Precalculus 2: Polynomials and rational functions

🎉 Precalculus 2: Polynomials and Rational Functions 📚

Course Description:

Chapter 1: Polynomials

🚀 S1. Introduction to the Course 🎓

• What this course is all about: its content, structure, and optimal study methods.

🎬 S2. A General Overview 📈

• The significance of polynomials and rational functions in mathematics and beyond.
• An introduction to the key concepts you'll encounter throughout this course.

🧮 S3. Powers, Expressions, and Polynomials 🧰

• Mastering powers with various exponents, polynomial operations (addition, subtraction, scaling, multiplication), and the rules that govern them.
• Learning terminology: monomial, binomial, trinomial, and understanding monic polynomials.
• Solving linear systems and grasping their importance in polynomial manipulation.

📐 S4. Second Degree Polynomials 🌱

• Conquering quadratic equations through different methods: qualified guesses, completing the square, factoring, and graphing.

🤔 S11. Rational Functions and Their Domains 📊

• Understanding the definition of rational functions and how to identify their domains, zeros, and y-intercepts.

🔍 S13. Rational Equations and Inequalities 🔎

• Manipulating and solving rational expressions with precision.

👁‍⚛️ S14. Asymptotes 👁‍🗨️

• Intuitive understanding of horizontal and vertical asymptotes.

🪡 S16. Partial Fraction Decomposition 📐

• Learning the technique to break down complex rational functions into simpler components.

🤔 S17. Beyond Polynomials & Rational Functions 🚀

• Exploring the future topics where your newfound knowledge will shine.

🛠️ S18. Power and Algebraic Functions 📝

• Definitions and examples of power and algebraic functions to expand your mathematical toolkit.

Chapter 2: Rational Functions

🧐 S12. Domains and Transformations 🔍

• Identifying the domain of rational functions and understanding their transformations.

➰ S15. Plotting Rational Functions 📈

• Sketching graphs using rational expressions and understanding their connection to polynomial functions.

📊 S18. A Closer Look at Power and Algebraic Functions 🧐

• Exploring the world of power functions, which are a type of algebraic function, and learning their significance.

Extras & Resources 📚✨

• Comprehensive list of all course videos and problems solved, available in the resource file "001 List_of_all_Videos_and_Problems_Precalculus_2.pdf".
• Detailed course description including all video titles and texts for problems. (Located in video 1.)

Important Note:

📣 "Make sure that you check with your professor what parts of the course you will need for your final exam."

• The content needed for your final exam can vary, so it's crucial to align with your instructor's requirements.

Your Journey Awaits! 🛣️

Embark on this mathematical adventure with confidence, as you navigate through the world of polynomials and rational functions. With clear explanations, engaging video content, and a wealth of problems to solve, you'll gain a deep understanding of these fundamental concepts that are crucial for your mathematical journey.

📚 Dive into Precalculus 2 now and transform your mathematical skills! 🚀