How to Find the Horizontal Asymptote (NancyPi)

Published on May 15, 2018 by

MIT grad shows how to find the horizontal asymptote (of a rational function) with a quick and easy rule. Nancy formerly of MathBFF explains the steps.

For how to find VERTICAL asymptotes instead, jump to the video:

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The degree of a function is the highest power of x that appears in the polynomial. To find the horizontal asymptote, there are three easy cases. 1) If the degree of the numerator expression is less than the degree of the denominator expression, then the horizontal asymptote is y=0 (the x-axis). 2) If the degree of the numerator is equal to the degree of the denominator, then you can find the horizontal asymptote by dividing the first, highest term of the numerator by the first, highest term of the denominator. This will simplify to y = some constant (just a number). 3) If the degree of the numerator is greater than the degree of the denominator, then there is no horizontal asymptote.

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  • Abhay Mehta 5 years ago

    It would be of ur great help if u could explain the chain rule.. Please..
    Student from INDIA.

    • Math and Logic 5 years ago

      PTA: power, trig, argument. Differentiate each part with the rest untouched and multiply those results.

    • Abhay Mehta 5 years ago

      DV Thank u 😊😊

    • Mike Keenan 5 years ago

      She has some calculus videos on her old channel. I imagine they’ll migrate here eventually.

  • Abel Lopez 5 years ago

    Don’t stay up too late.

    • Harjit Singh 4 years ago

      Haha, 5am already. I’ll take note of this next time…….

    • Billy K 3 years ago

      I don’t want to, but the test is tomorrow!

  • Saddam Ahmed 5 years ago


  • Hassan Malla 5 years ago

    clear thanks 👍👍👍

  • José Vivas 5 years ago

    You are the best Nancy! 😉

  • IvanMTG1 5 years ago

    I can’t maths at this hour of the night, but I’ll check these out later

    • Math and Logic 5 years ago

      Maths 24/7 brah.

    • SuperAwesomeCaptain McFluffyPants 4 years ago

      @Math and Logic totally brah. 24/7/365

  • Carlton Davis 5 years ago

    But what if we wanna mess with limits? Does the proof involve limits? Are we just letting x go to infinity?

    • Math and Logic 5 years ago

      Yes, taking the limit to pos. or neg. infinity is equivalent to finding horizontal asymptotes.

    • DavidOm 0221 5 years ago

      This is really for Algebra Students. For those who have not touched the studies of calculus. She says do not mess with limits not to stop the knowledge of limits but to prevent unnecessary confusion.

    • Carlton Davis 5 years ago

      DavidOm 0221 I get that. This is review for me, but it makes a lot more sense now. It seemed completely arbitrary at the time and I forgot the rule again already so it helps me to try to make sense of it all.

    • theboombody 4 years ago

      @DavidOm 0221 That’s why I stuck to 2 dimensions in my geodesic equation derivation. Sometimes I’m willing to sacrifice total accuracy for clarity, even though it’s usually very frowned upon.

  • MR. AJ 5 years ago

    Nice video 👌👏

  • Shirazi Ahmed Sheikh 5 years ago

    Happy to Learn from You

  • Toujours Trippin 5 years ago

    can you do one for Vertical Asymptote

    • MOizSUAVE14 5 years ago

      vertical asymptote is setting the denominator of a polynomial to = 0. then just solve for x

    • Brian V 4 years ago

      Unless the numerator has that same zero. You need the rational function to be in lowest terms for your solution to be valid.

  • amty 5 years ago

    i dont even have math to learn or do, i just watch because of nancy….

    • Math and Logic 5 years ago

      I guess the second hand smoke method of learning is better than nothing.

  • Slayerx 5 years ago

    Hey Nancy
    You look very sad and tired
    What happened?

    • Harto wijaya 5 years ago

      Ya , i also fell it, namcy take your time. We all here for you

  • Nomon Munir 5 years ago

    love the quick rules that you used for HA’s!

