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Playing with Polynomial Transformations: Graph Cubic and Quartic Functions!

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Divi Zamora

9/27/2023

Algebra 2

Polynomial Transformations

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Algebra 2

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Transformations

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Symmetry of Functions

Playing with Polynomial Transformations: Graph Cubic and Quartic Functions!

A comprehensive guide to polynomial transformations in graphing, covering function types, end behaviors, and symmetry properties.

  • Introduces fundamental concepts of polynomial functions, including cubic and quartic functions
  • Explains end behavior patterns based on degree (odd vs even) and leading coefficients
  • Details methods for identifying even and odd polynomial functions through symmetry tests
  • Demonstrates graphing cubic and quartic functions manually with step-by-step examples
  • Covers function translations and symmetrical properties around axes
...

9/27/2023

160

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Subjects

Algebra 2

Transformations

Symmetry of Functions

 

Algebra 2

•

160

•

Sep 27, 2023

•

1 page

Playing with Polynomial Transformations: Graph Cubic and Quartic Functions!

user profile picture

Divi Zamora

@divizamora68

A comprehensive guide to polynomial transformations in graphing, covering function types, end behaviors, and symmetry properties.

  • Introduces fundamental concepts of polynomial functions, including cubic and quartic functions
  • Explains end behavior patterns based on degree (odd vs even) and leading... Show more

POLYNOMIAL TRANSFORMATIONS POLYNOMIAL FUNCTION: A function composed of one or more terms, at least one of which contains a variable. 3 □CUBI

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Understanding Polynomial Functions and Their Transformations

This page provides a detailed exploration of polynomial functions and their graphical behaviors. The content focuses on essential definitions, end behaviors, and symmetry properties.

Definition: A polynomial function consists of one or more terms, with at least one containing a variable.

Vocabulary:

  • Cubic Function: A polynomial function of degree three f(xf(x=x³)
  • Quartic Function: A polynomial function of degree four f(xf(x=x⁴)

Highlight: End behavior of polynomial functions depends on two key factors:

  1. Degree of polynomial oddvsevenodd vs even
  2. Sign of leading coefficient positivevsnegativepositive vs negative

Example: For odd degree polynomials:

  • Positive leading coefficient: Left side goes down, right side goes up
  • Negative leading coefficient: Left side goes up, right side goes down

Example: For even degree polynomials:

  • Positive leading coefficient: Both sides continue upward
  • Negative leading coefficient: Both sides continue downward

Highlight: Function symmetry can be determined by checking if:

  • f−x-x = fxx for even functions symmetricalabouty−axissymmetrical about y-axis
  • f−x-x = -fxx for odd functions symmetricalaboutoriginsymmetrical about origin
  • Neither condition met for neither even nor odd functions

The page concludes with practical examples of graphing cubic functions and determining function symmetry through coordinate plotting and analysis.

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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❗️❗️⚠️

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Knowunity is the BEST app I’ve used in a minute. This is not an ai review or anything this is genuinely coming from a 7th grade student (I know 2011 im young) but dude this app is a 10/10 i have maintained a 3.8 gpa and have plenty of time for gaming. I love it and my mom is just happy I got good grades

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

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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!

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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.

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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

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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

The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.

Stefan S

iOS user

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

Android user

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

iOS user

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

iOS user

Knowunity is the BEST app I’ve used in a minute. This is not an ai review or anything this is genuinely coming from a 7th grade student (I know 2011 im young) but dude this app is a 10/10 i have maintained a 3.8 gpa and have plenty of time for gaming. I love it and my mom is just happy I got good grades

Brad T

Android user

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

iOS user

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

iOS user

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

iOS user

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