Rational functions finally explained in simple, clean language. In this full lesson, we go step by step through how to read, simplify, and graph rational functions—without confusion or complicated terms. If you’ve ever struggled with asymptotes, holes, restrictions, or graph behavior, this video will give you clarity and confidence. I teach everything the way I teach my own students: logically, visually, and with real understanding. ⸻ WHAT YOU WILL LEARN 1. What rational functions are and how they behave 2. How to find vertical asymptotes and what they mean 3. How to identify horizontal asymptotes fast 4. How to check for holes in the graph 5. How to simplify the function safely 6. How to sketch the rational graph step by step 7. A full worked example from start to finish ⸻ ⏱ VIDEO SECTIONS 00:00 Introduction 00:38 What is a rational function 02:15 Restrictions and undefined points 04:40 Vertical asymptotes 07:55 Horizontal asymptotes 10:30 Holes and how to identify them 13:45 Simplifying rational expressions 17:20 Understanding graph behavior 20:55 Full worked example from the lesson 28:40 Common mistakes students make 31:10 Final summary and tips (If your real timestamps are different, tell me — I’ll customize them exactly.) ⸻ RELATED VIDEOS ⸻ HOMEWORK Try these practice questions to master rational functions: 1. Identify the vertical asymptotes of y = (x^2 - 9) / (x - 3). 2. Determine the horizontal asymptote of y = (4x - 1) / (x + 5). 3. Find the domain of y = (x + 2) / (x^2 - 1). 4. Check if y = (x^2 - 1) / (x - 1) has a hole and where. 5. Sketch y = (3x + 6) / (x - 2) including asymptotes. ⸻ I’m Maryam — international school math teacher. I don’t sugar-coat algebra; I show you the tricks, the traps and how to win. 📧 For personalized practice, one-on-one tutoring, or extra question sets, contact me at maryam_nr71@ I work with students around the world to build confidence in algebra and beyond. ⸻ #️⃣ HASHTAGS #rationalfunctions #algebra #asymptotes #functions #mathteacher #graphing #education #highschoolmath #learnmath #mathtiredclub #mathed #studywithme