  • Miriam Torres 5 years ago

    I love your videos <3

  • Nikul Bhati 5 years ago

    Hi u r beautiful and plz make more videos in calculus

  • Oliver Hoyos Dominguez 5 years ago

    You should tutor people online

  • Nikul Bhati 5 years ago

    Hi Nancy do u use what’s app 9825783397 i love the way u explain with me or also check NIKUL K BHATI on face book

  • Suki Suuuki 5 years ago

  • Nameless 5 years ago


  • DavidOm 0221 5 years ago

    She said DONT MESS WITH LIMITS with such devilish eyes 😂

    • Awais Fenrir 5 years ago

      true dat xD

  • 1995 5 years ago

    Priest nanci

  • Hassan Hussein 5 years ago

    how are you writing in the air

  • Jozef Aerts Wiskunde 5 years ago

    In case the degree of the top is higher than the degree of the bottom , you have a slend asymptoot , ONLY when the upper degree = bottom degree + 1 . The long division gives you a a line . When the difference is higher than 1 , you will not have a slend asymptoot

    • Brian V 4 years ago

      In all those cases, if the top is of higher degree, then the quotient you get from long division is the (end behavior) asymptote. For example, if you did the long division and you got a quotient of degree 2, then the end behavior asymptote would be that 2nd degree polynomial. Horizontal and slant asymptotes are for linear end behavior asymptotes, but for higher degree asymptotes, they haven’t given them names. So one could say “quadratic asymptote” to indicate a 2nd degree asymptote, or “cubic asymptote” for a 3rd degree asymptote – go on from there.

      Whatever the end behavior asymptote, if you let your graphing calculator graph the original function together with the asymptote and zoom out enough, the graphs would seem to be identical; the idea being that for large values of x, the function and its asymptote are pretty much the same.

  • Uber Adventures 5 years ago

    Saved my life! Thanks.

  • tabona badzili 5 years ago

    Hey I am a student in Botswana working on a project to help students my email is please send me yours so I can give you the full review.

  • This Yellow Face 5 years ago

    for top degree, it’s none, but a more formal and exact way to write it is infinity.

  • Viktor Johansson 5 years ago

    But I do like math!!!

  • Jovilyn Greg 5 years ago

    Such a great help for our exam tomorrow! I love how u write and explain. Thank you! ❤

  • Jean Carlos Ortiz 4 years ago

    You’re videos are always helpful. You’re an amazing teacher

  • jawahaar theella 4 years ago

    mam plz give a detailed explanation of horizantal asymptotes, its origin, related concepts , where they are used and some examples if u explain them u r the one will become the person who helps me a lot. waiting for answer . plz post it soon or make a video on it

  • Mansimar Bhatia 4 years ago

    for engineering level first year is this much enough

  • surya duraivenkatesh 4 years ago

    Your tip to find horizontal asymptote really helped me. Now I don’t have to get to the standard asymptote form.

  • naveen lucky 4 years ago

    Superb Nancy

  • Miroo Kim 4 years ago

    so, what is this rule call?

  • Quin'darius Lyles-Woods 4 years ago

    This kicked ass

  • mercia vere 4 years ago

    Thanks to this video i made my homework 😂

  • Kari John 4 years ago

    You saved me thank you 🤧

  • Lawrence Oteyza 4 years ago

    Thank you! I was on the verge of smashing my head on my bed out of frustration

  • Will Pearson 4 years ago


  • Ralv 4 years ago


  • Demigod Amit Bag 4 years ago

    Plz post more videos
    Love your teaching Nancy

  • Francis Hendershott 4 years ago

    Nancy, why is it that you can take a simple concept and make it simple, while my professor takes a simple concept and make it extremely difficult. IT’S BECAUSE MY PROFESSOR WANTS TO SOUND SMART!!! You, on the other hand are humble and good. You don’t want to impress anyone, you just love math. So beautiful!!! Inside and out!!! YOU!!!

  • Will T 4 years ago

    It was very clear! Thank you!

  • LOD ing 4 years ago

    Isn’t (x-1)/(x^(3)+1) for x = 1 a contradiction to: “top degree < bottom degree -> H.A. is y = 0″?… What am I looking at differently here?? Thanks!

  • Jonny dob and Liam Ried 4 years ago

    Ok like great trick, but can u explain Y that works, I’ll get fucked if I have to explain why or do an application question with it.

