Vertical Asymptotes… How? (NancyPi)

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Published on May 17, 2018 by

MIT grad shows how to find the vertical asymptotes of a rational function and what they look like on a graph. To skip ahead: 1) For the STEPS TO FIND THE VERTICAL ASYMPTOTE(S) and an example with two vertical asymptotes, skip to 0:19. 2) For an example in which FACTORS CANCEL and that has one vertical asymptote and a HOLE, skip to 5:58. 3) For an example with NO VERTICAL ASYMPTOTES, skip to time 10:12. Nancy formerly of MathBFF explains the steps.

Follow me on Instagram! https://instagram.com/mathnancy
Follow me on Twitter: https://twitter.com/nancypi

For how to find the HORIZONTAL ASYMPTOTE jump to: https://youtu.be/qJrrZQgSkO8
For how to FACTOR quadratics jump to: https://youtu.be/YtN9_tCaRQc
For how to find the DOMAIN of a function jump to: https://youtu.be/GQGFMUfr10M

What is a vertical asymptote? It's an invisible vertical line that a function gets really really close to but never reaches. How do you find the vertical asymptote(s) from the given equation?

THREE STEPS TO FIND THE VERTICAL ASYMPTOTE(S): For a rational function, there are three main steps you can always follow to find all the vertical asymptotes, if there are any:

STEP 1) FACTOR: The first step is to factor the top and bottom (numerator and denominator) if you can, and as much as you can. For instance, in the function f(x) = (x^2 + 3x - 10)/(x^2 - 4), you can factor both the top and bottom. The numerator, x^2 + 3x - 10, is a quadratic that factors into (x + 5)(x - 2), and the denominator, x^2 - 4, is a difference of squares that factors into (x + 2)(x - 2). You then rewrite the whole function with both of these factorizations so that you have f(x) = [(x + 5)(x - 2)] / [(x + 2)(x - 2)].

STEP 2) CANCEL: Next, simplify the function by canceling any factors that are the same on top and bottom. If there are no common factors, you can leave it alone. In our example from Step 1, there is an x - 2 term on both the top and bottom, so we can cancel those two factors. You can rewrite the function after getting rid of those similar factors so that it looks like: f(x) = (x + 5)/(x + 2).

STEP 3) SET THE DENOMINATOR EQUAL TO ZERO: After simplifying and getting rid of any common factors, the last step is to find the real zeros of the denominator by taking the bottom of the simplified function and setting it equal to zero. You then solve that equation for x, and any real numbers you get as a solution for x are where there are vertical asymptotes. You can write your answers as just "x equals [some number]". If you have vertical asymptotes, they will always be in that form, such as x = 3 or x = -2. These represent vertical (invisible) lines on the graph that your function approaches but never crosses.

Remember that if you get an imaginary answer when you solve for x (such as a square root of a negative number), then there are no vertical asymptotes. If there is no real solution when you solve for x, then there are NO VERTICAL ASYMPTOTES. Note: By the way, if you had factors that cancelled in Step 2, that created a "hole", or removable discontinuity, on the graph where the function was indeterminate.

For more of my math videos, check out: http://nancypi.com

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202 Comments

  • Carlton Davis 4 years ago

    Her titles be like…
    *Verticle Asymptotes… WTF*

    • Carlton Davis 4 years ago

      Abhishek Patil My students usually like my jokes, but whatever. Can’t please everybody.

    • Vegs 4 years ago

      ๐Ÿ˜‚

    • Carlton Davis 4 years ago

      Looks like somebody deleted their comment LOL

    • DG French 4 years ago

      i thought it was kinda funny

  • amty 4 years ago

    NAAAAAAANNNCCCCYYYYYY

  • Abhishek Patil 4 years ago

    You are math goddess really ๐Ÿ”ฅ

    • AJ Walid 4 years ago

      You guys scared the shit of out this poor girl. She is not a Goddess. I think you people say that because is cute. ๐Ÿ˜›

    • Kartik Ahlawat 4 years ago

      LOL….That’s Mirroring Boi…..But she really is math goddess cuz she made maths way too much easy.

