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.

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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

Her titles be like…

*Verticle Asymptotes… WTF*

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

๐

Looks like somebody deleted their comment LOL

i thought it was kinda funny

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

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

This goddess got braces

๐๐๐๐๐can u please even make a video how you got into mit i m very inspired by the way i love vertical asymptote

Ankur Giri all about practice and love

I already know this, watched for her

my bois a scholar

Happy to see you back again

VERY happy to see her ๐

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

From Indonesia. Hebat, semangat Nanci

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

Lucid way of teaching! love from ๐ฎ๐ณ

Can you post videos on integration

TECHNICAL ADDA she didd in her previous channel Math Bff

youre welcome.

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

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

Your math videos are really good quality. Excellent job.

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

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.

I know this topic but I am here for ASMR

Kk omg yes!!! Her voice is so soothing! โบ๏ธ I actually have a math exam in the morning (8am) and now itโs 1am and her voice is making me so sleepy I have to stop studying and go to bed. ๐คฃ

yeah math tutorials are great for it

ASMR?

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

I missed you ๐

awesome, great video

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)

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

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.

lim x {x:–>(1/0)}

x=happiness after watching your lessons.

A feeling I have missed for decades.

Thank you.

thanks…..ur so sweet….

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

she is sooooo relaxing

I think its fun

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

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

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

it’s so nice to see you again nancyyyy

ph

ur hot

Thanks A Lot U Dont know How Much U Helped

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

Is she writing the opposite way?

the video is flipped horizontally

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!!!

You FREAKING ROCK!

I love u

Damn I get sidetracked easily. this whole time Iโve 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 ??๐ค maybe she edits it ?? So many question, only getting VA answers.

I know my response is pretty late but here you go

@T0XIDITY holy shit thank you ๐

@T0XIDITY oh my god duhhhh!! Thank you!

joe manuel lol no problem lol๐

@Allie Perez no problem

Thank you so much!! Youโve helped me so much through Calculus & Pre Calc! You explain everything so well. Thank you thank you โค๏ธโค๏ธโค๏ธ

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 ๐คง

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

She said hi and I instantly liked the video

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.

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

hot white chick

What do you think shes saying at 9:18

thank u

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E. yousef AL-Aga what

She makes it look so simple thatโs why I like her so much ๐๐

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

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.

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!

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

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

May I put My Vertical Asymptote in your Horizontal Asymptote

thanks Nancy ๐ฉ๐ฉ๐ฉ

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

โค

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

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

x would simply be zero, I think.

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.

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.”

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.

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.

Thank you mam.It was really helpful.

thx for every thing

Ur better than my own math teacher thnxxx

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

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.

@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.

@MinerBoB I think you missed my point

+iionic stfu

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

๐

๐ยฐ

๐ยฉ~ยฐ

Maybe the helicopter when the engine turn on

Are this coantety vertical asymptotic

Horizontal lines

Dinmometr + horizontal +asymptotic = vertical no show byonic speed

How are we supposed to concentrate when ur so hot๐๐ฅ๐ฅ

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!

In example 2, is it a curiosity that the reduced form “x+5/x+2” is wow ๐magically 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.

Mam how to we Find Asymptotes of transcendental Functions?

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

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

She is ๐

Lovely

fancynancy

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

Hard to concentrate when youโre this hot nancy

dont be a creep

Thank you that was really helpful

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

A calculus goddess

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.

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.

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

she needs a joint

I found your trick you simply flip the video.๐๐๐

Thats not trick man

Just simple logic

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

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

Easy..

Great video, reviewing for finals. Thanks!

Doubt cleared….Thank You… Nancy Pi

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

Is that limit ?

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

Thank you

Thanks nancy๐

Your method of delivering the lectures is superb

damn i cant focus cuz ur so beautiful

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!!!

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?

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

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.

@reese ok

Thanks

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

Saved me tears.

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

Kudos!!

She is the math queen!!!!

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

Hilarious … i am trying

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@Nursin 1999 ุงุฏุฑู ุจุณ ู ู ุจุงุจ ุงูุชููุน ูู ุงููุบุฉ ูู ุงูุชุนูููุงุช

Your great

Hottest math major

Nice videos! very well explained!!

Keep up the good work!

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

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.

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

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.

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

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

Maybe just 5 mins

How tf does she write like that

thanks a lot sir

you are great

if only my math teacher looked like this

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

Unique ๐๐โฃ๏ธ

Is this using the limit definition?

Gracias NancyPi ๐

Da

nyc vediu dear! ummah!

I need Horezantal Asmyptotes too ๐

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

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?

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

Fuck math can I marry you??

Tf Iโm still confused

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

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

It is very helpfull video

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

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

aight, okay 10 year old

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

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

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!!

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

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

Can anyone tell which type of board she is using

What is the name of this type of writing board

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

Life saver!

I WANT THAT TOP

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

Please make a video about relative position of asymptote

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

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!!!

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

Very useful and easy method ,thanks mam

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

Excellent teacher – makes the math easy to comprehend.

I STAN MY MATH QUEEN!!!