Finding horizontal and vertical asymptotes | Rational expressions | Algebra II | Khan Academy

[@colbyroach3509]

Thank you Sal for singlehandedly saving my math grade for the last 3 years

[@Drewhardin96]

He explains in 10 minutes what takes my professor over 1 hour. No wonder people get so bored in class

[@Dontworryboutit247]

Where is Mr. Khans Noble Prize God Damn it!!!!!

[@aden4153]

Helped me get into college algebra.

[@bennetthuman]

language

[@thomassmith1823]

Someone get Mr. Khan a Fields Medal.

[@TheEighthAct]

Vertical asymptotes at 4:24

[@betselottesfa7572]

I read this comment when I was at the 4th min :)

[@iliriacum666]

The same voice in most of Khan's video...you should be a genius knowing all subjects!

[@theneongamer4957]

He is the creator and founder of Khan Academy his name is Salman Khan/ Sal Khan

[@aravjain]

My teacher “taught” this in 1-2 hours, and sir you explained it much better in just 11 minutes. Thank you so much!

[@connors.9181]

He teaches an easy topic in the most complicated way possible

[@xxxYouTunesxxx]

No shit....I didn't even finish the video

[@ethanp4050]

well your dumb af

[@rogonislocusts3359]

Ethan Palinkas If you’re gonna be calling someone dumb it would be a good idea to have basic grammar skills first

[@jobs.1518]

lol its pretty easy but whatever

[@synthwavescience2111]

No Name your?

[@pcl5636]

This is why I like these videos over classroom lectures. Too much "hand wavy" math goes on there. I need my hand held the whole time, thank you Mr. Khan!

[@omaxshendy5732]

khan academy is smart....khan academy has brain...thank you mind people!

[@AlfaHanen1]

You are one of the best in the World. Thank you for your idea. It helps to understand the world we living in, and hop that we one day can live without War IN Harmony and Peace ONE DAY. Knowledge is the key for that.

[@serumser1]

parenting is the key for peace in the world

[@irfanakhanam9956]

AlfaHanen1 don't you thing you are over reacting a little bit?

[@imcurious5491]

Irfana Khanam a little is not too much or over

[@ticcerz1790]

Can we take a moment to appreciate Mr.Khan helping us through math class?

[@KaylahH]

Thank you!!! I have a calculus packet due and a test on Friday, this is a lifesaver!

[@bradybiesterfeld2706]

im in algebra 2 and i do this...

[@nuelle2361]

@@bradybiesterfeld2706 Math repeats a lot. They teach the same stuff over and over and just add little by little.

[@scuti7073]

Menue I’m in algebra 1.....

[@halisselamozmen5658]

This is very interesting, other videos show these with examples simple enough to just set the denominator/s to zero. You mentioned it clearly that not every value for a variable, for which the expression goes undefined, is also an asymptote itself. And also quickly explaining relevant but maybe overseeable topics like qualifiers helps alot. This is the depth I'd rather like to understand in than the depth of maths being taught in school. Thank you very much.

[@unknown-re9vv]

Actually your explanation is complex a bit but it shows all the steps and why this and that become the answer, I suggest you making a video of a lesson with different explanations for different skill learning level and i think this will be very helpful. Thanks a lot for your efforts 👍👏👏👏

[@AddctFrk14]

yo this helped me out a lot, teacher confuses me prob cause I zone out easily

[@Gavolak]

AddctFrk14 do you also zone out in English class? Jk I'm just giving you shit lmao

[@malek.704]

Did you graduate now ?

[@andrewku6683]

horizontal asymptotes: what happens if the highest degree terms are not the same on the numerator and denominator?

[@juniorbini8930]

The upper degree will either be greater or less than the lower degree and in that case if its greater there is no Horizontal asymptote if its less the HA will be zero.

[@owen551]

Sal Khan is a life saver. Much better teacher than Ms. Cornett, who decided it was better to play 2 truths and a lie rather than go over the summer review packet on the first day of school :) And We've got an exam tomorrow :DDDDD. THANKS MS CORNETT

[@sunnykin7649]

Khan Academy is the best one as far as I know. Thanks.

