Finding Vertical Asymptotes of Rational Functions

[lovemybooks15]

thank you so much. please keep making these vidoes! they really help. I have a quiz tomorow, and this video is saving my grade!

[dubloser]

.... thank you so much, i'm in A honor roll now :I

[1891shooter]

Thank you sir

[Churluh]

Thank you so much!

[macanrox]

Thanks Patrick! You saved me the extra time I'd spend pondering over these problems!

[bcalhoun100]

thank you so much! you made it soo simple=)

[chickmitten]

Later on when I do math I'll put T of x which is my name (tracy) instead of f(x) :))

[patrickJMT]

@chickmitten lol

[MrRzguitario]

Hi patrick, I don't understand what you meant by a "hole in the graph". Isn't the answer of zero divided by zero undefined? If so, how can it not be an asymptote when the answers of a numerator divided by zero is also similarly undefined?

[patrickJMT]

@MrRzguitario well, the calculus reason is because the limit exists but it is not continuous. it is only zero/zero at that specific point. what happens if you plug in a number close to it, but not equal to the offending value?

[gagirl1231]

This really helps me do my advanced math project and study for finals as well!

[coolgirl9527]

Now I get it!

[kozak317]

You rock, saved my life! Fingers crossed on my pre-cal exam

[ufailkid]

Dear Patrick....you just saved my ass big time. And for that words cannot express how much I love you. I think you should win the nobel peace prize.

[juicyballsok]

wow this guy is amazing .. thank you

[SILENTIMACT74]

I sometimes go to this channel just to read the comments, thinking to myself, these people are talking about me.

[iForIshtar]

awesome! it helps a lot!

[TheSchwaggs]

Patrick, you're AWESOME!

[petershin95]

You are a great teacher....! Beats mine...! No matter how many times she explained, I was like duh... But once with your video I'm like... What? That's it? She couldn't explain it like this??? Thanks!

My final I tomorrow and I think I will be watching all your videos till my final...

[nishatu331]

you are awesome.

[kickit246]

I still say that Calculus is made of pure evil, but its less evil with PatrickJMT and Khan Academy around. Final on thursday (15th) hopefully it goes ok... :S

[mamuchita14]

Thank you so much for your help you do an amazing job explaining things and you use awesome examples .... Thank you again! :D

[malotyxz]

thanksss a lot patrick.now i can skip my class and will just watch your videos :)

[patrickJMT]

@malotyxz go to class. : ) and watch my videos ; )

[AliceOfMay]

You just saved my life. We had a sub and my textbook isnt much help.

THANK YOU

[eskimoninjafaerie]

thank you so; so much

[horizontaljumper1991]

Best math teacher Ive ever had. Thanks Patrick!

[patrickJMT]

@horizontaljumper1991 you are welcome :)

[RepZi34]

Nice, now i finally understand.. cheers :D

[tamibooty]

THANK YOU i finally understand it now :) !

[Reedalot1]

thank you

[buffsfreak]

my math teacher must suck...i basically just learned what we have been doing the past two weeks in 8 minutes

[MrDanikify]

lol i dont learn shit in my school maybe i should leave my school :/ from start of this year till now its 1 month to christmas we are working on it :D and nobody knows shit about it

[ronnyrizat]

@MrDanikify i think i might be in your class lol

[MrDevin666]

What's the difference between undefined and hole in a graph?

[ViggoTW]

You know what? You're awesome, Patrick! I've been using your videoes so much, and you're so much better than my lecturer!

[whatifchris]

what does the hole mean ? how is the graph going look like? please help

[DjRyuZX]

Dude... you are great! You helped me understand my whole pre-calculus chapter in only 20 minutes! Instead of the 2 weeks spent in school. Thank you! :)

[Joelito231]

This kid is awesome. I was wasting time reading my Business Calculus book and he quickly helped me to understand Horizontal and Vertical Asypmtotes quickly. Hope to see many more videos made by him in the near future.

[DennisBayazitov]

If you were my math teacher, I wouldn't have a problem learning anything!

[TheOriginalBattler]

I'd rather have you as my math teacher.....Mr.Patrick :P

[ninjahotty503]

thank you very much you helped ALOT!!

[BeckyGoesMoo]

YOU ARE A LIFE SAVER!

[vjca]

Thank you a lot!!! ^_^

[PraDUH13]

I would have failed my precalc test wihtout you!!!!!!

[isabe1001]

this is a great video!!!

[rsmoth37]

Your voice is annoying

[samacoy]

I've learned more from you in the past 30 minutes than I have in the past three months in my college Algebra class.

[patrickJMT]

@samacoy feel free to come back and watch any time : )

[Pwnstar57]

@samacoy omg thats what happened to me too

[o0xHorizoNx0o]

What about ( sqrt x ) / (x + 4) ?