  • mangobanana 4 years ago

    You remind me of Violet from the Incredibles

  • Marin 476 4 years ago

    what if theres no powers?

  • Zuhair S 4 years ago

    great as usual. lighting is kinda bad here but no problems ur other vids are fine

  • Jessica C 4 years ago

    You don’t have a video for slant/oblique asymptotes? 😫

  • DARIEN Ford 4 years ago

    Stop making things this easy it is starting to scare me

    • Na Zombie 3 years ago

      It shows your learning if it looks easy to you!!! It was hard before right? Now you truly understand

    • Nico Piazza 3 years ago


    • Krronx 3 years ago

      @Nico Piazza ….

    • No. K 3 years ago

      @Nico Piazza you’re so cringe

  • Luisa Velez 4 years ago

    you are amazing!! 😱i cant believe someone made it so simple…. now i look at my class notes and wonder if my teacher made it so complicated on purpose🤔

    • alex hernandez 3 years ago

      for real. I feel like he wants to make it harder to seem smarter

  • Emmanuel Olguin 4 years ago

    would you take me to prom?

  • Lambros Pittas 4 years ago

    i like how u write opposite

  • Jorge Ramos 4 years ago

    Awesome videos!

  • Jason.A 4 years ago

    What if the rational function is factorable, do I do that before solving for HA, because then I would have 2 factors which I’m stuck on

    • Brandon Beins 4 years ago

      To my knowledge you would not factor first. You would take the degree given.

    • Jason.A 4 years ago

      Brandon Beins so would I simply the rational function then foil it to find the highest degree and just leave it as that to find HA?

  • Ben 4 years ago

    such HQ work- great job Nancy.

  • ِ 4 years ago

    Hi nancy

  • Jokey Joe 4 years ago

    this video saved my life

  • Spencer Blair 4 years ago

    Yo somebody feed nancy

  • Saisriram G 4 years ago

    Clicked on it when I saw MIT grad xD

  • emaan presswala 4 years ago

    This video makes H.A. so much easier to solve. Thanks!

  • Greg Johnson 4 years ago

    How in the hell are you writing backwards????

    • Thejas Kodoth 3 years ago

      @Waqqi Ali i know im just trolling

    • Thejas Kodoth 3 years ago

      @Waqqi Ali well, she writes on glass just like you and me write on paper, records it from the other side of the glass and the uses a software to mirror the whole video so that we can read it.

    • Waqqi Ali 3 years ago

      @Thejas Kodoth Wow, I didn’t see that, thanks

    • Na Zombie 3 years ago

      She is wizard Harry!!!

    • lukas graumans 3 years ago

      @Detiz Dynamite no that’s impossible then she’d still be writing weird i think

  • Julio Carballo 4 years ago

    I love you Nancy Pi💚❤️, thank you and thanks god for running into your videos , keep going your helping so muchhh

  • Danymok 4 years ago

    I cannot believe it is that simple! Thank you so much!

    Also, you are very skillful to be able to write backwards that well. 👍

  • max m 4 years ago

    shes so smart she can do this and write backwards!

  • Anar Valehli 4 years ago

    You are fantastic thanks a lot.

  • oscar caballero 4 years ago

    Thanks, NancyPi, you make Math so easy for me. Good job

  • Bun Bacon 4 years ago

    you look like a robot

  • Inayah Cee 4 years ago

    How are u able to write backwards, that’s crazy. And u write so neat and straight, mind blown.

  • Mary Jon 4 years ago

    you got the scariest eyes

  • oscar caballero 4 years ago

    You deserve a Nobel prize since you help the students overcome one of biggest rock in the way pursue a career or major; Maths.
    You make Maths seem so simple. God bless you, Nancy for doing a good job

  • udit saxena 4 years ago

    Thank you so much you make maths so easy

  • HostageTurkey 4 years ago

    I hope you record theses writing normals and then mirror the image. If not you are possessed. But hey helpful video thanks!!!

  • عبدالعزيز الامام 4 years ago

    Thanks ms. Nancy my final exam about 3 hours later and you give me a huge favor by explane me this semple rules peace🌹👍

  • Emma Smith 4 years ago

    OMG! I have a quiz tmw. And I’m freaking out, but you made it so easy!!!!

