Graphing Rational Functions and Their Asymptotes

You might think we are all set with graphs, but you're wrong! We will learn about many other types of functions as well as how to graph them. First up is rational functions, which are quotients of polynomials. How can we graph these? We have to find their asymptotes. What's that? Sounds sexy. Well, it is, kind of.
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[@Nram10]

Bro why do teachers not teach like this. It actually pisses me off why they don’t teach so well and simple with patience. I’ve learned more in 7 minutes than my teacher did in a week

[@sharipotter-i8g]

probably graphics teachers don't have access to and you listened and he doesn't have to classroom manage.

[@basketguitar9768]

Your teacher probably has poor public speaking skills, making it difficult to focus on what they're saying.

[@pw.m_0987]

not a lying story, our teacher is teaching this to us, and everytime we got the answer wrong, she always cuss at us sometimes, and calls us idiots many times, I don't rlly understand what she is saying, all of her examples are nonsense

[@leiwansue6024]

Thanks math jesus❤️

[@yeetdelete2816]

He's the mathiah! lol

[@abellevanceryans.6775]

Our Lord and Solver

[@chocolatecandyfruithoneybutter]

Lmfao

[@cindychilufya9220]

😂💀

[@aramacabenlar4786]

No you did not 🤣🤣🤣

[@rinofrancisxavier]

a video with 7.24 duration taught me better than 2 hours of pre-recorded lecture by a lecturer

[@tambuwalmathsclass]

3:51 Great👍 There could be an asymptote if m>n by just 1. That's slanted asymptote

[@RadoHudran]

Yup On my exam they literally gave me such a problem where m>n and I couldn't do it. Lesson learned: Even if your source seems reliable, always check multiple sources to be sure

[@jeremyfowler26]

This was my first time watching one of your videos, and the into alone made me smile.

[@omarifarrow7043]

Thank you! I am currently using Aleks for my Precalculus course and the instructions and explanations were very unclear but this video answered every question I had.

[@geolescano4695]

Correction sir on 3:49 you thought that when n > m then y = 0? and when m > n then y = NHA? But according to the books and some references it is not. The correct is: If n > m , then y = 0 If n < m or m > n then y = No Horizontal Asymptote..

[@ashauna3916]

you said the same thing twice....

[@HDrea]

I remember "Our asymptotic love story" :'

[@jazzphetmacahig4578]

awts gege

[@scarletblue8685]

@@jazzphetmacahig4578 HAHAHAHAHAHAHA gege

[@festuslubinga6168]

Your lessons have helped me so much thanks once again

[@marufhossain6697]

Thank you so much for this tutorial. I am learning things I've never known before because I realize that there are so many things in life that I don't know about. The truth is, I'm learning Further Maths due to having some interest in mathematics and I wanted to know my true capabilities by learning things beyond what I'm supposed to cover because I'm only in year 9. I've done the same thing in some Oxford university maths lectures. I want to finish watching the ones on complex numbers and dynamics.

[@starangel951]

*just the word thank you cant express my feelings and i cant seem to express in words just how much your lessons means to me*

[@justsomesaltyboi8716]

Im sick with covid and missing this portion of the class where my professor did not extend the time for homework for me to rest. Once more, she told me to reach out to tutoring to teach me this stuff when it is due tuesday and they are only open on the monday. You are a lifesaver, thank you so much! This video has cut through brain-fog more effectively than the textbook and exercises posed by my college algebra class.

[@denissemedina4619]

You make math seem so easy 😌

[@lynx3953]

fr

[@Bixcei]

I still don't get this 😂

[@ErinRaciell]

Its because instead of making a multistep process so its easy to digest he go straight to the the no intuitive part of the rational function.

[@YLprime]

maybe your are just not at that level yet to be able to understand it. I find it very easy to understand

[@etzjunior_]

@@YLprime i don't understand the graph. He was saying, "as we plug in numbers, we get closer and closer to 0", but as he was saying that, the dots that were appearing were moving away from 0. Tf

[@jokersjoke1204]

@@etzjunior_ lol bro I feel the same way tf

[@makgabomashala4859]

You are not alone I'm also lost in the asymptote😢

[@plm.agsikapin2025]

on 4:18, it should be n

[@ProfessorDaveExplains]

n refers to the denominator

[@plm.agsikapin2025]

@@ProfessorDaveExplains oh sorry in our school n refers to the numerator, but nevertheless thanks for helping me out prof dave! 🥰

[@wingsoffreedom7138]

I thought so WHEN N LESS THAN M IT SHOULD 0

[@Faisalmussa0]

I swear you are making me love maths

[@ЖанарТемирбекова-с2х]

Why is he talking like he's at a gunpoint?