[fpsisfun]

i fucking love this guy

[plzletmelive1]

Thanks very helpful :D

[robertoz250]

this seems so easy now

[biscuitice1994]

wow. who knew it was this easy!!!! My teacher made it seem so difficult. THANK YOU ^^

[pjwarmy]

Thank you so much, you saved my life. I have a big test tomorow and I didn't understand any of this but now I do!

[aaz101]

just had a question, kinda off topic but i hope youll see this. could you do a vid about finding the domain of composite functions? thanks so much.

[rctelles]

WITCHCRAFT! Haha, nah j/k thanks. I needed this for precalc.

[Clap4TheMoment]

i love you

[aldude100]

I was blind (pre-calc teacher sucks) but now i see



[blueblook]

Perfect! Examples were actually useful, especially (d). Thanks!

[patrickJMT]

@hnumber11 because the limit exists.

[Crunka]

I learned the P in P(x) is for Patrick

[patrickJMT]

@Crunka yes!! : )

[TheAdmiralPancake]

@Crunka

I don't get it. What's the joke?

[ViggoTW]

@TheAdmiralPancake haha, yes! x)

The guy posting the videoes is named Patrick x)

[4BrownBrotha]

Thank you good sir.

[Eels12]

Did...you...misspell 'values' ..in the first screen?? hahaha (correcting the teacher never gets old :P)

[patrickJMT]

@Eels12 yes, i think i probably did : ) and to think... i won the spelling bee in 4th grade

[Helenabeanable]

thank you so much! im trying really hard not to get behind in precal and these videos really help. youre awesome!

[patrickJMT]

@Helenabeanable happy to help : )

[quinton2532]

Thanks a lot

[manit7]

Thank you so much, I have an exam tomorrow about V.A. H.A. S.A. you are a big help.

[patrickJMT]

@manit7 good luck on the exam!

[ryu921022]

i dont understand why some people hate this video O.o this guy is like brilliant and awesome.

[khoinguyen88]

thank you sir

[goshiluvarchie]

For the last problem, do you mean no REAL solutions? Or does it have no solutions at all?

[SimplyCindy214]

I am in honors pre-calculus this year, and I have a C so far. That is such a terrible grade for me, and I didn't know why I wasn't understanding anything! Well, now I have figured out that it is due to the mundane way my teacher teaches this topic, so I end up not understanding her as I try to pay attention. I knew nothing of what she was speaking, so I decided to look up the topic that we were on, and voila! You have become my savior! Thank you so much for the help, I love you man! :DDD

[patrickJMT]

@SimplyCindy214 good luck in your class : ) 

[Icecube88]

@patrickJMT you have any videos on finding the oblique asymptotes of rational functions?

[tazzenders]

@SimplyCindy214 aha same here!

[SjefeNoverSjef]

This semester i have Functions. And some of you videos, people keep saying its calculus. Is this calculus, or functions? lol.

[torrihall]

this video helped me so much! i keep failing all my calculus tests but i believe i can learn something by just watching this video! you helped very much and all if this finally makes since!!!

[patrickJMT]

@torrihall trying watching more videos and see what happens ; )

[torrihall]

@patrickJMT i watched some more and went back to my test and re-did the problems i got wrong and i now i can do them! thank you :)

[flowiepanda]

my algebra 2 teacher taught me that to find the VA, you have to find the zeros of the denominator, but i never realized that it was because a VA occurred every time the denominator was 0, therefore, the function could not exist at that line. only now do i see that the VA is like the rational function's way of compensating for that "undefined" part of the graph

[patrickJMT]

@flowiepanda just cause the denominator is zero does not mean you have a vertical asymptote

[DakotaWyne]

I am looking for the vertical asymptote of (x²-16)/(e^(x+8)(cos x)). How would I do this?

[GetPrizes]

thanks, this really helped a lot!!

[RobogooberOfficial]

Patrick! What would the vertical asymptote of (2x-1)/(3x+5) be?

[horizontaljumper1991]

Patrick, I had a homework problem that asked to find the horizontal asymptotes of the function x/(xsquared + 7). I answered x=-square root of 7. The answer was no vertical asymptotes. Why is this?

[patrickJMT]

@horizontaljumper1991 there is no value that makes this function undefined (nothing that makes the denominator equal to zero); this is the first thing that i look for (but not the only thing)

[horizontaljumper1991]

@patrickJMT O ok I see. Thanks!

[ces38847]

Thank you so much man.

[CorporatePilot7]

omg dude...you just explained in 8 minutes what took my pre-cal teacher 4 weeks!! and im not not exagerrating!!!

