Rails API using SmithyGenerating a custom Ruby SDK for your web service or Rails API using Smithy
Generating a custom Ruby SDK for your web service or Rails API using Smithy
g2nightmarescribd
 
Encryption in Microsoft 365 - ExpertsLive Netherlands 2024
Encryption in Microsoft 365 - ExpertsLive Netherlands 2024Encryption in Microsoft 365 - ExpertsLive Netherlands 2024
Encryption in Microsoft 365 - ExpertsLive Netherlands 2024
Albert Hoitingh
 
FIDO Alliance Osaka Seminar: Passkeys at Amazon.pdf
FIDO Alliance Osaka Seminar: Passkeys at Amazon.pdfFIDO Alliance Osaka Seminar: Passkeys at Amazon.pdf
FIDO Alliance Osaka Seminar: Passkeys at Amazon.pdf
FIDO Alliance
 
LF Energy Webinar: Electrical Grid Modelling and Simulation Through PowSyBl -...
LF Energy Webinar: Electrical Grid Modelling and Simulation Through PowSyBl -...LF Energy Webinar: Electrical Grid Modelling and Simulation Through PowSyBl -...
LF Energy Webinar: Electrical Grid Modelling and Simulation Through PowSyBl -...
DanBrown980551
 
Essentials of Automations: Optimizing FME Workflows with Parameters
Essentials of Automations: Optimizing FME Workflows with ParametersEssentials of Automations: Optimizing FME Workflows with Parameters
Essentials of Automations: Optimizing FME Workflows with Parameters
Safe Software
 
Software Delivery At the Speed of AI: Inflectra Invests In AI-Powered Quality
Software Delivery At the Speed of AI: Inflectra Invests In AI-Powered QualitySoftware Delivery At the Speed of AI: Inflectra Invests In AI-Powered Quality
Software Delivery At the Speed of AI: Inflectra Invests In AI-Powered Quality
Inflectra
 
Key Trends Shaping the Future of Infrastructure.pdf
Key Trends Shaping the Future of Infrastructure.pdfKey Trends Shaping the Future of Infrastructure.pdf
Key Trends Shaping the Future of Infrastructure.pdf
Cheryl Hung
 
Empowering NextGen Mobility via Large Action Model Infrastructure (LAMI): pav...
Empowering NextGen Mobility via Large Action Model Infrastructure (LAMI): pav...Empowering NextGen Mobility via Large Action Model Infrastructure (LAMI): pav...
Empowering NextGen Mobility via Large Action Model Infrastructure (LAMI): pav...
Thierry Lestable
 
GDG Cloud Southlake #33: Boule & Rebala: Effective AppSec in SDLC using Deplo...
GDG Cloud Southlake #33: Boule & Rebala: Effective AppSec in SDLC using Deplo...GDG Cloud Southlake #33: Boule & Rebala: Effective AppSec in SDLC using Deplo...
GDG Cloud Southlake #33: Boule & Rebala: Effective AppSec in SDLC using Deplo...
James Anderson
 
Slack (or Teams) Automation for Bonterra Impact Management (fka Social Soluti...
Slack (or Teams) Automation for Bonterra Impact Management (fka Social Soluti...Slack (or Teams) Automation for Bonterra Impact Management (fka Social Soluti...
Slack (or Teams) Automation for Bonterra Impact Management (fka Social Soluti...
Jeffrey Haguewood
 
To Graph or Not to Graph Knowledge Graph Architectures and LLMs
To Graph or Not to Graph Knowledge Graph Architectures and LLMsTo Graph or Not to Graph Knowledge Graph Architectures and LLMs
To Graph or Not to Graph Knowledge Graph Architectures and LLMs
Paul Groth
 
How world-class product teams are winning in the AI era by CEO and Founder, P...
How world-class product teams are winning in the AI era by CEO and Founder, P...How world-class product teams are winning in the AI era by CEO and Founder, P...
How world-class product teams are winning in the AI era by CEO and Founder, P...
Product School
 
FIDO Alliance Osaka Seminar: The WebAuthn API and Discoverable Credentials.pdf
FIDO Alliance Osaka Seminar: The WebAuthn API and Discoverable Credentials.pdfFIDO Alliance Osaka Seminar: The WebAuthn API and Discoverable Credentials.pdf
FIDO Alliance Osaka Seminar: The WebAuthn API and Discoverable Credentials.pdf
FIDO Alliance
 
