In this lesson, I break down how to graph rational functions that have holes — the “invisible points” students always miss. If you’ve ever struggled with when to factor, how to cancel terms correctly, or where the hole actually lives on the graph, this video will clean it up fast. WHAT YOU WILL LEARN 1. How to factor the numerator and denominator correctly 2. How to identify a removable discontinuity (the “hole”) 3. How to find the exact coordinates of the hole 4. How to rewrite the simplified function for easy graphing 5. How to graph rational functions quickly using intercepts, asymptotes, and behavior patterns TIMELINE 0:00 — What is a hole in a rational function? 0:28 — Quick factoring review (why we factor first) 1:10 — How to spot a removable discontinuity 2:00 — Finding the hole’s x-value and y-value 3:10 — Simplifying the function after cancellation 4:20 — Graphing step-by-step (asymptotes, intercepts, shape) 6:00 — Final graph and common student mistakes 6:45 — Related videos for extra practice 7:10 — Homework section RELATED VIDEOS (Your Channel) Graphing Basic Rational Functions Vertical and Horizontal Asymptotes Explained Removable vs Non-Removable Discontinuities Factoring Review: Difference of Squares and Trinomials How to Find Limits Using Graphs Understanding Domain and Range Quickly HOMEWORK Try these rational functions and find: 1) the hole 2) the vertical asymptote 3) the simplified function 4) the final graph A) y = (x² – 9) / (x² – 6x + 9) B) y = (x² + 3x) / (x² – 4) C) y = (x² – x – 12) / (x² – x) Write your answers in the comments — I reply to everyone. 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 #algebra2 #removablediscontinuity #mathteacher #graphing #algebrahelp #functions #mathclass #asymptotes #highschoolmath #ibmath #precalculus #mathshorts #mathwithmaryam