    • ZEE LOW 3 years ago

      This goddess got braces

  • Ankur Giri 4 years ago

    ๐Ÿ˜๐Ÿ˜๐Ÿ˜๐Ÿ˜๐Ÿ˜can u please even make a video how you got into mit i m very inspired by the way i love vertical asymptote

    • Nikul Bhati 4 years ago

      Ankur Giri all about practice and love

  • Paolo Perrusi 4 years ago

    I already know this, watched for her

    • Creampie 4 years ago

      my bois a scholar

  • Sayan Khan 4 years ago

    Happy to see you back again

    • Creampie 4 years ago

      VERY happy to see her ๐Ÿ˜‰

  • Nikul Bhati 4 years ago

    Hi Nancy,you are beautiful, plz make more videos in calculus…check Facebook ‘nikulkbhati’

  • Harto wijaya 4 years ago

    From Indonesia. Hebat, semangat Nanci

  • Leonardo Camargo 4 years ago

    It would be cool if you had advanced math videos too.

  • Abhinav Kumar 4 years ago

    Lucid way of teaching! love from ๐Ÿ‡ฎ๐Ÿ‡ณ

  • Vishwas Mishra 4 years ago

    Can you post videos on integration

    • Hiromi Shimada 4 years ago

      TECHNICAL ADDA she didd in her previous channel Math Bff

      youre welcome.

  • Nikul Bhati 4 years ago

    Nancy you should answer about questions of your viewer,this is increase your viewer to billions

  • Ee bsy 4 years ago

    Hi Nancy! Could we please get a video for partial fractions?

  • gameking008 4 years ago

    Your math videos are really good quality. Excellent job.

  • Daniel Lopez 4 years ago

    Finding asymptotes is so much fun. Graphing them, oh my goodness yes!

  • Walt R. Buck 4 years ago

    Unpaid Cringy Advertisement: Before I started watching NancyPi, I didnt know my asymptote from a hole in the graph. Now I wipe math problems all day long. Thanks Nancy! (cheesy smile).

    On a serious note. Excellent, clear, easy to understand videos. Thank you.

  • Kk 4 years ago

    I know this topic but I am here for ASMR

    • Samanta Rizzi 3 years ago

      Kk omg yes!!! Her voice is so soothing! โ˜บ๏ธ I actually have a math exam in the morning (8am) and now itโ€™s 1am and her voice is making me so sleepy I have to stop studying and go to bed. ๐Ÿคฃ

    • PatWizard 2 years ago

      yeah math tutorials are great for it

    • Ogle Noelle 2 years ago

      ASMR?

  • Chaminda Silva 4 years ago

    Thanks for teaching me how to find the vertical asymptotes of a rational function.

  • Mario 4 years ago

    I missed you ๐Ÿ™

  • Sal Carrera 4 years ago

    awesome, great video

  • Chaminda Silva 4 years ago

    Nancy,
    Please help me to find the Holes and the Vertical Asymptotes of the following Rational function.

    F(x)=(x+1)/(x+1)(x+1)

  • Jozef Aerts Wiskunde 4 years ago

    You cannot remove x-2 from the function ! Like you explain , x= 2 is a hole and (x+5)/(x+2) does not have a hole x= 2

  • Dyne 4 years ago

    As always thanks for taking the time to do these videos. Great quality and easy to understand, well done. Glad to see you are back.

  • Iadministrator Iadministrator 4 years ago

    lim x {x:–>(1/0)}
    x=happiness after watching your lessons.
    A feeling I have missed for decades.
    Thank you.

  • joanna pera 4 years ago

    thanks…..ur so sweet….

  • Adam Wizard 4 years ago

    I thought this would be hell, but you have a good way of calming down peoples nerves. You know math is hell, thank you for reducing it to hell-2x^2

  • ramzan ali 4 years ago

    she is sooooo relaxing

  • annavictoria12345678 4 years ago

    I think its fun

  • Jason Radford 4 years ago

    Thanks Nancy!
    I’ve watched a few of your videos to help catch onto some basic stuff for college algebra quickly. You are a natural educator! Love the see-thru board for visual reference and your approach to the material. You know how to make people watching feel like “relax… we got this!”
    Please keep posting. I plan on getting all my math knocked out with your videos! LOL

  • Casper Rishad 4 years ago

    You are so relaxing!! But don’t get confused about your viewers’ thoughts!

