Shortcut to Find Horizontal Asymptotes of Rational Functions

[ThatPeenoAlvin]

I think my teacher is amazing and is very intellectual when it comes to math. He made me love math but you patrick make me realize just how easy math can be!

I always overthink in class and feel that I'm doing everything wrong. You're here to re-assure me :)

[andreasmagil]

thanks so much for the example. This is my first year teaching pre-calculus, I'm at a new school, and unfortunately my students have a lot of holes in their algebra 2 understanding. This video helped me out a lot. I knew that there had to be a shortcut...now i'm going to see if you have slant asymptote video:)

[patrickJMT]

@andreasmagil there are slant / oblique asymptote videos. and yes: the reason i saw people have problems with calculus, pre-cal, stats, etc was usually due to algebra stuff, 95% of the time.

explain the shortcut, but explain intuitively why it works! i used to talk about limits a little bit here, if the book i was using for pre-cal did not mention them yet.

[11panama11]

Please switch jobs with my teacher.

[patrickJMT]

@11panama11 then people would say: patrick sucks, that guy is so boring and lame. :)

[hashmat187]

PATRICK YOU MATH GENIOUS I LOVVVVVVVVVE YOU

[ThePaperkimberly]

Patrick! I love you! Thank you for helping me pass my online pre-calc class... ok... thank you for helping me ACE it.

[patrickJMT]

@ThePaperkimberly happy to help :)

[chocolate11001]

omg,, i never thought it would be that easy until i watched this video :O

[IAmJMizz]

Great videos so simple and easy to understand!

[patrickJMT]

@IAmJMizz that is how i try to make them!

[thelostbobby7]

watching videos on youtube is soo much easier, faster, and funner than going to class. i love you.

[LAPG5]

Thank you so much, I have a quiz tomorrow!

[jmoran1994]

thank you so much this helped a lot.. hope you get a cookie :)

[SooBeautyFull]

I have to thank you again. What I didn't understand in more than one class period you addressed in one video!

[wadiere]

you made it look very simple thank you so mush ! it realy helped me

[sarawrkang]

Thank you so much :)

[melanierich12]

Thank you so much! Seriously I thought I was going to have to drop but you rock!

[yoshifannumba3]

This asymptote video really helped me in mymathlab. Thanks.

[itzzspencer]

amazing



[thedustwhispered]

Thank you so much for this. I was lost in pre-calc all week and you cleared it up in five minutes.

[flowiepanda]

do you have a video on slant asymptotes?

[riverar1220]

I am having a problem with these rules for horizontal asymptotes, specifically the rule that says that if the degree of the numerator is less than the degree of the denominator then the horizontal asymptote is the line y=0. This seems to be the accepted rule everywhere, but when you look at for example f(x)=(x-2)/(x+3)(x-4) then you can have an x-intercept of 2. So this contradicts the rule. Can you help my understand how this happens and what I am missing.

[patrickJMT]

@riverar1220 this does not contradict the rule at all though. for some reason, everyone thinks the graph can not cross the horizontal asymptote, which is 100% not true. the definition of a horizontal asymptote only has to do with limits. in the definition, it never says anything about the graph not crossing it! HOWEVER, it IS TRUE that a rational function will never cross its VERTICAL asymptotes. i think this is the issue :)

[Ireallyneed2think]

Patrick you are a gift from God!!!!! I'm not going

to lie I'm pretty good at math, but since I haven't

done this in a while I'm a bit rusty :(

Your videos make me understand EVERYTHING

in just a few minutes!! My brother is actually a math

teacher but I hate asking him for help, because he

ALWAYS yells at me - THANK YOU for solving that

problem for me and giving me an alternative source

to seek help from!!!!! :D

[lurker4eva]

are you a teacher..

[patrickJMT]

@lurker4eva i used to teach at a university, then i was doing a lot of private tutoring. now i only teach via youtube

[CarlosSpicyWeiner7]

an odd function has 3 vertical asymptotes, one is x =3 what are the other two

need a bit of help with this, for some dumb reason i forgot how -_-

[Churluh]

I don't get why we even go to school when we learn things in a better way by watching videos.

[MsBlooShoo]

Oh my god. It only took 50 seconds. I UNDERSTAND

[asakyololz505]

I LOVE YOU!!!

[patrickJMT]

@asakyololz505 ;)

[richyrich356]

<3

[Pikzilla]

Just wanted to express my appreciation for how simply and reasonably everything is presented here. Thanks for removing me from potential hours of frustration!

[yisoonshin12]

You make everything too easy... :)

[oDZRgaming]

Life saver. Made sooo much more sense

[tjdaman2324]

i love you... no homo

[Blad771]

Dude so would I get all the points if I do it in this way?