The Future of Platform Engineering
The Future of Platform EngineeringThe Future of Platform Engineering
The Future of Platform Engineering
Jemma Hussein Allen
 
FIDO Alliance Osaka Seminar: Passkeys and the Road Ahead.pdf
FIDO Alliance Osaka Seminar: Passkeys and the Road Ahead.pdfFIDO Alliance Osaka Seminar: Passkeys and the Road Ahead.pdf
FIDO Alliance Osaka Seminar: Passkeys and the Road Ahead.pdf
FIDO Alliance
 
The Art of the Pitch: WordPress Relationships and Sales
The Art of the Pitch: WordPress Relationships and SalesThe Art of the Pitch: WordPress Relationships and Sales
The Art of the Pitch: WordPress Relationships and Sales
Laura Byrne
 
Knowledge engineering: from people to machines and back
Knowledge engineering: from people to machines and backKnowledge engineering: from people to machines and back
Knowledge engineering: from people to machines and back
Elena Simperl
 
Builder.ai Founder Sachin Dev Duggal's Strategic Approach to Create an Innova...
Builder.ai Founder Sachin Dev Duggal's Strategic Approach to Create an Innova...Builder.ai Founder Sachin Dev Duggal's Strategic Approach to Create an Innova...
Builder.ai Founder Sachin Dev Duggal's Strategic Approach to Create an Innova...
Ramesh Iyer
 
Bits & Pixels using AI for Good.........
Bits & Pixels using AI for Good.........Bits & Pixels using AI for Good.........
Bits & Pixels using AI for Good.........
Alison B. Lowndes
 
GraphRAG is All You need? LLM & Knowledge Graph
GraphRAG is All You need? LLM & Knowledge GraphGraphRAG is All You need? LLM & Knowledge Graph
GraphRAG is All You need? LLM & Knowledge Graph
Guy Korland
 

Recently uploaded (20)

Generating a custom Ruby SDK for your web service or Rails API using Smithy
Generating a custom Ruby SDK for your web service or Rails API using SmithyGenerating a custom Ruby SDK for your web service or Rails API using Smithy
Generating a custom Ruby SDK for your web service or Rails API using Smithy
 
Encryption in Microsoft 365 - ExpertsLive Netherlands 2024
Encryption in Microsoft 365 - ExpertsLive Netherlands 2024Encryption in Microsoft 365 - ExpertsLive Netherlands 2024
Encryption in Microsoft 365 - ExpertsLive Netherlands 2024
 
FIDO Alliance Osaka Seminar: Passkeys at Amazon.pdf
FIDO Alliance Osaka Seminar: Passkeys at Amazon.pdfFIDO Alliance Osaka Seminar: Passkeys at Amazon.pdf
FIDO Alliance Osaka Seminar: Passkeys at Amazon.pdf
 
LF Energy Webinar: Electrical Grid Modelling and Simulation Through PowSyBl -...
LF Energy Webinar: Electrical Grid Modelling and Simulation Through PowSyBl -...LF Energy Webinar: Electrical Grid Modelling and Simulation Through PowSyBl -...
LF Energy Webinar: Electrical Grid Modelling and Simulation Through PowSyBl -...
 
Essentials of Automations: Optimizing FME Workflows with Parameters
Essentials of Automations: Optimizing FME Workflows with ParametersEssentials of Automations: Optimizing FME Workflows with Parameters
Essentials of Automations: Optimizing FME Workflows with Parameters
 
Software Delivery At the Speed of AI: Inflectra Invests In AI-Powered Quality
Software Delivery At the Speed of AI: Inflectra Invests In AI-Powered QualitySoftware Delivery At the Speed of AI: Inflectra Invests In AI-Powered Quality
Software Delivery At the Speed of AI: Inflectra Invests In AI-Powered Quality
 
Key Trends Shaping the Future of Infrastructure.pdf
Key Trends Shaping the Future of Infrastructure.pdfKey Trends Shaping the Future of Infrastructure.pdf
Key Trends Shaping the Future of Infrastructure.pdf
 
Empowering NextGen Mobility via Large Action Model Infrastructure (LAMI): pav...
Empowering NextGen Mobility via Large Action Model Infrastructure (LAMI): pav...Empowering NextGen Mobility via Large Action Model Infrastructure (LAMI): pav...
Empowering NextGen Mobility via Large Action Model Infrastructure (LAMI): pav...
 