  • A. Farah 4 years ago

    I have a great respect for you you , you save my life

  • Hiromi Shimada 4 years ago

    it’s so nice to see you again nancyyyy

  • Ginormous Lemon 4 years ago

    ph

  • GigglezGoHam 4 years ago

    ur hot

  • Mimo 4 years ago

    Thanks A Lot U Dont know How Much U Helped

  • Mystic Trinket Shop 4 years ago

    Question – When does the infinity or negative infinity symbol apply??

  • Just Me 4 years ago

    Is she writing the opposite way?

    • Shahid Ilyas 4 years ago

      the video is flipped horizontally

  • Mark Landau 4 years ago

    i’ve been away from the maths for a couple years but now have to wade through calc. SO thankful that i found you again!!!

  • Mark Cabrera 4 years ago

    You FREAKING ROCK!

  • Dalyssa Moya-Rodriguez 4 years ago

    I love u

  • DreamKeem 4 years ago

    Damn I get sidetracked easily. this whole time Iโ€™ve been trying to figure out what type of sorcery is this?! Are you writing inverted or backwards? Hmm is the camera inverted and your really writing with your right hand instead of your left ??๐Ÿค” maybe she edits it ?? So many question, only getting VA answers.

    • T0XIDITY 2 years ago

      I know my response is pretty late but here you go

    • joe manuel 2 years ago

      @T0XIDITY holy shit thank you ๐Ÿ˜‚

    • Allie Perez 2 years ago

      @T0XIDITY oh my god duhhhh!! Thank you!

    • T0XIDITY 2 years ago

      joe manuel lol no problem lol๐Ÿ˜‚

    • T0XIDITY 2 years ago

      @Allie Perez no problem

  • Johura Mumin 4 years ago

    Thank you so much!! Youโ€™ve helped me so much through Calculus & Pre Calc! You explain everything so well. Thank you thank you โค๏ธโค๏ธโค๏ธ

  • Kari John 4 years ago

    so I did the example on my own just to see if I really knew how to do it & I factored the denominator into (x+6)(x-1) help me ๐Ÿคง

    • Ashley Blue 4 years ago

      if you foil this, you times 6 by -1 which equals -6. In the polynomial, the 6 is a positive.

  • LivingLIEfe 4 years ago

    She said hi and I instantly liked the video

  • Ralv 4 years ago

    i dont know what i would do without you. Dr-teachers in uni cant explain a simple thing when you explain the whole thing in couple of mins when they take an hour and 50 mins for a single idea and still people confuse to solve them lol.

  • UltraPhoneGamer 12345 4 years ago

    So is the VA just the values the domain of the function doesn’t include

  • greenelephant1231 4 years ago

    hot white chick

  • Brandon ignacio 4 years ago

    What do you think shes saying at 9:18

  • Nashwan Muthana 4 years ago

    thank u

  • yousef Al-Moustafa 4 years ago

    ูŠุณุณุณุนุฏ ุงู„ู„ู‡ ุงู†ุง ุจุฏูŠ ุงูู„ู„ ุงู„ูƒุงู„ูƒูˆู„ุงุณ ู…ู† ูˆุฑุงูƒูŠ โคโคโค๐Ÿ˜๐Ÿ˜๐Ÿ˜๐Ÿ˜

    • JayDog 1407 4 years ago

      E. yousef AL-Aga what

  • Je No 4 years ago

    She makes it look so simple thatโ€™s why I like her so much ๐Ÿ’›๐Ÿ’›

  • YJ Jung 4 years ago

    can’t focus on the lecture. She is distracting!

  • Republic BMC 4 years ago

    My only regret is that I did not discover this channel earlier. You are making calculus way too easy. Thank you for saving my grade.

  • Jon Searle 4 years ago

    he he, slight error with the plot of f(x)=(x-1)/(x^2+5x+6), at f(0)=0 but at as x->+infinity, f(x) -> +0 from the positive side, so the graph goes up and though the origin and then comes down and approches the x axis as the horizontal asymptote. Whacky graph!