  • Madam Marie 4 years ago

    Wow, my textbook and professor made it so complicated. I love your video and you are excellent! I’m so glad I found you, may you have a successful and bright future!

  • Xoned Out 4 years ago

    The video is inverted. Your welcome

  • Joshua Kuebler 4 years ago

    wow. beautiful, smart, and explains it clear and concise so i am able to understand. subbed! thank you.

  • Marietta AH 4 years ago

    Slant asymptote ??

  • Math Fx 4 years ago

    You’re so beautiful and smart c:

  • O L 4 years ago

    her voice gives me ASMR ha ha:)

  • Mitch Match 4 years ago

    Weird flex, but okay

  • Vemitha Bandara 4 years ago

    Thank you very much. please keep up doing more videos. Really appreciated!!

  • Loreina Joseph 4 years ago

    Okay but asides from the fact that she’s a great teacher she’s now reached the top tiers of awesomeness because of her ability to write backwards so perfectly

  • Afnan !! 4 years ago

    You make it so easier to me thanks a lot 😍

  • Ömer Kılıçkaya 4 years ago

    what is this h.a
    @nancypi thanks

  • Todd Hood 4 years ago

    Thank you so much

  • shukor asmar 4 years ago

    what if you don’t have a x on the numerator and just have it on the denomintor what do you do then

  • Mathematics - the god's language 4 years ago

    But what is a horizontal asymptote?🤔

  • jecruz66 4 years ago

    Thank you!

  • Sinan 4 years ago

    People really came here to learn about asymptotes and are still confused on how she rights backwards

    I’m really confused right now

  • Sergiu George 4 years ago

    But oblique asymptotes? These are the hardest

  • GBIEL PASCAL 4 years ago

    Your way of tackling math problems is just amazing. Love you so much. You make math easy for me

  • Mohammed Al-Shatub 4 years ago

    Awesome. Thank you so much

  • SSR 4 years ago

    Yay, thank you!

  • Solid F 4 years ago

    thank you . you made my day : )

  • Sonneth Sawyers 4 years ago

    Nancy look tired in the vid , and tyyy I understood now 😘

  • Sky Fly 4 years ago

    What the fudge. I know every student is different and learns differently but gosh I wish I had this kind of teaching in high school. I’m here struggling in college algebra … in college. I have my exam tomorrow and youe videos are helping me so much. I wanna cry lol. Omg God bless you! Thank you!!! 🙌🏽

  • Mike Xue 4 years ago

    you look tired, don’t do too much hard work.

  • Marietta AH 4 years ago

    Slant asymptote?

  • Marietta AH 4 years ago

    Thank you Nancy

  • zack hebert 4 years ago

    You fine 😭

  • Deana Rossi 4 years ago


  • Karen Macpherson Wessinger 4 years ago

    how do you make it so easy? Thank you so much, if it weren’t for your videos I’d be failing!

  • Mikiminach Edits 4 years ago

    This don’t make no sense my equation looks a lot more different

    • Sven 4 years ago

      simplify ur equation dude

    • Mikiminach Edits 4 years ago

      This was three days ago lol

  • Kevin Malone 4 years ago

    thank you so much. you are a genius!

  • Elaine L 4 years ago

    thank u! u explained it so much quicker and easier than my textbook

  • rowdyruffbrick123 4 years ago

    i love u

  • Harold Andrade Borbor 4 years ago

    Thanks a lot.

  • Kevin Loftus 4 years ago


  • Jeffrey Jordan 4 years ago

    What if the numerator is inside a square root?

  • Chosen 4 years ago

    That’s why you didn’t write anything in the thumbnail because it’s none which means invisible.

  • ricky spanish 3 years ago

    Thanks alot, books and teachers tend to over explain such a simple concept.

  • ThvtSyDneYlyf3th0 3 years ago

    I don’t wanna mess with limits so i liked your video 🙂 Cheers Nancy !

  • TheBoss V 3 years ago

    Thank you madam I didnt know how to study the horizontal asymptotes

  • Odiggidydog 3 years ago

    Nancy Pi is my HERO!!!!!!!

