Graphing Rational Functions with Transformations (Precalculus - College Algebra 39)

How to graph rational functions with transformations by considering two basic graphs. Emphasis is placed on finding vertical asymptotes and accurately determining their multiplicity and behavior.

[Idunno]

Man, i see everybody posting on here about you helping them, but i just wanted to tell you that i cant thank you enough. I am taking courses online and working 60+ hours a week and taking care of a wife and kids and there is no way i would be able to get through this class without your videos. I havnt taken a math class in like 15 years. My teacher is non existent and i thought i was never going to pass and im halfway through the semester and ive only got 1 grade that wasnt an A, and it was an 85. Your a dang ole hero man lol

[SilentEagle]

"Pay attention, don't lose focus here" as I pull out my phone... lol, yes professor Leonard you have my full attention, he really has the best videos! xD

[cillakatt]

I had taken college algebra and trigonometry and passed both with an A but lacked true understanding of the concepts and it really showed when I began Calculus. I decided to backtrack and take precalc this semester to sort of relearn/ understand the concepts so that I can excel in my later math courses. My current professor has us watch videos but they all lack the in depth explanation and often use a plug and chug method to find an answer without knowing what the answer even actually means. Your videos have truly helped me to understand the why and as one who always considered myself "bad" at math, I have gained an immense amount of confidence in the subject because of you!

[ammishtandon]

Professor Leonard, you're the true definition of a great teacher... Thanks for helping me out in Calculus 3, Differential Equations and now in Probability and Statistics...Lots of Love and Gratitude

[adebayoemmanuel]

Watching from Nigeria. You made me understand graphing any functions.

[louiscullman]

Thank you for 37:50 to 39:00. Excellent. Answers a big question that I have not been able to resolve with other resources. Superb instructor.

[dpmike]

One of the best math teacher’s on the internet

[موسىموسى-تحخ]

استاذ،هل تعلم انك انتشرت في الوطن العربي خصوصا في دولة العراق🇮🇶 وأصبحت افضل مدرس لدينا😂


على الرغم أنني لم افهم اللهجة لكني فهمت الشرح، شكرا جزيلا لك💐

[plaid]

I just want to say thank you! You helped me get through Calc II and Calc IV. Sadly, my Calc III was done so differently that I wasn’t able to find any help. It’s always great when the professor starts by letting us know we are a guinea pig class. I tried to use you for an understanding but unfortunately it didn’t follow close enough to be of much use. But you were my biggest help for Calc II. You were currently making video for Calc IV when I was going through it and so you did help a decent amount. You are above and beyond the best at teaching out there!!! I still watch your videos every now and then just as a refresher.

[JuanPabloMartinez-bm]

You always smash our dificulty, Prof. Leonard

[upmysIeeves]

Thank you, Professor! I don't even start Pre-Calc till January but I'm starting early, going through all the videos you have out now hahah

[IMadeOfClay]

I've been really busy with work for a while so I haven't been able to watch your videos professor but I still drop by to give you a thumbs up :)

[georgesadler]

Professor Leonard, thank you for a well-planned/ incredible video/lecture on Graphing Rational Functions with Transformations. These graphical tools are very important in all levels of mathematics, science and engineering. These videos are helping students all over the world.

[acentasecond]

Amazing lecture as usual Professor Leonard! You inspire many of the ideas for my videos :)

[guilhermefavaretto]

The best Professor. Please, Laplace and Fourier Transform for us. Calculus 4 please

[GravitySix-G]

Professor, I think you meant horizontal shift 2 units down at 22:05 ich

[alenbkuriakose]

Great videos! When are you going to do PDEs and Linear algebra?

[tasfiaahsan]

Thank you again for another amazing video on function.
But i just wanted to ask that if there is any possibility of you making a playlist on CIRCLES, because i am facing a lot of problems with That, and i have always got answer of my every question on math through your vidios.so a playlist on circles would be very very helpful Professor.

[jithinthomas]

hello professor. i have been watching you since your cal 1 videos and now i am taking differential equations. I was wondering if you were going to make videos on cauchy euler equations. I have watched all of your videos until 2nd order homogenous linear equations and found that the videos end there. I was wondering if you are going to proceed with the videos. M y professor through my uni has the thickest russian accent making it impossible to understand him so i am in dire need of your help.

[kingay]

How much do u think professor leonard deadlifts