  • Vannia Flores Forsyth 4 years ago

    HOW CAN I FIND OUT THE DIFFERENT ASYMPTOTE EQUATIONS FROM A GRAPH? WITHOUT HAVING ANY INFORMATION ABUT THE FUNCTION EQUATION?! PLEASE!

  • Alexito Pro 4 years ago

    NANCYPI…. YOU ARE JUST AMAZING!!!! MY FIRST VIDEO WAS INTEGRALS…… FROM PERU, I JUST WANT TO SAY: THANK YOU VERY MUCH!! NEW SUBSCRIBER HERE. HOPE YOU WILL KEEP POSTING REALLY USEFUL VIDEOS….. L.I.A.T.E <3 REALLY, FROM MY HEART, I JUST WANT TO THANK YOU :') REGARDS FROM PONTIFICAL CATHOLIC UNIVERSITY OF PERU

  • Talha Jat 4 years ago

    May I put My Vertical Asymptote in your Horizontal Asymptote

  • sophia munoz 4 years ago

    thanks Nancy ๐Ÿ˜ฉ๐Ÿ˜ฉ๐Ÿ˜ฉ

  • Kuikala Naeole 4 years ago

    9:17 funniest word twister i replayed it like 20 times. Great step by step process

  • Mr. Warrior 4 years ago

    โค

  • Sammy Sole 4 years ago

    Making my math world a lot easier to navigate. I love you Nancy!

  • vanessa chen 4 years ago

    Thanks, very helpful video.But if the denominator is just “X” value in a rational function, how can I find the vertical asymptotes .

    • kang of octopia 3 years ago

      x would simply be zero, I think.

  • IKKO 4 years ago

    Wow! Unlike most math teachers, this one actually speaks like a human being and explains stuff in the way a human being can understand.
    Thank you.

    • Lebrin Rajan Levi 3 years ago

      I know right!!! It’s like you going to a doctor and they say all this medical language to you for some time, and then you have to interrupt and say, “In English, please.”

    • Chosen 3 years ago

      But the way she writes is weird, inverse, and creepy. Despite for giving me creeps, she also gives me great knowledge that motivates me to become an engineer.

    • Anan Baban 3 years ago

      Wow, amazing. Even other youtube videos could not make it this clear. Also, I get a vibe that you are a human being on the side, I enjoy that too, it makes me feel less desperate for some reason.

  • aloke bachhar 4 years ago

    Thank you mam.It was really helpful.

  • Sara Aman 4 years ago

    thx for every thing

  • Noor Zua 4 years ago

    Ur better than my own math teacher thnxxx

  • iionic 4 years ago

    Y’all are all here to creepily hit on this woman who’s just teaching im just here for the math dawg im tryna pass this test

    • Veritas et Aequitas 3 years ago

      Y’all here to deny the biological mechanisms present in nearly all species.
      1. Female displays availability or not
      2. Males demonstrate interest
      3. Males compete
      4. Female chooses based on competition or competitive factors.

    • MinerBoB 3 years ago

      @MrAcebak Just because its a math video doesn’t mean you cant watch it without doing math. Its on the internet and people watch it.

    • MrAcebak 3 years ago

      @MinerBoB I think you missed my point

    • Cackling Muse 3 years ago

      +iionic stfu

  • George Polasky 4 years ago

    Very nicely explained, as always, Nancy. Crystal clear. And thank you for always being so personable and sweet in your presentations.

  • Abdulrahman Alanazi 4 years ago

    ๐Ÿš

  • Abdulrahman Alanazi 4 years ago

    ๐Ÿšยฐ

  • Abdulrahman Alanazi 4 years ago

    ๐Ÿšยฉ~ยฐ

  • Abdulrahman Alanazi 4 years ago

    Maybe the helicopter when the engine turn on
    Are this coantety vertical asymptotic

  • Abdulrahman Alanazi 4 years ago

    Horizontal lines

  • Abdulrahman Alanazi 4 years ago

    Dinmometr + horizontal +asymptotic = vertical no show byonic speed

  • Javier 4 years ago

    How are we supposed to concentrate when ur so hot๐Ÿ˜‚๐Ÿ”ฅ๐Ÿ”ฅ

  • Em Pierce 4 years ago

    Please do oblique asymptotes too! I had to go to PatrickJMT figure them out. Thanks for all this though. I’m doing well in my Calc I course thanks to you!

