Subjects

Subjects

More

Search

AI Knowunity

Subjects

/

Algebra 2

/

Polynomial Graphs

/

Positive and Negative Intervals of Polynomials

Easy Steps to Do Function Operations: Fun with Composite Functions!

View

Easy Steps to Do Function Operations: Fun with Composite Functions!
user profile picture

Trevor

@trevk

·

4 Followers

Follow

How to perform operations with functions and understand composition of functions step by step through comprehensive examples and practice problems.

A detailed guide covering function operations, composition, and practical applications in mathematical problem-solving.

Key points:

  • Basic operations include addition, subtraction, multiplication, and division of functions
  • Function composition involves applying one function to the results of another
  • Restrictions and domains must be considered when performing operations
  • Understanding notation and proper order of operations is crucial
  • Real-world applications demonstrate practical use of function operations

11/17/2023

23

SUM PRODUCT OPERATIONS WITH FUNCTIONS ƒ+8=(ƒ+8)(x)= f(x)+g(x) DIFFERENCE_ƒ-8=(ƒ-8)(x)=_f(x)-g(x) ƒ•g=(ƒ•g)(x) = f(x) •g(x) Operations with F

View

Page 2: Introduction to Function Composition

This section explores the concept of function composition and its notation methods.

Definition: Function composition is the application of one function to the results of another, written as (f∘g)(x) or f(g(x)).

Vocabulary: "f∘g" is read as "f of g" or "g into f"

Example: For f(x)=3x+2 and g(x)=2x-1, the composition (f∘g)(x)=6x-1

The page emphasizes:

  • Different notation methods for composition
  • Step-by-step process of composing functions
  • Importance of understanding input and output relationships
SUM PRODUCT OPERATIONS WITH FUNCTIONS ƒ+8=(ƒ+8)(x)= f(x)+g(x) DIFFERENCE_ƒ-8=(ƒ-8)(x)=_f(x)-g(x) ƒ•g=(ƒ•g)(x) = f(x) •g(x) Operations with F

View

Page 3: Evaluating Function Composition

This page details the process of evaluating function composition with specific values.

Highlight: To find (f∘g)(value), first calculate g(value), then use that result as input for f.

Example: For f(x)=x²+4 and g(x)=2x, to find (f∘g)(2):

  1. Calculate g(2)=4
  2. Then calculate f(4)=20

The page covers:

  • Composition with numerical values
  • Composition with variables
  • Multiple examples of both types
SUM PRODUCT OPERATIONS WITH FUNCTIONS ƒ+8=(ƒ+8)(x)= f(x)+g(x) DIFFERENCE_ƒ-8=(ƒ-8)(x)=_f(x)-g(x) ƒ•g=(ƒ•g)(x) = f(x) •g(x) Operations with F

View

Page 4: Properties of Function Composition

This section explores important properties and characteristics of function composition.

Quote: "In most cases (f∘g)(x)≠(g∘f)(x) therefore composition of functions is not commutative."

Example: Using ordered pairs and graphs to demonstrate composition: For f={(2,3),(-1,1),(0,0)} and g={(-3,1),(-1,-2),(0,2)}, find (f∘g)(0)

The page includes:

  • Visual representations of function composition
  • Working with ordered pairs
  • Non-commutative property demonstration
SUM PRODUCT OPERATIONS WITH FUNCTIONS ƒ+8=(ƒ+8)(x)= f(x)+g(x) DIFFERENCE_ƒ-8=(ƒ-8)(x)=_f(x)-g(x) ƒ•g=(ƒ•g)(x) = f(x) •g(x) Operations with F

View

Page 5: Advanced Operations and Compositions

This page presents more complex operations and compositions with various function types.

Highlight: When finding composite functions, always state necessary restrictions in the domain.

Example: For f(x)=2x+5 and g(x)=x²-1: (f∘g)(x)=2(x²-1)+5=2x²-2+5=2x²+3

The content covers:

  • Multiple function operations
  • Complex compositions
  • Domain restrictions
  • Practical applications
SUM PRODUCT OPERATIONS WITH FUNCTIONS ƒ+8=(ƒ+8)(x)= f(x)+g(x) DIFFERENCE_ƒ-8=(ƒ-8)(x)=_f(x)-g(x) ƒ•g=(ƒ•g)(x) = f(x) •g(x) Operations with F

View

Page 6: Practice Problems and Applications

The final page provides additional practice problems and real-world applications.

Example: Given f(x)=4x-1, j(x)=x²-6x, k(x)=-x+4: (f+j)(x)=x²-2x-1

Highlight: Pay special attention to restrictions when working with composite functions.