[TheBrizzlyBear]

Why can't you be my Calculus teacher?

[patrickJMT]

@TheBrizzlyBear cause i no longer bore people at the front of a classroom for crappy pay : )

[nightpwner]

@patrickJMT Private schools for the win?

[patrickJMT]

@nightpwner i honestly do not know

[XboxPwner94]

dude thnk you so much, i really appreciate this, thnkssss

[chaospoison6]

omg thank you so much!!!!!!!

[andrewvrodriguez]

You are 1000 times better than my math teacher lol.

[Aaushi1000]

awesome explanation ....



[sunnyd8740]

What do you mean by hole in the graph?

[spotlightman1234]

you taught me what my teacher took an hour to talk about, thank you :).

[J1mmyAva1on]

you make math look fun

[ericderafera09091994]

thanks alot :)

[Muzikjammin]

Awesome explanation. I'm taking my TeXes Math 8-12 this week, any tips?

[sosolovekom]

you're very helpful ..thanks ...

[tseguk]

Fantastic, I have midterm tomorrow!

[lenahmata]

You're my knight in shining armor..:)

[legitopossum]

Man thank you so much for taking your time out to help people like us with bad math teachers

[EMOTIONZ80]

YOU ARE JUST AWESOME. :D you and robert fom "yaymath.org" help me sooooo freakin much !!

[Camelopardalis31]

Great video thank you for taking the time to help so many people.. 2nd year of college and failing my summer math class test tomorrow and this helps so much I'm looking through all your videos to teach myself what my teacher has trouble explaining

[Camelopardalis31]

Great video thank you for taking the time to help so many people.. 2nd year of college and failing my summer math class test tomorrow and this helps so much I'm looking through all your videos to teach myself what my teacher has trouble explaining

[francesalexander]

THANK YOU THANK YOU THANK YOU THANK YOU THANK YOU THANK YOU THANK YOU THANK YOU THANK YOU THANK YOU THANK YOU THANK YOU

[chrisrock1990]

u make me win like charlie sheen

[Raymondlk]

I love you, <3

[1052230]

Mr PATRICK you are a GENIUS.I wish I had your Math video 40 years AGO when I was a student.THANK YOU ANYWAY

[Gazzawey]

Patrick for the win i never thought that i can understand calculas untill i start watching ur vedios now im a second year @civil engineers cuz of u thnx alot

[katiekandy2]

like this if you have your math exam tomorrow

[PS3Man141]

@katiekandy2 quiz :P

[TotallyInsaneShane]

patrickJMT # Winning

[DemiMileyJB4life]

THANK YOU! :)

[bulbucv1381]

thanks man you are the best, very easy to understand, all the best

[avatarmaster101]

Thank goodness I found your video!!! I finally understand why when a denominator factors that there may still be no VA's. You explain why there is a hole or no VA's. I have watched 7 VA videos trying to figure out why my VA's are sometimes not a real zeros. You are the first one to mention that the numerator can't be zero! Even after 7 videos I didn't know that. THANK YOU for being so thorough! It's great that someone who explains the WHOLE concept.

[BrettiniTiny]

can u take my math teachers job please??? its sad how i have to count on you tube to help me do my math and my teacher cant provide me with any help, thank you so much for postin this video! =D

[ibanezcrow]

I learn more from you then an hour from my Asian teacher. <3

[NumBaONeHaTeRz]

Am I supposed to be learning this in Algebra 2?

[AtsuikajiOtoko23]

I WANT YOU AS MY TEACHER!!!

[Iamorton]

this guy = my new math teacher 

[Iamorton]

YOU KNOW WHAT FUCK THIS OLD SCHOOL SYSTEM..I WANNA LEARN MATH LIKE THIS ..LIKE IF YOU AGREE

[ClutchG69]

@Iamorton fail lol

[mimiees]

Thank you for your videos! They has been incredibly helpful to me!!

[davethewave1223221]

great video

[jackieexmariexo3]

if i watched your videos in the beginning of the year, i probably would of gotten a 100 on every test..

[sgtxbadass]

this video saved on my test

[orly360]

My C became an A because of you thank you!

[shamelesslycool]

Thank you so much! I have a quiz on this stuff tomorrow & I hate going to the math tutoring lab on campus, so this is a big help. Thanks!

[iamTheNinjaHobo]

JESUS CHRIST HE WROTE 1/0...head explodes

[Sprocket54]

I'm looking at all these great comments and the vid isn't loading... looks like i'm missing out :(

[ParamedicChic1982]

Thank you for all your videos. They help so much!

[ailema15]

You've saved my life when the math lab is closed. I love you!

[Mzlily09]

dude you're AWESOME!!!