[@inseanity911]

Thanks to Sal, I love math again.

[@samadyou6133]

Wow Really Nice Tutorial, It Really Helped with my Business Cal problem Thank You Khan Academy!

[@wokeupcute]

this problem was a bit more in depth compared to the other tutorials found on youtube but I understood it because of you so thank you!!

[@mrspaz007]

congrats on 4,200th video ;) You've saved many lives including mine! Thank you!!

[@owenwu7995]

wait do you simplify the equation before using the degree rule to determine the horizontal asymptote?

[@raoulhery]

school at its finest! thanks Mr Khan

[@phonemicshorts6826]

The easiest way to figure out the shape of the function is to look at the factoring used for the vertical asymptote. This shows in the numerator that the function equals 0 only at 9, since 9 is greater than 3, and 0 is less than a 1/2. We know that it approaches 1/2 from below on the right of the asymptote and from above on the left

[@xc5838]

He didn't explain why -3 is not a vertical asymptotes. Is it because the numerator and denominator cancels out?

[@jobro6144]

this makes so much sense

[@MrDands]

You can also find the inverse of f(x) to determine the asymptote.

[@woolyski2862]

grats on your 4,200 video !

[@amare801]

I love the tutorial of khan Acady

[@SpookySkellyGurl]

Great video, but I couldn't find it anywhere on the actual site no matter where I looked.

[@passengerprincesspodcast]

If only I had this when I had my last last week!

[@wagsman9999]

So clear - thank you!!!

[@prasannakumar6008]

Thank You. Great explanation.

[@underhoodshadow8089]

thank you!

[@marceloampie460]

I love khanacademy and everything, but i feel this could have been explained easier and faster

[@xandrora]

Very helpful, thank you!!

[@DRK4C333]

lol thxs for getting me thru 3rd to 8th

[@sarahkelly9550]

lost me when he got to vertical asymptotes....

[@dannoinsertlastnamehere6004]

so we would say that there is a hole in the graph at x= -3 right?

[@someone5624]

finally!! thanks for the tutorial.

[@BelievinSP]

Hey Khan, can you finish/add to your differential equations playlist? You don't have anything on Power Series, Ordinary, Singular and Regular Singular Points or Fourier Series. It'd be great if you could do a bunch on this. Deciphering DiPrima and Boyce's book is a real pain.

[@ilovemusicd00d]

THANK YOU!!!

[@WhiterockFTP]

Why would the function be undefined in two places? At x=-3 the function value would be 0/0 which is 1 what's wrong with that? It fits into your sketch as far as I can estimate things... Please explain!

[@mrfrankincense]

0/0 is not 1

[@MrAlbashiri]

Thank you

[@Mets7chris]

Any videos on how to graph something like this?

[@alexandratrigg4778]

I have no clue about the vocabulary but I get the concept so I guess I'm okay.

[@soma7891]

Please make a video about oblique asymptotes

[@kennyborek615]

Vid was helpful

[@jaydan3537]

So what is the significance of vertical asymptotes in practical terms?

[@Gavolak]

Jayrold Amoggao limits. Extremely useful in advanced physics, and used to a degree in more basic 1D motion. Also, calculus. It's an entire field of math dedicated to limits.

[@saramahmood3462]

thanks

[@profeconomia]

A parenthesis is missing in the denominator ;).... great video, as usual!

[@linusbao8650]

How do u find the y value of the whole discountnity, if i plug neg 3 into x and solve for y it gives my undef

[@linusbao8650]

*hole discont

[@TheEasyInvestor]

Great vids

[@sibusisomashalaba7523]

i love this thing damn

[@JohnSmithSafe]

Yeah, and I don't know anybody else who can explain Bitcoin geometrically better than you - like linking all the blockchain records together to show movement of money. That kind of video is needed for all those people who's having difficulties of understanding Bitcoin (that's the reason why they don't use it)

[@sesarman]

it actually looks like -3 is a vertical asymptote once you graph the original function

[@kevin_lin]

Clearly you understand the content but you take forever to explain one question. A good tutor is able to get their point across to their students. An excellent tutor can get their point across both effectively and quickly.