The page includes:

  • Comprehensive practice problems
  • Multiple-step compositions
  • Domain restriction analysis
  • Complex function operations
SUM PRODUCT OPERATIONS WITH FUNCTIONS ƒ+8=(ƒ+8)(x)= f(x)+g(x) DIFFERENCE_ƒ-8=(ƒ-8)(x)=_f(x)-g(x) ƒ•g=(ƒ•g)(x) = f(x) •g(x) Operations with F

View

Page 1: Basic Operations with Functions

This page introduces fundamental operations with functions, focusing on sum, product, difference, and quotient operations.

Definition: Operations with functions involve combining two functions using basic mathematical operations to create new functions.

Example: For functions f(x)=4x²+6x-9 and g(x)=6x²-x+2, the sum (f+g)(x) = 10x²+5x-7

Highlight: When performing division of functions, always remember to state the restriction g(x)≠0.

The page demonstrates several key operations:

  • Addition and subtraction of polynomial functions
  • Multiplication of functions
  • Division with attention to restrictions

Similar Content

Know Midterm Study Guide: Review of the First Half of the Course thumbnail

119

1110

9th/10th

Midterm Study Guide: Review of the First Half of the Course

Simple review notes and examples for the first half of the algebra 2 course! Not all classes teach the content in the same order, but this study guide should have most of the more basic concepts from algebra 2!

Can't find what you're looking for? Explore other subjects.

Knowunity is the # 1 ranked education app in five European countries

Knowunity was a featured story by Apple and has consistently topped the app store charts within the education category in Germany, Italy, Poland, Switzerland and United Kingdom. Join Knowunity today and help millions of students around the world.

Ranked #1 Education App

Download in

Google Play

Download in

App Store

Knowunity is the # 1 ranked education app in five European countries

4.9+

Average App Rating

15 M

Students use Knowunity

#1

In Education App Charts in 12 Countries

950 K+

Students uploaded study notes

Still not sure? Look at what your fellow peers are saying...

iOS User

I love this app so much [...] I recommend Knowunity to everyone!!! I went from a C to an A with it :D

Stefan S, iOS User

The application is very simple and well designed. So far I have found what I was looking for :D

SuSSan, iOS User

Love this App ❤️, I use it basically all the time whenever I'm studying

Subjects

/

Algebra 2

/

Polynomial Graphs

/

Positive and Negative Intervals of Polynomials

Easy Steps to Do Function Operations: Fun with Composite Functions!

user profile picture

Trevor

@trevk

·

4 Followers

Follow

How to perform operations with functions and understand composition of functions step by step through comprehensive examples and practice problems.

A detailed guide covering function operations, composition, and practical applications in mathematical problem-solving.

Key points:

  • Basic operations include addition, subtraction, multiplication, and division of functions
  • Function composition involves applying one function to the results of another
  • Restrictions and domains must be considered when performing operations
  • Understanding notation and proper order of operations is crucial
  • Real-world applications demonstrate practical use of function operations

11/17/2023

23

 

10th/11th

 

Algebra 2

3

SUM PRODUCT OPERATIONS WITH FUNCTIONS ƒ+8=(ƒ+8)(x)= f(x)+g(x) DIFFERENCE_ƒ-8=(ƒ-8)(x)=_f(x)-g(x) ƒ•g=(ƒ•g)(x) = f(x) •g(x) Operations with F

Sign up to see the content. It's free!

Access to all documents

Improve your grades

Join milions of students

By signing up you accept Terms of Service and Privacy Policy

Page 2: Introduction to Function Composition

This section explores the concept of function composition and its notation methods.

Definition: Function composition is the application of one function to the results of another, written as (f∘g)(x) or f(g(x)).

Vocabulary: "f∘g" is read as "f of g" or "g into f"

Example: For f(x)=3x+2 and g(x)=2x-1, the composition (f∘g)(x)=6x-1

The page emphasizes:

  • Different notation methods for composition
  • Step-by-step process of composing functions
  • Importance of understanding input and output relationships
SUM PRODUCT OPERATIONS WITH FUNCTIONS ƒ+8=(ƒ+8)(x)= f(x)+g(x) DIFFERENCE_ƒ-8=(ƒ-8)(x)=_f(x)-g(x) ƒ•g=(ƒ•g)(x) = f(x) •g(x) Operations with F

Sign up to see the content. It's free!

Access to all documents

Improve your grades

Join milions of students

By signing up you accept Terms of Service and Privacy Policy

Page 3: Evaluating Function Composition

This page details the process of evaluating function composition with specific values.

Highlight: To find (f∘g)(value), first calculate g(value), then use that result as input for f.

Example: For f(x)=x²+4 and g(x)=2x, to find (f∘g)(2):

  1. Calculate g(2)=4
  2. Then calculate f(4)=20

The page covers:

  • Composition with numerical values
  • Composition with variables
  • Multiple examples of both types
SUM PRODUCT OPERATIONS WITH FUNCTIONS ƒ+8=(ƒ+8)(x)= f(x)+g(x) DIFFERENCE_ƒ-8=(ƒ-8)(x)=_f(x)-g(x) ƒ•g=(ƒ•g)(x) = f(x) •g(x) Operations with F

Sign up to see the content. It's free!

