Скачать с ютуб How to Graph ANY Rational Function! | Beginner to Master! 🥇 | Precalculus в хорошем качестве

How to Graph ANY Rational Function! | Beginner to Master! 🥇 | Precalculus

A step by step math tutorial from the absolute basics on how to graph any rational function (a ratio of two linear functions). The steps are: (1) We will explain how to find the domain of such a function (find out where you divide by 0). (2) We will explain how to find the x-intercepts (solve for x in f(x) = 0) and y-intercepts (set x = 0) of the function. (3) We will explain how to find the horizontal asymptotes by taking limits at ± ∞. We will explain this very intuitively, so you will understand what this means and how it works even if you have not seen limits before. If you have seen limits before, we will also briefly discuss the rigorous approach using dominant terms. (4) Finally, we will explain how to find the vertical asymptote by taking one-sided limits at the point where the denominator is 0. We will explain this very intuitively and numerically, so again you will understand this without prior knowledge of limits. (5) Finally, we will use all the information in (1) - (4) to sketch the graph of the function by "connecting the dots". Although the video is only 15 minutes, we go over a range of fundamental techniques in graphing that will be extremely applicable to problems that you will encounter at all levels in precalculus and calculus, and in high school math and college math on homework, assignments, tests and exams! You will be graphing ANY rational function like a pro after watching this video! 🥇 If you enjoy this video, I would love if you could please like ✅ , subscribe 🎉, and share ⏩ with students, classmates, friends and family - it means so much to help support me in my goal of creating elite infinite free accessible math education worldwide! 😊 If you would like to support my channel beyond this (which of course would mean so much to me 🤗), please check out my "Buy me a Coffee" and my "Patreon" page! Buy me a Hot Chocolate 😊: https://buymeacoffee.com/math_mastery... ☕️ Become a Patreon Member 🤩:   / mathmasterywithamitesh