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Fun with Parent Functions and Transformations

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haley lalor

10/23/2023

Algebra 2

Chapter 1.1-1.2

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Transformations

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Shifting Functions

Fun with Parent Functions and Transformations

Parent functions transformations in algebra guide breaks down essential concepts of function transformations and their graphical representations.

  • Covers three main function families: linear, absolute value, and quadratic functions
  • Explores key transformation types including translations, reflections, and stretches/shrinks
  • Demonstrates how to analyze and graph transformed functions using parent functions
  • Focuses on Understanding quadratic function translations and their effects on graphs
  • Includes practical examples of Graphing linear functions with transformations
...

10/23/2023

53

Chapter 1.1-1.2 Section 1.1-Parent Functions and Transformations (Day 1) Parent Functions Family Rule Graph Domain Range sinano Linear f(x)

View

Page 2: Practical Examples of Function Transformations

This page demonstrates practical applications of transformations through detailed examples using tables and graphs.

Example: gxx = x - 4 represents a vertical translation of the parent linear function fxx = x, moving 4 units down.

Example: pxx = -x² shows a reflection of the parent quadratic function fxx = x² across the x-axis.

Highlight: The page emphasizes the importance of using multiple points for accurate graphing and understanding transformations.

Chapter 1.1-1.2 Section 1.1-Parent Functions and Transformations (Day 1) Parent Functions Family Rule Graph Domain Range sinano Linear f(x)

View

Page 3: Transformation Review and Advanced Examples

This page provides a comprehensive review of transformations and introduces more complex examples.

Definition: Vertical stretches and shrinks multiply the function by a constant, affecting the graph's height and width.

Example: fxx = -x + 2 demonstrates both a reflection and vertical translation of the linear parent function.

Vocabulary: Domain refers to all possible input values, while range covers all possible output values.

Chapter 1.1-1.2 Section 1.1-Parent Functions and Transformations (Day 1) Parent Functions Family Rule Graph Domain Range sinano Linear f(x)

View

Page 4: Complex Transformations

This page explores more sophisticated transformation combinations and their effects on different parent functions.

Example: fxx = x + 4| - 3 shows a horizontal translation right 4 units and a vertical translation down 3 units of the absolute value function.

Highlight: Multiple transformations can be applied simultaneously, requiring careful attention to order of operations.

Chapter 1.1-1.2 Section 1.1-Parent Functions and Transformations (Day 1) Parent Functions Family Rule Graph Domain Range sinano Linear f(x)

View

Page 5: Advanced Function Analysis

This page focuses on analyzing more complex transformed functions and their relationships to parent functions.

Example: fxx = -2x+1x + 1² - 1 demonstrates multiple transformations of the quadratic parent function.

Highlight: The page emphasizes the importance of identifying the sequence of transformations for accurate graphing.

Chapter 1.1-1.2 Section 1.1-Parent Functions and Transformations (Day 1) Parent Functions Family Rule Graph Domain Range sinano Linear f(x)

View

Page 6: Practical Applications and Worksheets

This page provides practice problems and real-world applications of function transformations.

Example: Various transformed functions are presented with their parent functions for comparison and analysis.

Highlight: The worksheet format allows students to practice identifying transformations and graphing functions independently.

Chapter 1.1-1.2 Section 1.1-Parent Functions and Transformations (Day 1) Parent Functions Family Rule Graph Domain Range sinano Linear f(x)

View

Page 7: Assessment and Review

This page contains quiz materials and final review problems focusing on function identification and transformation analysis.

Example: hxx = x + 5| + 3 demonstrates a combination of absolute value function transformations.

Highlight: The assessment tests understanding of function families, domains, ranges, and transformation combinations.

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Subjects

Algebra 2

Transformations

Shifting Functions

 

Algebra 2

•

53

•

Oct 23, 2023

•

7 pages

Fun with Parent Functions and Transformations

H

haley lalor

@haleylalor_jdky

Parent functions transformations in algebra guide breaks down essential concepts of function transformations and their graphical representations.

  • Covers three main function families: linear, absolute value, and quadratic functions
  • Explores key transformation types including translations, reflections, and stretches/shrinks
  • Demonstrates how to... Show more

Chapter 1.1-1.2 Section 1.1-Parent Functions and Transformations (Day 1) Parent Functions Family Rule Graph Domain Range sinano Linear f(x)

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Page 2: Practical Examples of Function Transformations

This page demonstrates practical applications of transformations through detailed examples using tables and graphs.

Example: gxx = x - 4 represents a vertical translation of the parent linear function fxx = x, moving 4 units down.

Example: pxx = -x² shows a reflection of the parent quadratic function fxx = x² across the x-axis.

Highlight: The page emphasizes the importance of using multiple points for accurate graphing and understanding transformations.