Access to all documents

Improve your grades

Join milions of students

By signing up you accept Terms of Service and Privacy Policy

Page 4: Properties of Function Composition

This section explores important properties and characteristics of function composition.

Quote: "In most cases (f∘g)(x)≠(g∘f)(x) therefore composition of functions is not commutative."

Example: Using ordered pairs and graphs to demonstrate composition: For f={(2,3),(-1,1),(0,0)} and g={(-3,1),(-1,-2),(0,2)}, find (f∘g)(0)

The page includes:

  • Visual representations of function composition
  • Working with ordered pairs
  • Non-commutative property demonstration
SUM PRODUCT OPERATIONS WITH FUNCTIONS ƒ+8=(ƒ+8)(x)= f(x)+g(x) DIFFERENCE_ƒ-8=(ƒ-8)(x)=_f(x)-g(x) ƒ•g=(ƒ•g)(x) = f(x) •g(x) Operations with F

Sign up to see the content. It's free!

Access to all documents

Improve your grades

Join milions of students

By signing up you accept Terms of Service and Privacy Policy

Page 5: Advanced Operations and Compositions

This page presents more complex operations and compositions with various function types.

Highlight: When finding composite functions, always state necessary restrictions in the domain.

Example: For f(x)=2x+5 and g(x)=x²-1: (f∘g)(x)=2(x²-1)+5=2x²-2+5=2x²+3

The content covers:

  • Multiple function operations
  • Complex compositions
  • Domain restrictions
  • Practical applications
SUM PRODUCT OPERATIONS WITH FUNCTIONS ƒ+8=(ƒ+8)(x)= f(x)+g(x) DIFFERENCE_ƒ-8=(ƒ-8)(x)=_f(x)-g(x) ƒ•g=(ƒ•g)(x) = f(x) •g(x) Operations with F

Sign up to see the content. It's free!

Access to all documents

Improve your grades

Join milions of students

By signing up you accept Terms of Service and Privacy Policy

Page 6: Practice Problems and Applications

The final page provides additional practice problems and real-world applications.

Example: Given f(x)=4x-1, j(x)=x²-6x, k(x)=-x+4: (f+j)(x)=x²-2x-1

Highlight: Pay special attention to restrictions when working with composite functions.

The page includes:

  • Comprehensive practice problems
  • Multiple-step compositions
  • Domain restriction analysis
  • Complex function operations
SUM PRODUCT OPERATIONS WITH FUNCTIONS ƒ+8=(ƒ+8)(x)= f(x)+g(x) DIFFERENCE_ƒ-8=(ƒ-8)(x)=_f(x)-g(x) ƒ•g=(ƒ•g)(x) = f(x) •g(x) Operations with F

Sign up to see the content. It's free!

Access to all documents

Improve your grades

Join milions of students

By signing up you accept Terms of Service and Privacy Policy

Page 1: Basic Operations with Functions

This page introduces fundamental operations with functions, focusing on sum, product, difference, and quotient operations.

Definition: Operations with functions involve combining two functions using basic mathematical operations to create new functions.

Example: For functions f(x)=4x²+6x-9 and g(x)=6x²-x+2, the sum (f+g)(x) = 10x²+5x-7

Highlight: When performing division of functions, always remember to state the restriction g(x)≠0.

The page demonstrates several key operations:

  • Addition and subtraction of polynomial functions
  • Multiplication of functions
  • Division with attention to restrictions

Similar Content

Algebra 2 - Midterm Study Guide: Review of the First Half of the Course

Simple review notes and examples for the first half of the algebra 2 course! Not all classes teach the content in the same order, but this study guide should have most of the more basic concepts from algebra 2!

119

1110

2

Know Midterm Study Guide: Review of the First Half of the Course thumbnail

Can't find what you're looking for? Explore other subjects.

Knowunity is the # 1 ranked education app in five European countries

Knowunity was a featured story by Apple and has consistently topped the app store charts within the education category in Germany, Italy, Poland, Switzerland and United Kingdom. Join Knowunity today and help millions of students around the world.

Ranked #1 Education App

Download in

Google Play

Download in

App Store

Knowunity is the # 1 ranked education app in five European countries

4.9+

Average App Rating

15 M

Students use Knowunity

#1

In Education App Charts in 12 Countries

950 K+

Students uploaded study notes

Still not sure? Look at what your fellow peers are saying...

iOS User

I love this app so much [...] I recommend Knowunity to everyone!!! I went from a C to an A with it :D

Stefan S, iOS User

The application is very simple and well designed. So far I have found what I was looking for :D

SuSSan, iOS User

Love this App ❤️, I use it basically all the time whenever I'm studying