[@Chakamatics]

Faxxx😂

[@Hadeeth_]

I always get so excited watching his videos that I even start dancing when the iconic into starts 😂

[@SamLuv07]

*immaculate precise explanation* 💕

[@lushgreendesert3523]

Amazing ! Wonderful ! You cleared so many things in so efficiently!

[@lio9575]

Thanks man ,I have an exam tomorrow and this really helped out

[@Gust52]

Thank You Professor Dave, but you did not talk about Curvilinear Asymptotes.

[@dildobaggins2759]

the plotting the points on the asympotes is too hard there must be an easier way...

[@nandini2040]

there is! for the horizontal asymptote, our teacher told us to calculate the value of the limit of x approaching infinity for the function. if you've done limits, it's pretty easy to get it right. for the vertical one, check for points where the denominator is zero. this is because the vertical asymptote is defined as the finite value of x where y approaches + or - infinity. hope that helps!

[@radia4752]

@@nandini2040 what? I dont fucking understand anything, goddayumn

[@Trynnagetmydegree__]

@@radia4752 lol, man I hate calc....I wish I had this guy as my teacher

[@alexiadd636]

thank you! my professor doesn't teach these things...

[@YLprime]

u should have learnt these in high school

[@alexiadd636]

@@YLprime "learned " and no unfortunately not i was a slacker and only took up to algebra 2 in highschool then accounting

[@Juuqe]

​@@alexiadd636 learnt* Americanised English only makes up a small percentage of all english speech, grammar and spelling. To correct someones spelling when they are a part of a larger, more popular group is probably incorrect. Know your place woman.

[@jmarvinarnigo4w]

N>m is y=0, but the other teach as n

[@ashauna3916]

at 0:41 seconds you mentioned the denominator cant be 0 but during checking comprehension answers your denominator came out to be 0.

[@wintanahabtu7259]

My problem is that i cant just came up with random numbers strategically for drawing z graph

[@CJ-cy3mm]

this is amazing thank you

[@mickodonnell890]

Great video and put me right on a few things there, thank you Professor Dave :-)

[@mtycoder]

amazing stuff thanks

[@spacecadet3779]

Thank you good sir

[@chrisc708]

Really nice job explaining this!

[@HellooDae]

I have been watching this series since December. Now I can solve math equations I never thought I was ever able to even comprehend. I am forever grateful

[@timber9440]

The solving of horizontal asymptote is wrong In the video its shown N>m means y=0 When in reality it means theres no horizontal asymptote

[@AhmedAMayow]

Thnks prof but we need more examples in order to understand thnksr again and again

[@inuwagaming]

How do you pick the points tho

[@twinkelry2410]

Pretty sure you just pick some points on the graph to draw it, mostly the ‘x’es in which the graph would lie

[@Arushaaaa]

Really good please guide if the numerator leading degree power is higher than denominator leading degree power

[@carultch]

If the denominator has a higher degree, it will have vertical asymptotes at each pole, and horizontal asymptotes at y=0. If the two degrees are equal, it will also have a vertical asymptote at each pole, but its horizontal asymptotes will be shifted to a different vertical position. If the numerator is of a higher degree than the denominator, it will have oblique asymptotes instead of horizontal asymptotes. The vertical asymptotes will still oxxur at the poles.

[@RaffaelloLorenzusSayde]

What about oblique asymptotes and holes?

[@carultch]

Oblique asymptotes are asymptotes that aren't parallel to either of the two coordinate axes, but instead approach a diagonal line. You'll see this for rational functions, when the numerator has a higher degree than the denominator. As an example, y = x^2/(x + 4) has a behavior, where in the long run, it approaches the line y = x - 1. This occurs both as x approaches infinity, and as x approaches -infinity.

[@__ICT__1288]

Thanks a lot professor Dave!

[@marykinfe6127]

Add more explanation professor Dave

[@katiew912]

3:24 Does that mean there can never be more than one horizontal asymptote in ANY function? or just in the given function

[@jamikemichelohia2615]

I always had time but you explained it explicitlu

[@erikahazy6369]

your mother must be very proud of you. :)

[@girummogos]

Thank you every much!

[@s.m.h.m8804]

I'm watching many of your series. Fantastic teaching. I Always stop your videos at any important hint and look for it on other videos or search google bard etc to complete my tutorial. Thank you

[@dellisandwich]

how do we interpret the results gathered when testing selective x values? how do we know where the points are specifically?