Chapter 1.1-1.2 Section 1.1-Parent Functions and Transformations (Day 1) Parent Functions Family Rule Graph Domain Range sinano Linear f(x)

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Page 3: Transformation Review and Advanced Examples

This page provides a comprehensive review of transformations and introduces more complex examples.

Definition: Vertical stretches and shrinks multiply the function by a constant, affecting the graph's height and width.

Example: fxx = -x + 2 demonstrates both a reflection and vertical translation of the linear parent function.

Vocabulary: Domain refers to all possible input values, while range covers all possible output values.

Chapter 1.1-1.2 Section 1.1-Parent Functions and Transformations (Day 1) Parent Functions Family Rule Graph Domain Range sinano Linear f(x)

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Page 4: Complex Transformations

This page explores more sophisticated transformation combinations and their effects on different parent functions.

Example: fxx = x + 4| - 3 shows a horizontal translation right 4 units and a vertical translation down 3 units of the absolute value function.

Highlight: Multiple transformations can be applied simultaneously, requiring careful attention to order of operations.

Chapter 1.1-1.2 Section 1.1-Parent Functions and Transformations (Day 1) Parent Functions Family Rule Graph Domain Range sinano Linear f(x)

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Page 5: Advanced Function Analysis

This page focuses on analyzing more complex transformed functions and their relationships to parent functions.

Example: fxx = -2x+1x + 1² - 1 demonstrates multiple transformations of the quadratic parent function.

Highlight: The page emphasizes the importance of identifying the sequence of transformations for accurate graphing.

Chapter 1.1-1.2 Section 1.1-Parent Functions and Transformations (Day 1) Parent Functions Family Rule Graph Domain Range sinano Linear f(x)

Sign up to see the contentIt's free!

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Page 6: Practical Applications and Worksheets

This page provides practice problems and real-world applications of function transformations.

Example: Various transformed functions are presented with their parent functions for comparison and analysis.

Highlight: The worksheet format allows students to practice identifying transformations and graphing functions independently.

Chapter 1.1-1.2 Section 1.1-Parent Functions and Transformations (Day 1) Parent Functions Family Rule Graph Domain Range sinano Linear f(x)

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Page 7: Assessment and Review

This page contains quiz materials and final review problems focusing on function identification and transformation analysis.

Example: hxx = x + 5| + 3 demonstrates a combination of absolute value function transformations.

Highlight: The assessment tests understanding of function families, domains, ranges, and transformation combinations.

Chapter 1.1-1.2 Section 1.1-Parent Functions and Transformations (Day 1) Parent Functions Family Rule Graph Domain Range sinano Linear f(x)

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Page 1: Introduction to Parent Functions and Transformations

This page introduces fundamental concepts of parent functions and their transformations. The content covers three main function families and their basic properties.

Definition: Parent functions are the simplest form of a function family from which other functions can be derived through transformations.

Vocabulary: Transformations are changes to the size, shape, position, or orientation of a graph.

The page outlines key function families:

  • Linear function: fxx = x
  • Absolute value function: fxx = |x|
  • Quadratic function: fxx = x²

Highlight: Two main types of transformations are introduced: translations horizontal/verticalmovementshorizontal/vertical movements and reflections mirrorflipsmirror flips.

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This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.

Samantha Klich

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Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.

Anna

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I think it’s very much worth it and you’ll end up using it a lot once you get the hang of it and even after looking at others notes you can still ask your Artificial intelligence buddy the question and ask to simplify it if you still don’t get it!!! In the end I think it’s worth it 😊👍 ⚠️Also DID I MENTION ITS FREEE YOU DON’T HAVE TO PAY FOR ANYTHING AND STILL GET YOUR GRADES IN PERFECTLY❗️❗️⚠️

Thomas R

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Brad T

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Not only did it help me find the answer but it also showed me alternative ways to solve it. I was horrible in math and science but now I have an a in both subjects. Thanks for the help🤍🤍

David K

iOS user

The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!

Sudenaz Ocak

Android user

In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.

Greenlight Bonnie

Android user

I found this app a couple years ago and it has only gotten better since then. I really love it because it can help with written questions and photo questions. Also, it can find study guides that other people have made as well as flashcard sets and practice tests. The free version is also amazing for students who might not be able to afford it. Would 100% recommend

Aubrey

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Best app if you're in Highschool or Junior high. I have been using this app for 2 school years and it's the best, it's good if you don't have anyone to help you with school work.😋🩷🎀

Marco B

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THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE THE SCHOOLGPT. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮

Elisha

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This app is phenomenal down to the correct info and the various topics you can study! I greatly recommend it for people who struggle with procrastination and those who need homework help. It has been perfectly accurate for world 1 history as far as I’ve seen! Geometry too!

Paul T

iOS user