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! 🥇
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[@MathMasterywithAmitesh]

Also, check out my tutorial on how to graph the equation of ANY circle: ua-cam.com/video/w7gYxE7oN1c/v-deo.htmlsi=OOQ16vf4e-FE6xeW Like ✅, Subscribe 🥇 and Share ⏩ with classmates, friends, students, and family for **infinite elite free accessible math education** at all levels and across all topics in math. I love making free content to help you and this helps motivate me to create more videos and change lives through math education! 🥳

[@scienceofsleep08]

Keep up the great content! We are especially the pre-calculus material!

[@MathMasterywithAmitesh]

Hi @scienceofsleep08 thank you so much for your kind and supportive comment! 😊 I am so happy to read it and I am excited to continue producing more precalculus videos! 🥳 I hope you have an amazing day/evening/night! 😊