  • Doug Spurell 4 years ago

    In example 2, is it a curiosity that the reduced form “x+5/x+2” is wow ๐ŸŽ‰magically now defined at x = 2 ….by virtue of just cancelling the x-2 terms top and bottom? …..the inequality must be because f(x) at x=2 has been negated.

  • Adarsh Van Persie 4 years ago

    Mam how to we Find Asymptotes of transcendental Functions?

  • Serat Bhuiyan 4 years ago

    did u attend to MIT and why r u so beautiful?

  • Matthew Fuller 4 years ago

    Nancy, You are not only lovely but your videos are very helpful and you explain things simply. Thank you for doing what you do.

  • fernando valck 4 years ago

    She is ๐Ÿ˜

    • Chosen 3 years ago

      Lovely

  • Arsalan Khosrojerdi 4 years ago

    fancynancy

  • Abraham Hamadi 4 years ago

    For the first example is the vertical asymptotes infinite or removable?

  • Alex Casanova 4 years ago

    Hard to concentrate when youโ€™re this hot nancy

    • MrAcebak 3 years ago

      dont be a creep

  • tuhin Imrul 4 years ago

    Thank you that was really helpful

  • A. Jel 3 years ago

    Can I just have NancyPi from now on please?? Thank you.

  • Jessica N 3 years ago

    A calculus goddess

  • GBIEL PASCAL 3 years ago

    NancyPi i really love your step by step approach to this math problem. God bless you. But i have a problem with the question two. The answer you got was -2 and that was dependent on the factors you chose, i.e, +5 and -2. I on the other hand chose -5 and +2 as my factors and as such the answer is +2. Does that mean my answer is wrong??? Please get back to me.

    • Hyujabut44 3 years ago

      The order of your signs matter. Because you have to look at the original equation. Even though you got the numbers right, if you put your sign in the wrong place, it will screw up your answer. When you foil out the factors, you should get your original quadratic. If you do not have the same signs as the original, then you put them in the wrong place.
      Original Quadratic: x^2+3x-10
      EX: (x+5)(x-2) These are the correct factors. Why?
      FOIL = First, Outer, Inner, Last
      First term: x^2
      Outer Term: -2x
      Inner Term: 5x
      Last: -10

      Ergo when you combine like terms, 5x-2x = +3x
      Therefore your signs match the original. We have a postivite x^2 a positive 3x, and a negative 10.

      What you did would have been right if the signs of the original quadratic were -3 and +10. Does that make sense? I really am not good with math, but I hope I helped you somewhat.

    • GBIEL PASCAL 3 years ago

      @Hyujabut44 Thank you very much. You are right and I understood you. God bless you too.

  • bnr32 3 years ago

    she needs a joint

  • Ajmal Maad 3 years ago

    I found your trick you simply flip the video.๐Ÿ˜๐Ÿ˜๐Ÿ˜‰

    • Mahendra Sankhe 3 years ago

      Thats not trick man

    • Mahendra Sankhe 3 years ago

      Just simple logic

  • Samoshke 3 years ago

    As I checked, it seems both of your graphs are wrong. please check it on Grapher or Mathcad.

  • SSR 3 years ago

    Thank you so much, I checked out a lot of vids but this one’s the clearest ๐Ÿ™‚

  • ๊น€์šฉ๋ฏผ 3 years ago

    Easy..

  • Nathan Bruce 3 years ago

    Great video, reviewing for finals. Thanks!

  • RutuRaj Patil 3 years ago

    Doubt cleared….Thank You… Nancy Pi

  • Bill 3 years ago

    You can factor x^2+1 with imaginary #’s. (just FYI)

  • Mahendra Sankhe 3 years ago

    Is that limit ?

  • AO Infiltrater 3 years ago

    You said everything except what I fing needed, you teachers always forget something, what if you have x squared+9/x squared – 2x – 15. You teachers always miss something and never fing say it. And when. Some one like me is searching for it you guys never cover it!
    If your going to teach cover every angle of an equation, is stupid how yous guys do that, its frustrating! COVER EVERY ANGLE! Please

  • H Malik 3 years ago

    Thank you

  • Smaail Ouadi 3 years ago

    Thanks nancy๐Ÿ˜

  • islam' s beauty 3 years ago

    Your method of delivering the lectures is superb

  • Andy Martir 3 years ago

    damn i cant focus cuz ur so beautiful

  • Zaiadiaco Joao 3 years ago

    Hi Nancy. under what conditions can we find the vertical asymptotes? does the degree of the numerator has to be smaller? can we still find the vertical asymptote if the degree of the numerator is greater than the degree of the denominator??? please!!!