  • Burke Becklund 3 years ago

    Great videos. Multi Color and Writing backwards is amazing. Oblique Asymptotes Please

  • Luiz França Martins 3 years ago

    I’ve been wondering all through my math classes, “there has got to be an easier way to learn these things”. Thankfully, youtube made it possible for us students to see those ppl who found a simpler way to explain math!

  • Isabel Lopez-Santiago 3 years ago

    NancyPi saving my math grade AGAIN 😀

  • kaelyn 3 years ago

    all i have to say is thank you for making this soooo simple:)

  • Eric Jaramillo 3 years ago

    Literally have an assignment due in the morning and u saved my guts tysm:)

  • Henry Ulloa 3 years ago

    gracias fue de gran ayuda,se me abia olbidado

  • muhammad saeed yamin 3 years ago

    asympototes of

  • Veritas et Aequitas 3 years ago

    A-symptote with a long A as in asympomatic or atypical, from greek a “not” + symptote “coming together, rather than “ass’m tote”.

  • Ryan Dyjur 3 years ago

    lol the ads at the start of these videos always pander to anxious students with bad instructors… like get outta my face, NancyPi is about to teach me exactly what I searched for

  • Epotimet93 3 years ago

    Thank you!

  • Nessy Ndipolifa 3 years ago

    you made me love math and have a dream to teach it to my learners to be the way you do it. stay cool

  • Bimal Shahi 3 years ago

    Thank you so much.Your 5 min video is way more better then couple of months in math function class.

  • Ibrahim Lawal 3 years ago

    Pretty and SMARTTTTT

  • Eyad Karkadan 3 years ago

    Thank you Nancy, passed the test with full mark.

  • nancy 3 years ago

    is horizontal asymptote the same as end behavior?

  • Abdikader Abdi 3 years ago

    Thank you. You’re the best.

  • Alex Dollar 3 years ago

    Ha ha ha

  • Mike Batres 3 years ago

    Your videos are amazing, I have to take my algebra final on monday and i know im going to pass it because you explain these concepts in a way I can understand them.

  • Ehsan Khokhar 3 years ago

    thanks a lot

  • Chloe Longman 3 years ago

    thank you SO much for this. i’ve been crying all morning not understanding horizontal asymptotes and this has literally saved my life

  • Allan Morales 3 years ago

    If i get an A on my Calculus test can i go on a date with you?

  • Adrian Gonzalez 3 years ago

    Hey you make a cute hobo.

  • Beesafree 3 years ago

    are you writing backwards? o.O
    holy hell…

  • Jane Margaret McEachin 3 years ago

    i wish my skin looked this good

  • AgentK200 3 years ago

    Thank you!

  • Maketa Nine 3 years ago

    Thank you for your teachings.

  • Maths Explained 3 years ago

    Awesome 🙂 thanks

  • Jose Luna 3 years ago

    Nancy, you are beautifully smart

  • Quavo 2k 3 years ago

    thanks nancy

  • Caramel Woodpecker 3 years ago

    Haha “you dont have to like math but u can like my video”

  • Caramel Woodpecker 3 years ago

    Can u make a video about oblique/slant please???

  • İbrahim Gökpınar 3 years ago

    this is the best video for this subject . u’re the best teacher i had ever seen.

  • Tryggi N 3 years ago

    Very excellent explanation

  • Steven Sealey 3 years ago

    I have been seriously stressing over this stuff. Your videos have made this extremely easy to follow and understand!

  • prum chhangsreng 3 years ago

    Damit, i learn so many thing from Nancy and its funny how most of the thing that u thought it hard, it actually very easy🤣
    I learned Limit, Verticle, horizontal asymptote and derivative from u so far. Limit and derivative, i havent reach those lesson yet, but i alr know how to do it all by watching those 10-15mn videos. Its just so “work” that i find it funny. 🤣

  • Clea H 3 years ago


  • Peter Lohnes 3 years ago

    Not true for y=(-x^2 +6x +2) divided by (2x^2 +14x +12) which should have a y asymptote of -1/2, unless you are saying you ignore negative symbols, than true for y=1/2…still confusing

  • Eria Kiyemba 3 years ago


  • Lebogang Moloto 3 years ago

    Thank you Nancy

  • Michael 3 years ago

    sup boys

  • fatima ali 3 years ago

    is not she the cutest?