[manchestarawey]

Great explanation for my exam tomorow!

[hapaxjalapenox]

You just taught me in 4 minutes how to do what my stupid teacher took 90 minutes FAILING to explain. I love you.

[patrickJMT]

@hapaxjalapenox glad i could help : )

[brijay1415]

@hapaxjalapenox Omg!!!!! I so agree with you. Its really sad that we have to resort to Youtube videos to learn what these incompetent teachers fail to show. Thanks so much to @patrickJMT

[yisoonshin12]

@brijay1415 I think it's an example of the benefits of advancing technology. we can use a website intended for entertainment, for education. 

[hero4nour93]

is it just me who has final tomorrow ?!

[patrickJMT]

@hero4nour93 not me! : )

[TheSnookiPower]

@hero4nour93 i have a final tomorrow :)

and this guy just saved me :D

[Blad771]

Ok this is great and much faster!

But what if you have: 1/1+x^2

Can you help me with this one?

[thezachster18]

@Blad771 technically the numerator has 1x^0. So the denominator has a higher power in the first number.

[LordoftheDuh]

Awesome video!  This makes sooooo much more sense than whatever my Pre-Cal teacher is babeling on about

[DennisBayazitov]

JMT: Saving my butt since Grade 10! :)

[silvershark55]

This made the concept of horizontal asymptotes SO MUCH easier, man..you're a genius ;) thanks

[224singh]

I LOVE YOU SIR!!!! :D

My book can't explain is properly

[mabelc1994]

Aren't horizontal asymptotes manifestations of limits at negative infinty too? How do I show calculations for that? : )

[patrickJMT]

@mabelc1994 yes, they are. in general, you just calculate limit as positive infinity and also at negative infinity. however, for rational functions, that value is always the same.

[kwakyi]

I CLEARLY have the worst pre calculus teacher ever. i often find myself coming to youtube for clarification. she makes things sooooo much harder then they should be.

[lighttenbie]

are horizontal asymptotes the same as end behavior asymptotes of a ration function

[thrashinthursday]

thanks! now i feel a littttle more confident for final....GAAHHh

[Nughug2]

Thank you, precalc final today and now I fully understand asymptotes. :)

[carsonmarj]

thank you, this helped so much!!

[opiumkidx]

lol and what if i told you all this is wrong.

[Uberman231]

I am depending on you now. My final is at stake here.

[XenionTech]

god i love youtube

[snowboarddude117]

Im still lost... =/ Ive got the function (3x^4)-(6x^2)+(5/3) and im somehow supposed to find if it has both vertical or horizontal asmptotes.

[channellebell]

LIfe is so much easier !

[JJ4mNJ]

thank you for your detailed yet down to earth, plain jane explanation. relle appreciated! :D

[novemberpgh]

Thanks for the video, that was actually understandable. Much easier than how my professor was explaining it.

[fknzack]

Your videos reinforce what my cal teacher says: "Calculus is easy!" Your approach clarifies concepts very well

[patrickJMT]

@fknzack well, most things are easy once you can do them : )

[birchicrizatu]

@patrickJMT hi but what if y= 2x+1/x-3 what is the answere...sry im in highschool and if i don't get a 6(C) tomorow i won't pass at math this semester...

[iverson92123]

This always seems to be the video I end up at when I forget how to do this. Thanks for the upload!

[bucklspace]

youre helping many lives up to +infinity. thanks a lot teacher

[systemsteven]

THANKYOUTHANKYOUTHANKYOUTHANKY­OUTHANKYOU!

[1silverboy]

Thanks you very much you just made this 10x much easier and shorter then how my teacher explained it too us thank you

[Fun2Run89]

if its lets say 16/8 do you simply put the ratio 16/8 or do you simplify it to 2 so y=2?

[ICOD73]

mm This was useful but now i am confused because I do this using limits at infinity which is the same so for limits I divide both the numerator and the denominator by the highest degree in the denominator so if the highest degree is X^2 I divide the numerator and the denominator by X^2 but my professor divides the numerator by the highest degree in the numerator and the denominator by the highest degree in the denominator and this confuses me because each way gives different solution???

[patrickJMT]

@ICOD73 you can not divide the numerator by one thing and the denominator by another. i doubt that is what he is doing

[ICOD73]

@patrickJMT mm sorry I expressed that wrong :) What he does is that he takes the common factor in the numerator and the common factor in the denominator???

[sparkster48]

i wish you were my teacher

[Crossoverzz]

This is actually so sick. <3 patrickJMT

[NorwegiaProductions]

thank you so much

[wtfbru]

bro but why does this occur? can you prove it?

[Chaddixprod]

thank you so much!

[coocookachoo7]

Thank you sir!