  • M.Cs. Felipe Fresno R.- 3 years ago

    A good exercise would be: Find V.A of the following functions: y = tan(x) and f(x)=e^x+e^{-x}. This are not rational functions so….. how do you determine the V.A in this cases?

  • Vishal Kumar 3 years ago

    I have a doubt, when we have cancelled x-2 from the function then why it is not defined at x=2

    • reese 3 years ago

      because then, it means that an x-value does meet 2 where as in a vertical asymptote, it means that it never touches that number. if i’m not mistaken.

    • Vishal Kumar 3 years ago

      @reese ok
      Thanks

  • mario arrizon 3 years ago

    Simple, clear and precise, Math is a lesson in logic. Tank you, Nancy.

  • serrano 0.l 3 years ago

    Saved me tears.
    My teacher taught this yesterday and now wants us to know it by heart for tomorrow. You saved my grade.
    Kudos!!

  • Emily Haustein 3 years ago

    She is the math queen!!!!

  • pvn wong 3 years ago

    focus the right side of your screen! don’t forget you are learning math here , not watching girl.

    • Edward Mulenga 3 years ago

      Hilarious … i am trying

  • ___ 3 years ago

    ูŠุนุทูŠูƒ ุงู„ู ุงู„ู ุนุงููŠุฉ ุนู„ู‰ ุงู„ุดุฑุญ ู…ุชุงุจุนูƒ ู…ู†kfupm ุงุญุณู† ู…ู† 100ุฏูƒุชูˆุฑ ู…ุฌุชู…ุนูŠู†

    • ___ 3 years ago

      @Nursin 1999 ุงุฏุฑูŠ ุจุณ ู…ู† ุจุงุจ ุงู„ุชู†ูˆุน ููŠ ุงู„ู„ุบุฉ ููŠ ุงู„ุชุนู„ูŠู‚ุงุช

  • Elijah Hooper 3 years ago

    Your great

  • russpit34 3 years ago

    Hottest math major

  • Jose Amarante 3 years ago

    Nice videos! very well explained!!

  • Manoj Sonwane 3 years ago

    Keep up the good work!

  • V. M. 3 years ago

    This is a lot easier than graphing calculus concavity. I’m still struggling with that… 8c

  • Veritas et Aequitas 3 years ago

    4:30 to 5:00 One correction, you say the functions never cross the asymptotes which is true, but they actually will never REACH them. The difference between x < 2 and x <=2.

    • PomPom 3 years ago

      I think she mentioned that at another time in the video, I can’t remember where though.

  • Tucker The Dog 3 years ago

    I love her channel. Because she is pretty I do not get bored of the video and I can focus on learning if that makes sense lol.

  • Vincent Ortega 3 years ago

    Thank you, Nancy, excellent explanation like always. God bless you.

  • Christopher Walsh 3 years ago

    those littlel moments where she writes in fast forward, imagine how much clock time it takes to edit that in.

    • epic passion 3 years ago

      Maybe just 5 mins

  • God of Destruction 3 years ago

    How tf does she write like that

  • Ehsan Khokhar 3 years ago

    thanks a lot sir

  • Muhammad Shaheer Hussain Sipra 3 years ago

    you are great

  • Cooorsbanq 3 years ago

    if only my math teacher looked like this

  • MrAcebak 3 years ago

    wow Im seriously embarrassed that guys cant seem to keep in in their pants on a flipping math video… Im ashamed of my own gender yet again. nobody comments this sort of shit on math tutorials with guys instructing

  • Madhusoodan Prasad 224 3 years ago

    Unique ๐Ÿ‘๐Ÿ‘โฃ๏ธ

  • Zionioa Traoion 3 years ago

    Is this using the limit definition?