GDG Cloud Southlake #33: Boule & Rebala: Effective AppSec in SDLC using Deplo...
GDG Cloud Southlake #33: Boule & Rebala: Effective AppSec in SDLC using Deplo...GDG Cloud Southlake #33: Boule & Rebala: Effective AppSec in SDLC using Deplo...
GDG Cloud Southlake #33: Boule & Rebala: Effective AppSec in SDLC using Deplo...
 
Slack (or Teams) Automation for Bonterra Impact Management (fka Social Soluti...
Slack (or Teams) Automation for Bonterra Impact Management (fka Social Soluti...Slack (or Teams) Automation for Bonterra Impact Management (fka Social Soluti...
Slack (or Teams) Automation for Bonterra Impact Management (fka Social Soluti...
 
To Graph or Not to Graph Knowledge Graph Architectures and LLMs
To Graph or Not to Graph Knowledge Graph Architectures and LLMsTo Graph or Not to Graph Knowledge Graph Architectures and LLMs
To Graph or Not to Graph Knowledge Graph Architectures and LLMs
 
How world-class product teams are winning in the AI era by CEO and Founder, P...
How world-class product teams are winning in the AI era by CEO and Founder, P...How world-class product teams are winning in the AI era by CEO and Founder, P...
How world-class product teams are winning in the AI era by CEO and Founder, P...
 
FIDO Alliance Osaka Seminar: The WebAuthn API and Discoverable Credentials.pdf
FIDO Alliance Osaka Seminar: The WebAuthn API and Discoverable Credentials.pdfFIDO Alliance Osaka Seminar: The WebAuthn API and Discoverable Credentials.pdf
FIDO Alliance Osaka Seminar: The WebAuthn API and Discoverable Credentials.pdf
 
The Future of Platform Engineering
The Future of Platform EngineeringThe Future of Platform Engineering
The Future of Platform Engineering
 
FIDO Alliance Osaka Seminar: Passkeys and the Road Ahead.pdf
FIDO Alliance Osaka Seminar: Passkeys and the Road Ahead.pdfFIDO Alliance Osaka Seminar: Passkeys and the Road Ahead.pdf
FIDO Alliance Osaka Seminar: Passkeys and the Road Ahead.pdf
 
The Art of the Pitch: WordPress Relationships and Sales
The Art of the Pitch: WordPress Relationships and SalesThe Art of the Pitch: WordPress Relationships and Sales
The Art of the Pitch: WordPress Relationships and Sales
 
Knowledge engineering: from people to machines and back
Knowledge engineering: from people to machines and backKnowledge engineering: from people to machines and back
Knowledge engineering: from people to machines and back
 
Builder.ai Founder Sachin Dev Duggal's Strategic Approach to Create an Innova...
Builder.ai Founder Sachin Dev Duggal's Strategic Approach to Create an Innova...Builder.ai Founder Sachin Dev Duggal's Strategic Approach to Create an Innova...
Builder.ai Founder Sachin Dev Duggal's Strategic Approach to Create an Innova...
 
Bits & Pixels using AI for Good.........
Bits & Pixels using AI for Good.........Bits & Pixels using AI for Good.........
Bits & Pixels using AI for Good.........
 
GraphRAG is All You need? LLM & Knowledge Graph
GraphRAG is All You need? LLM & Knowledge GraphGraphRAG is All You need? LLM & Knowledge Graph
GraphRAG is All You need? LLM & Knowledge Graph
 

Products And Quotients

  • 1. Introduction: Products and Quotients of Functions
  • 2.
  • 3.
  • 4.
  • 5.
  • 6. Investigation (continued) 3. Examine the pattern of symmetry of the function on the left side and right side of each identity in step 2. Copy and complete the table. q(x) = x 4 (even) g(x) = x 2 (g(x)) 2 = q(x) g(x) = x 2 (even) f(x) = x (odd) f(x)f(x) = g(x) q(x) = x 4 (even) f(x) = x (odd) p(x) = x 3 (odd) f(x)p(x) = q(x) p(x) = x 3 (odd) f(x) = x (odd) g(x) = x 2 (even) f(x)g(x) = p(x) Symmetry of Product Function Symmetry of Factor Functions Identity
  • 7.
  • 8. Investigation (continued) f(x) = sin x h(x) = cos x g(x) = x y(x) = x 2 v(x) = tan x w(x) = x 3 5. Test your conjecture by exploring the graphs of various products of the following functions:
  • 9. Quotient Graphs f(x) = 1 (odd) x g(x) = 1 (even) x 2 p(x) = 1 (odd) x 3 q(x) = 1 (even) x 4
  • 10.
  • 11.
  • 12.