[@kilozilo]

+Kevin Lin I agree. He spends a lot of time repeating what he says as he writes.

[@rollsreus3862]

ok then go watch someone else my guy

[@Handle12456]

It hurts everytime you say, "Let's do it for fun." 😭

[@scuti7073]

Erina Khadka it’s very fun ma’am

[@Bethelehem2458]

falling out of focus with sal is never ok. thats like day and night.

[@tomphuable]

This was extreme helpful but watching video makes me want to swallow my spit when i hear him talk lol

[@sheharyarbhatti56]

Why -3 is not in the domain of given equation? You should have explained this.

[@rosea164]

if someboy doesnt have any concept of this subject,the explanation seems so insufficient. I couldnt get the points and failed to follow

[@Shogundelogan]

Rosa s This is advanced high school levels of maths, not meant to be easily understood outside of school teaching and certainly not without previous experience. Saying that, try applying his working to other questions, helped out a lot for my work at Scottish college level. Of course feel free to discard this comment, it is youtube after all

[@yingxiuwang8329]

Well he explained very well tho. Idk y u don't get it. Maybe u didn't know the previous stuff

[@bahrozehaleem9278]

but wouldn't you have either a hole or a Horizontal Asymtote in an equation ???????????????? please answer?????

[@thetravellerfeeds]

When do we need slang asymptote

[@SURAJSINGH-vx5rm]

Sir ji make it in hindi

[@MiggyLumaniog]

for the vertical asymptote, why not just make the denominator's equation equal to zero like: 6x^2-54=0 then do math. it's much more easier.

[@Gavolak]

Samiha Sajida I think what he's saying is that you can make that equation, and then what you solve for is going to be your asymptote.

[@chrisvo203]

and hes saying that x = -3 is wrong when you solve that equation. lmao. he even explains it after he factors out the equations. he says that x = -3 is where the function is undefined. that x = -3 is called a hole. thats why he says the the setting the denominator's equation to 0 and solving for x will not be the correct answer.

[@KS-bo6tq]

time to make a table of values lmao

[@griffinhudson6232]

Is there sound to this

[@defnenurgumus9354]

yes

[@greywolf4246]

You must mean x can not be +3 since that is the only vertical asymptote, x = -3 works just fine

[@aznumi2544]

1:34 cringe

[@pinkman9927]

lol

[@JohnSmithSafe]

C'mon, Khan you know that we're all expecting you to make more Bitcoin videos of the other level. How about making some explanatory video in a kids style like (by showing visually limited amount of the Bitcoin money) "Here's the digital blocks that we need to protect with the keys, imagine that this geometrical room is all of the world Bitcoins - now look - if somebody claims to have 1 million of BTC, that takes too much space" - or you can use examples as an earth, to explain that purchasing 100 BTC is like purchasing New York city for cheap 300 years ago. You know, something like that. We're like a kids - we don't need complicated stuff. At least sometimes make something simple.

[@amirsaif2889]

vertical asymptote =-3 not 3 and thank U

[@brentjones3094]

Oh I hate this stuff! I can't do it. I hate math!

[@samuelagyemanprempeh9705]

+Brent Jones You can! You have more power than you can imagine :-)

[@brentjones3094]

+Samuel Agyeman-Prempeh thank you for those encouraging words!

[@joshcompetente8946]

Can he ever pronounce numerator and denominator right?

[@NotKoiy]

I dont understand how they can draw on the computer

[@matteofong8132]

I am Matteo

[@sashas9405]

noice

[@zing3r_]

This is not algebra 2 bro

[@zing3r_]

@Daniel Leslie yeah thats what i thought lol

[@chinnudanturi9730]

Thanks