Thank you for your help :))

[anabolicErik]

on part d when you said lets do p of x now... p of x is for patrick for some reason i seriously lmao!!

[superkoolkid1000]

Damn come be my teacher

Elkins high school Missouri city Texas!

[jackxzx]

what if..what if you get a real number in both num and deno?

is it still considerd as VA?

[ephue]

Youtube > School

[lexinaut]

Higher than any fireworks display and longer than any empire

Is the pure flight of the curve seeking infinity.

[hannuhliz]

THANKYOU! you helped me finish my math hw that ive spent the last 2 hours trying to understand. you did; not the text book, not the math help website provided by my teacher, not my tutor, YOU...i would die if you were my math teacher!

[LtGeneralJoe]

Patrick you should be wearing a cape, because your a super hero!

[turniptod12]

Thank you for saving my grade multiple times in my trigonometry class. My current teacher decides to not teach us most days so i get lost very easily on the material. Keep it up bud i love you

[asim9420]

Dam

Ma college teacher sux 4 real

Thank u alot

[love0070803]

thanks alot~ this really helps:)

Do you also have a teaching video for "Reciprocal function"?

where?

[DangerousPirate]

After two entire years of math at this school. It's captivating to find out I finally have one good teacher before the end of my high school years. A good teacher I recognized lectures from his/her standards and not strictly according to the textbook. The worst ones are those who teaches vaguely and assumes that everyone knows as much as they do. And you my friend is a damn fine teacher, just like the one I am currently having right now, thanks for this video.

[Pipes0311]

Thank you so much, I am in Business at the university of new brunswick (canada). My teacher is less than helpful, you can just tell he does not want to be there;so it makes you not want to be there. He has made me and my class mates feel less than helpless. I came to youtube with little hope but found your videos. Now I am ready to conquer Management Calculous. Thanks so much. I wish instead of teachers in class they just showed your videos, you have a gift :)

[PinoyAznLee]

THIS HELPS A LOT. dude when my teacher was trying to explain it was a piece of shit. you on the other hand. you say it clear and straight forward. :DDD

my boyfriend's name is patrick too. are all patricks amazing at math? xDD

[JakeDobyns]

for the sake of making this country less retarded will you replace 90% of the math teachers in the US?

[patrickJMT]

@JakeDobyns ha, sure, at only 1% of the cost : )

[STRmonstruo]

@patrickJMT it costs 10million dollars to make these videos?!???~!??

[jeffreyyiu19]

@patrickJMT pls replace all the teachers in the world :)

[LeCancionista]

@JakeDobyns I agree. Thanks a lot, patrickJMT!

[markster55555]

patrick you are an Amazing teacher, no joke.

[Pinkishblue1020]

@JakeDobyns

Or not.

Someone who says "could have went" is not teacher material.

[dovegirl17]

You are saving alot of people lives Patrick :)

[TDAKitana]

I was tearing my hairs out of my scalp reading the book and searching online as i couldnt understand anything my teacher taught me.

I came across your video, and let's just say, GOD answered my prayers.

[Kibo0]

Jesus christ... HOW ON EARTH could my math teacher explain something so simple in such a hard way... Thank you patrickJMT you are fu**ing godly

[JojoFan4Evr]

I'm having my math midterm tomorrow and this is a LOT of help. I never could get asymptotes x')

Your videos are great! Even my friends/classmates watch them. I'll keep watching them -with me going to college next year, I'll be sure to watch them if I need them.

Thanks again!

[patrickJMT]

@JojoFan4Evr good luck on the exam!

[JojoFan4Evr]

@patrickJMT

Thank you very much. Things went nicely ^^

[toda9008]

@JojoFan4Evr ur gonna need them im a junior in college and my calculus prof confuses the crap outta me i have 2 tune him out and come here.

[JojoFan4Evr]

@toda9008

XD

I just put on a look like I know what my teach is talking about and take down notes

[toda9008]

@JojoFan4Evr lol me 2 but he's russian so sometimes he be talking and i be like huh what u say and he never speaks in laymen terms i be wondering to myself can he dumb it down a little. lol

[JojoFan4Evr]

@toda9008 Oh gosh X')

Well thankfully we have wonderful peeps like Patrick on here right?

[NoelRL2]

OMG I've been getting so mad in my math class because my teacher taught us this and I didn't understand it until just now when I saw this video and the one on Horizontal Asymptotes. I took notes and have been looking over them and I'm confident that I will be able to understand the work much easier now, thank you so much!!!!

[LtGeneralJoe]

Thank you once again Patrick, you have helped my expand my knowledge through your thorough teaching, your teaching skills are impeccable.

[blackberry8319]

come teach at my schoooolllll!!!!

[h3artCOOKIES]

Thanks again! You are so much help with your videos!