  • Jose Luna 3 years ago

    Gracias NancyPi ๐Ÿ˜

  • ChristianOnyeike2020 3 years ago

    Da

  • Amjad Arshad 3 years ago

    nyc vediu dear! ummah!

  • Omar Al-Shehri 3 years ago

    I need Horezantal Asmyptotes too ๐Ÿ™

  • epic passion 3 years ago

    Oh god!! Where will you find a woman like her, who looks so beautiful and is a Mathemagician… She’s awesome!

  • prum chhangsreng 3 years ago

    At 4:13
    Do u just able to predict what the graph might look like and where the curve might be just by looking at the equation? I see u done that a lot.

    I would need to find at least 6 different point on graph to draw those. But u seem to just draw it out without calculate any point. Do u pre-calculate it or u actually able to get an idea of what the graph might look like?

  • ShaphanDale 3 years ago

    This helped. And thank you for including the steps in the description ๐Ÿ™‚

  • Ryan Mutiri 3 years ago

    Fuck math can I marry you??

  • Irvin Garcia 3 years ago

    Tf Iโ€™m still confused

  • what a drag! 3 years ago

    you tell us what to do but you don`t tell us why

  • Maddie E 3 years ago

    Thank you! I missed the past week of math class and this really helped!

  • Ali Waheed 3 years ago

    It is very helpfull video

  • Supersaiyancarlos7 3 years ago

    Perfect video, this is what I needed help with. I would have an A+ in your class

  • DenviousMars 3 years ago

    I didn’t get what u were saying, your way too beautiful. I got distracted XD

    • Luke Naoumovitch 2 years ago

      aight, okay 10 year old

  • Cidny 3 years ago

    omg thank you so much for your videos I genuinely understand what I’m doing know

  • Syrena Xhaferi 2 years ago

    you cant use this method, because the cross canceling get’s rid of one of the answers in differently formatted problems.

  • Dennis Rendfrey 2 years ago

    Rocket Science! When my professor hears that from me she knows I’m in Trouble. With Nancy explaining it. Well, it does make sense. Again I thank you for taking the time to do these tutorials. I just happen to be in College Majoring in Math!!! and I’m 68 years young. If I can understand it so can You !! Just Don’t give up, but learn to take a break, and get back to it!!

  • L Kru 2 years ago

    “…but you can like this video…” – Shrek 2 – puss in boots eyes scene

  • Legit Lam 2 years ago

    Am I the only one noticed she wrote all words reversed??

  • Physics Hotspot - Abhishek Kumar 2 years ago

    Can anyone tell which type of board she is using

  • Physics Hotspot - Abhishek Kumar 2 years ago

    What is the name of this type of writing board

  • Saifullah Rahu 2 years ago

    Ma’am your so beautiful and the way you teach is very lovely and understandable.

  • andtrrrot 2 years ago

    Life saver!

  • Ogle Noelle 2 years ago

    I WANT THAT TOP

  • Jassem Toumi 2 years ago

    But Wait !! When she did the factorization and then she canceled out the factors from the top and the bottom, she left with (x+5)/(x+2) which suppose to be a simplified form of the initial one (means any input in the factorized equation should give the same output as the initial equation! ) However, if we put 2 in the simplified equation we get 7/4 but it gives 0 in the first Equation? …. Who can help clean up these shit thoughts in my Mind Plzz thanks

  • Avilash Thakur 2 years ago

    Please make a video about relative position of asymptote

  • SquidSquirtHD 2 years ago

    hold the fuck up she’s writing backwards and that shit looks better than my handwriting forwards.

  • Na Zombie 2 years ago

    This was explained very easy!! I could never graph or understand how to graph lines of vertical asymptotes and solve the functions. This really helped me practice!!!

  • Halime Kaya 2 years ago

    Can you make a video about holes how can we find holes

  • Sharma ji 2 years ago

    Very useful and easy method ,thanks mam

  • Feather Tail 2 years ago

    I think this just became my favorite math channel. The ability of writing backwards, her calming tone and voice, her examples and graphs, and the way she explains everything

  • Aaron Speer 2 years ago

    Excellent teacher – makes the math easy to comprehend.

  • twerkformemes 2 years ago

    I STAN MY MATH QUEEN!!!

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