  • josh vsss 3 years ago

    Violet from increíbles

  • rambo ma490 3 years ago

    thanks for the video. I tried to understand what my book said about horizontal asymptotic, but they can’t present it in a way easy to understand. they like to complicate everything

  • Ruby Honda 3 years ago

    Thank you Nancy! You’re the best

  • haechan 3 years ago

    ahh.. thank you for making this so simple 😭

  • Rickey P 3 years ago

    you saved my life during quarantine. if it wasn’t for you, i’d fail algebra

  • Patricia Anahi Estrada 3 years ago

    Nancy, your videos have assisted me greatly in my Business Calculus Class. You are able to break down the concept and problem in such an incredible way that people like myself who have struggled all my life to understand Mathematics can learn problems I never thought imaginable. Thank you!

  • CandieP0PK!T 3 years ago

    what does it look like on a graph…. that would help thanks

  • Saidov Jamshid 3 years ago

    So basically, it is what is called ‘limits’, isn’t it

  • Adekola Akanni 3 years ago

    Good Work. Learning made easy. Thanks.

  • Raj Farakh 3 years ago

    how is everything this easy, what is my college professor being paid for? making me watch nancy do his job?!

  • esmeralda saxenian 3 years ago

    i have failed one exam because i got these wrong, i wish i could go back, you have made it so easy

  • Fahim Islam 3 years ago

    can someone PLEASE tell me how she’s writing from behind the glass but still the letters aren’t flipped

    • Arda Atmaca 3 years ago

      She writes on a glass in front of her, and then edits the video so the image flips horizontally. She is actually right handed.

  • Raquel Domingos 3 years ago

    excellent teacher Nancy, you earned more one subscribe.

  • Na Zombie 3 years ago

    Great explanation!!! I am still going to practice the oblique or slate asymptote. Can you make a video on long division with equations?

  • Ak &co 3 years ago

    Thank you ma’am 😄

  • Add it 3 years ago

    Whyyy did my lecturer teach me limits and not this simple rule 🤦🏾‍♂️

  • HyperStrike 3 years ago

    I have a visual representation as to the three rules why they are the way they are:

    1) top degree>bottom degree: in this case, as x gets arbitrarily large (which always happens on an infinitely large plane), the quotient (x/x2) becomes lightheaded, on other words, when approaching large values of x, the x squared on the bottom is always larger than the top, so it is approaching a 1/∞ case (an infinitesimal) that’s why the graph approaches 0 but not quite zero, same as the property of 1/∞.
    2) second case x2/3×2, same degree top and bottom, any term that is not the highest degree will be negligible in value once x reaches near ∞ (which, large x values will always be present on an infinitely big number line). So in this case, the leading coefficient matters a bunch, because as x gets arbitrarily large, the ratio of the large leading terms will be determined by the leading coefficients (∞/3∞) which is 1/3, but not quite, so it approaches horizontal lines in the ratio of the top and the bottom leading coefficients.

    3) top being greater than bottom degree, this case, the bottom will get smaller the larger x values you put in. And again, any non highest degree terms will be negligible with high enough numbers, like adding 1 to 10000 is 10001, but approximated ten thousand, just as (10000+1)/(100+3) is 10001/103, approximately ~100. But as x gets larger, the gap between the top number and lower number increases because of the degree difference, so the value approaches infinity. For this, there is not defined asymptote, because the asymptote is located at y=∞, where the hyperbolas are gradually approaching. ( the asymptote exists but we can never see it, it’s ‘so high up’ that it’s undefined).

  • Sam Trieu 3 years ago

    Nancy is 10/10

  • Blessing Mare 3 years ago

    I absolutely love how u make it so understandable ❤️💕💕❤️and so simple I absolutely love you 💖

  • Yosh 3 years ago

    I was not taught this and became confused in my final review. This ideas seems to be the only one I could find that didn’t mess about and just explained it. By far the best video on this topic.

Comments are closed.