Finding Vertical Asymptotes of Rational Functions (Precalculus - College Algebra 38)

How to find Holes (Removable Discontinuities) and Vertical Asymptotes of Rational functions, why they exist, and how the multiplicity effects the way the graph interacts with them.

[ИринаНазарова-лз]

haha, at 5:54 Professor Leonard talking about domain being similar to relationship baggage "it never goes away" - that really helped me remember domain issues. Thank you for making lectures fun, Professor!

[georgesadler]

Professor Leonard, this is a solid lecture on Finding Asymptotes of Rational Functions. Finding vertical and horizontal asymptotes of rational functions are very important in Calculus One. All students in Precalculus should fully understand this material before advancing to Calculus One and beyond.

Way to go math classes + arm pump motivation! 👊🏻🔥💯

[gunnar]

Thank you sooo much! It was very clear explained. We are all humans. Sometimes it's hard to believe, but you, Leo - you are a human too!

[tasfiaahsan]

I literally can not tell how how much your videos hepls me in my math study....

[jeremiahfourtwenty]

I'm gonna like every single video in this playlist! Thanks for everything Prof Leonard

[dougd]

It is important to learn what rational functions are and finding vertical and horizontal asymptotes of them.

[WyattHerren]

At 30:12 you can see Professor Leonard contemplating on whether to make the hole pun that he had on mind, or spare the masses

[ericmatthews]

So why is this, along with a lot of College Algebra lessons, re-learned in Calc I during curve sketching? I'm just confused why you learn this stuff potentially a couple years before you get to Calc, where it's actually used. Most people don't even take College Algebra, but it seems these things are really important to learn. The only things here you don't see repeated in ch. 3 of Calc I are inflection points and concavity. Everything else is already covered in College Algebra.

[YZZY-zbqu]

I am confused about the last rational equation; shouldn't it be positive? I thought the graph will look like x approaches negative infinity from the left and positive infinity from the right). Why is the graph not the same as I thought?

[Joey_Avocado]

Very strange I get your notifications while I’m in class for the EXACT same subject matter. Wonder if this is the same or similar for everyone else

[hassanharoon]

Great lectures but please add subtitles in old videos of calculus

[sushilroyal]

From which book i can practice questions on asymptote

[quakers]

For fifty to eighty bucks a graphics calculator will draw a fairly clear idea of what the graph will look like!!

[davidginono]

Sorry there are some V.A which do not obey the multiplicity Odd and Even rule ....why?

[ashutosh-kumar]

Professor, please recommend a textbook or book where should I practice question for Precalculus & Calculus I.

[theaveragemegaguy]

I LOVE YOU I LOVE YOU I LOVE YOU I LOVE YOU I LOVE YOU I LOVE

[piotrgraniczkowski]

I can safely say I didint waste time during quarantine

[zooqanpawar]

❤ Proffessor you are always in my prayers (duas). The second i have 5000 British pounds to spare, ill give you 1000 pounds to your patreon

[annapalsdottir]

Starting to believe Leonards fav number is 7