[TheOriginalBattler]

y=15/x-9 +3

the 15/x-9 is a fraction

the +3 is out on the side

whats the asymptote?

[TheOriginalBattler]

What if it has a plus 3 at the end of the fraction

y=15 ----- +3 x-9

like that? then what would be the horizontal a.

[nb0822]

my teacher said if it doesn't have a horizontal then it has a slant asymptote. if

X^3-5/X+4 doesn't have a horizontal then does it have a slant? but the top power is not one greater than the bottom..

[starstrukk280]

you sir, are my saviour. thankyou.

[apatton6]

I have this on a calculus exam and I need to do it without the shortcuts. Could you help?

[avb252]

thanks

[tcgstore2018]

my teacher told me if the degree of the numerator is > than the degree of the denomincator, then there is a "slant asymptote". is it true??

[patrickJMT]

@tcgstore2018 only if it is exactly one degree larger

[Eazy2113]

@patrickJMT wouldn't it be an "oblique" asymptote, use synthetic division to get an x^2 degree polynomial. A horizontal asymptote shaped like a parabola ???

[Vegetaworshipper92]

Thanks so much for the help! Just what I was looking for.

[igotoearth]

amen

[lifesays1]

I love your video, but I have a question.

Why does x/(x-1) have a horizontal asymptote of y=0?

[patrickJMT]

@lifesays1 it doesnt

[lifesays1]

@patrickJMT

So then how should I find the asymtote?

[daddydabbs]

@lifesays1 It would be 1. Since you have 1/1 that would just divide out as 1. Silly you.

[TheDthom97]

God Bless the internet...

[TheDiscoPat]

Thank you, I just needed a quick reminder before my test.

[misskendraATL]

you just saved my life....thankyouuuu

[patrickJMT]

@misskendraATL no problem

[Jadiz09]

I JUST LOVE YOU ! ... really !

[trashtalker133]

thanks a lot now i can do the rest of my hw no problem



[faelynne130]

but what about when the degree is 1 for both? such as f(x)= 15/(4x-10)?

[patrickJMT]

@faelynne130 well, in your example, the degree of both the numerator and denominator is NOT 1. the degree of the numerator is 0 if it is only a constant since 15*(x^0) = 15*1 = 15

[TakoyakiiMantoman]

youtube's featured videos should be like this, not some useless crap >:)

[magnapillow]

this is exactly what the internet is for, sharing USEFUL information, thank a bunch man, helped a lot! my textbook insists on making this 10 times more complicated than it needs to be!

[patrickJMT]

@magnapillow well, math is tricky, a book can not help it : ) always nice to hear someone explain it and fill in some of the details!

[arielartista7]

Thank you!

[BobTubeStudios]

I UNDERSTAND! Because a horizontal asymptote occurs when x approaches infinity! I feel like such a nerd for using Calculus to simplify Algebra...

[ipodnano4eva]

thank you so much!!! you have no idea how helpful this is, everything is so clear now :D you're making me love math!

[DWSimmy]

My text book says the exact opposite thing, it says that if the degree of the numerator is LESS than or equal to the degree of the numerator...

[patrickJMT]

@DWSimmy if the degree of the numerator is less than or equal to the degree of the numerator...?

i assume you mean: if the numerator is less than or equal to the degree of the denominator, which is 100% correct. it is in these cases that a horizontal asymptote exists.

[DWSimmy]

@patrickJMT Yeah, that is what I meant. Thanks for your prompt and helpful response

[patrickJMT]

@DWSimmy no problem!

[YungRimz]

thanks alot!!!

[kelpfusion]

Just 4 minutes helped me understood what my teacher was trying to teach our class for a few days. Thank you so much and keep up the work! I'd be so lost without your help

[patrickJMT]

@kelpfusion glad i could help : )

[omlettexpert]

I -3 you

[eddyluva327]

what about an equation like x/sqrt((x^2)-4)?

[SimplyMariahElise]

this is a GREAT explanation of this. i understood greatly. thanks so much. wish you were my college professor -___-

[mZtNaPaY17]

Thanks so much! This helped me out A LOT. I don't understand how or why my professor left these important parts out. This makes me understand math so much better! Thanks again! :D

[patrickJMT]

@mZtNaPaY17 glad i could help : ) 

[rockrgrl637]

Ohmygosh... I love you. My math teacher always uses the stupid method of end behavior, then expects us to find the horizontal asymptotes without a calculator... then when we ask for help, he tells us "Good luck finding another way to do it". :P WELL I DID. SO THERE. >:O

[mrblahhh67]

professor did not explain that "y = the ratios of the leading coefficients".. thank you so much!!!

[patrickJMT]

@mrblahhh67 only if the highest degree of numerator and denominator are the same!