[@ayushsingh5517]

is there any way to use transformations directly, like derive the graph of these polynomial functions directly from its parent function?

[@lpsrosekitty2114]

Your saving my math grade

[@manpierre571]

these stuffs are gold

[@Elis_veta]

Thank you very much!

[@elishagunasekara4038]

This helped me a lot! Thanks!

[@club6525]

The definition for asymptotes is incorrect. Asymptotes are not lines since lines are real object. Rather, they are boundaries. Second, the function can touch and even cross asymptotes such as in the case of (x-1)/(x^2 - x - 6)

[@umibrahimkebir4159]

A real hero 👏

[@michaelhawkingphd]

we stan professor dave

[@ridiculouscrap]

Are you doing this in Powerpoint?

[@MuhammadRafi-yh4xo]

Thanks a lot sir❤

[@Bandicoot1982z]

Thanks!

[@thedestrolled]

moist critical in a parallel universe

[@jenanali5919]

Thank you so much

[@sorryihaverehearsal5764]

Thank you!

[@navedabbasi163]

What if there is a mod

[@Sir_Drakarius]

Thank you math Jesus!

[@lynjunemorbos6677]

what is the video app change background the background? thank you

[@kholoudmohmed4083]

many thanks

[@sawankumar1450]

Thanks sir

[@jmslr]

Thank you po

[@jennifer_3683]

Thanks for the video

[@ridmicmeena4123]

hi it looks like you get everything in this video I have a doubt plz help me so in the first and last Q of Checking comprehension the y = 2 and y=3 so did we take 2/1 and just ignore the 1 and same in last one did we take 3/1 and ignored the 1 and wrote only 3 plz help me as soon as possible

[@jennifer_3683]

@@ridmicmeena4123 hi there! It's been long since I watched this video... I will rewatch and revert u back soon!

[@ridmicmeena4123]

@@jennifer_3683 thank you so much i really appreciate it 💜

[@lapatria100]

4:24..."we can test select values of ...y?

[@hidden_fear4166]

Doesn't show how to graph slants. Ugh

[@xtremesssss]

i love your intro

[@takki9238]

😊intro

[@johnlark8995]

great video but its half knowledge , you didn't talk about x,y intercepts - those are key metrics for plotting,

[@soumapriyamondal3808]

thank you professor...but can you pls tell me what kind of functions do have slant asymptotes...

[@ProfessorDaveExplains]

hmm, hyperbolas come to mind

[@RafaelTNSG1245]

thank you math jesus

[@a.henderson22]

thanks

[@scarletblue8685]

Thankyouu

[@mirahamdan7369]

ur amazingggg

[@CardinalPopia]

Thank you Dave Grohl

[@thecosmos7671]

Professor,why the coordinates of 2/(X-1) are (2,1) at 5:30 when it should be( 2,2) I may be wrong please explain me

[@buggsguide6978]

THANX FOR MORE CONFUSION

[@elainegracebanday9321]

Wala akong naiintindihan lord

[@froopi2]

ohmygod thanks

[@jadeluigitaniii2416]

Hello! What website was used in graphing the function?

[@davidliketogame2120]

Mind giving me a shoutout homie?

[@giovannasimon7083]

i love you

[@LegendaryLimeYT]

Thank you Jesus

[@sadbear01]

Ty Jesus 🙏😀

[@mamadwali4278]

❤❤❤

[@hisokageyming4990]

I give 7mins of my life on learning things.. I still don't understand 🤦‍♂️🤦‍♂️

[@mickstone7380]

The Freddie Mercury Rule: If a rational equation is bottom heavy, its horizontal asymptote will be equal o zero. This is because of the fact that Fat Bottomed girls make the rockin' world go round, Zeroes are round. QED

[@ronachico7449]

Wala parin akong maintindihan 😍

[@mahmoudaboheif4814]

thx jesus

[@manjumishra1896]

Being an indian villagers watch this video

[@sani8365]

he aamhi kelay ;(

[@martinezjhoncedrickd.7901]

u look like jesus

[@nyinanajulu4905]

That is not a nice name to call him.

[@zkskakksis1514]

math jesus thx

[@averynye]

This doesnt help at all

[@sahilafnan427]

Thanks sir

[@nailach2039]

Thanks

[@ridmicmeena4123]

hi it looks like you get everything in this video I have a doubt plz help me so in the first and last Q of Checking comprehension the y = 2 and y=3 so did we take 2/1 and just ignore the 1 and same in last one did we take 3/1 and ignored the 1 and wrote only 3 plz help me as soon as possible