[Penguino099]

Very simple and clear. Thanks!

[mythsheep]

does this work with F'(x) and F"(x)?? *i am talking about calculus*

[almondswag]

u write left handed?? i think we're the only two left in the world!

[JademanX]

Im quite confused here. In the third example he says y=0 is a horizontal asymptote yet if you set x=1 then y=0 (1-1)/6= 0. In the last example if you set x=-4 then you get y=0 since (-4+4)/59= 0. What am I getting wrong? By the way i plotted the last equation into a graph in my calc. and in the table it says that when x=-4 then y=0.

[ColourMeErin]

i love you. thank you so much.

[monkeyshinobi]

so what would the asymptote be if it's not in a fraction form say like y= x+1 would the asymptote by y=1? 

[kingdomshaman]

you have earned a subscriber my good sir!

[thrashinthursday]

Finaly I get...thanks!!!

[Kalen1457]

Thanks for the concise explanation!

My textbook didn't explain this good enough.

[sargentdix]

Thanks for the short cut method. i still don't understand the theory behind the asymptotes. Plus, do you have any videos on end behaviors? I'm really confused about that.

[Winna8123]

This was way better explained. Much appreciated :)

[adammissel]

dude you are like jesus, passing calc thanks to you

[shadowcat0909]

Hey, love your videos, I was just wondering how to find if a function crossed an asymptote w/out graphing it. And if it does cross an asymptote, where that happens. When I watched your video on asymptotes, I did not see this mentioned. If I missed it, or you have another video addressing this, directing me to it would be very helpful; if not, I would appreciate if you could clarify. Thanks!

[patrickJMT]

@shadowcat0909 once you find the asymptote, set the function equal to that number and solve the equation. if there is a solution, it crosses the asymptote at that x-value.

[suzan698]

your video helps so much , thanks

[ZeeReeGee]

What are the horizontal asymptotes of: p(x) x^2-25x+114 / x^3+32x^2+212x-560

2. x^2+26+160 / x^3-35x^2+374x-1120

3. x^3-14x^2-29x+546 / 2x^3+34x^2+100x-352

4. x^2-x-6 / x^3+12x^2-169x-202

[subfourrun]

when I was in school we had no calculators (not invented), no videos, no You Tube and really cryptic texts. i also had to walk 10 miles uphill both ways in a blizzard. We did have slide rules which we used to hit ourselves in the head with ...:)

[m2m1992]

this is very clear and neat. thank you.

[Mounsdshroud7]

We haven't done this in class yet, but now I'll know what to do before everyone else! Thanks, this is great!

[angeldv]

THANK U SOOOOO MUCH!

[WhyDITLMangos]

This is pure genius, I wish math books were this easy to follow.

[suzan698]

thanks **

[aprz1385]

Damn, i would have rather gave this guy 175 dollars for his video then spend it on this confusing math book i just bought

[jpmoench21]

you're simply a great teacher!

[KixPL]

your channel serves as the best math notes i could ever find at home :)

[tazzenders]

wish the graphing calculator had a patrickJMT function on it.

[XxJoeDaKILLAxX]

Nice video man. I have no clue how someone could dislike this video. Thanks for the help

[dgwrigh58]

What do you do for a living? Im interested, you are a very good teacher, easy voice to listen to aswell.

[shawnkilledyou]

God bless.

[goshiluvarchie]

i love youuuu

[kingmutez]

thanks so much! i was so frustrated with calc since i took precalc 5 yr ago, my teach wont give any examples, he just uses they theory and moves on! the board is full of letters and no numbers! *cry*

[94jmcorrea]

I LOVE YOU DUDE THANKS!

[Alexwkj]

Hey Mr. Patrick, I've got a question. What if the equation of the curve is 2 - a/(2x-3)? (where a is an unknown positive constant)

[hatchbizzle777]

God bless you!

[videogirlsk]

ooh you're a left handed! we leftys are smart :)

[AlecMescudi]

can you use this on power functions?(might be dumb question)

[ILM760]

I wish I would have found this video about 5 hours earlier............... this simple video just saved my grade on tomorrows test, i could not find a simple , and clear explanation like yours anywhere! THANK YOU SO MUCH!

[patrickJMT]

@ILM760 no problem, now you know where to turn to in times of trouble : )

[Icecube88]

@patrickJMT do you have any videos on how to graph rational functions?

[tazzenders]

@Icecube88 just plug random numbers into X.

[Icecube88]

@tazzenders yeah, I know that now. thanks.

[pectoreferrum]

This is beautiful.

[patrickJMT]

@pectoreferrum now that's the spirit! : ) 

[Chunmeista]

Are you... God? Ǫ_Ǫ