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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Пікірлер: 142

  • @nickyplayz2329
    @nickyplayz23296 ай бұрын

    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

  • @user-mr7xw1mr9z

    @user-mr7xw1mr9z

    3 ай бұрын

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

  • @basketguitar9768

    @basketguitar9768

    2 ай бұрын

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

  • @rinofrancisxavier
    @rinofrancisxavier3 жыл бұрын

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

  • @jeremyfowler26
    @jeremyfowler263 жыл бұрын

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

  • @festuslubinga6168
    @festuslubinga61686 жыл бұрын

    Your lessons have helped me so much thanks once again

  • @tambuwalmathsclass
    @tambuwalmathsclass2 жыл бұрын

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

  • @RadoHudran

    @RadoHudran

    2 жыл бұрын

    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

  • @omarifarrow7043
    @omarifarrow7043 Жыл бұрын

    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.

  • @HDrea
    @HDrea4 жыл бұрын

    I remember "Our asymptotic love story" :'

  • @jazzphetmacahig4578

    @jazzphetmacahig4578

    3 жыл бұрын

    awts gege

  • @scarletblue8685

    @scarletblue8685

    3 жыл бұрын

    @@jazzphetmacahig4578 HAHAHAHAHAHAHA gege

  • @leiwansue6024
    @leiwansue60243 жыл бұрын

    Thanks math jesus❤️

  • @yeetdelete2816

    @yeetdelete2816

    2 жыл бұрын

    He's the mathiah! lol

  • @abellevanceryans.6775

    @abellevanceryans.6775

    2 жыл бұрын

    Our Lord and Solver

  • @supcutiewannaride

    @supcutiewannaride

    2 жыл бұрын

    Lmfao

  • @cindychilufya9220

    @cindychilufya9220

    Жыл бұрын

    😂💀

  • @aramacabenlar4786

    @aramacabenlar4786

    Жыл бұрын

    No you did not 🤣🤣🤣

  • @justsomesaltyboi8716
    @justsomesaltyboi87164 ай бұрын

    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.

  • @starangel951
    @starangel951 Жыл бұрын

    *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*

  • @Hadeeth_
    @Hadeeth_6 сағат бұрын

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

  • @marufhossain6697
    @marufhossain66972 жыл бұрын

    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.

  • @katiew912
    @katiew912 Жыл бұрын

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

  • @SamLuv07
    @SamLuv07 Жыл бұрын

    *immaculate precise explanation* 💕

  • @lynjunemorbos6677
    @lynjunemorbos66774 жыл бұрын

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

  • @geolescano4695
    @geolescano46953 жыл бұрын

    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 n then y = No Horizontal Asymptote..

  • @ashauna3916

    @ashauna3916

    3 жыл бұрын

    you said the same thing twice....

  • @denissemedina4619
    @denissemedina46193 жыл бұрын

    You make math seem so easy 😌

  • @lynx3953

    @lynx3953

    Жыл бұрын

    fr

  • @lushgreendesert3523
    @lushgreendesert35233 жыл бұрын

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

  • @CJ-cy3mm
    @CJ-cy3mm4 жыл бұрын

    this is amazing thank you

  • @mtycoder
    @mtycoder6 жыл бұрын

    amazing stuff thanks

  • @chrisc708
    @chrisc7088 ай бұрын

    Really nice job explaining this!

  • @elishagunasekara4038
    @elishagunasekara40383 жыл бұрын

    This helped me a lot! Thanks!

  • @dellisandwich
    @dellisandwich22 күн бұрын

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

  • @__ICT__1288
    @__ICT__12889 ай бұрын

    Thanks a lot professor Dave!

  • @ayushsingh5517
    @ayushsingh55173 ай бұрын

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

  • @Faisalmussa0
    @Faisalmussa03 жыл бұрын

    I swear you are making me love maths

  • @wintanahabtu7259
    @wintanahabtu72593 жыл бұрын

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

  • @mickodonnell890
    @mickodonnell8904 жыл бұрын

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

  • @lio9575
    @lio95756 ай бұрын

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

  • @manpierre571
    @manpierre571 Жыл бұрын

    these stuffs are gold

  • @nathanvlh6655
    @nathanvlh66555 жыл бұрын

    I still don't get this 😂

  • @ErinRaciell

    @ErinRaciell

    4 жыл бұрын

    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

    @YLprime

    4 жыл бұрын

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

  • @etzjunior_

    @etzjunior_

    3 жыл бұрын

    @@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

    @jokersjoke1204

    3 жыл бұрын

    @@etzjunior_ lol bro I feel the same way tf

  • @makgabomashala4859

    @makgabomashala4859

    3 жыл бұрын

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

  • @spacecadet3779
    @spacecadet37792 жыл бұрын

    Thank you good sir

  • @marcui_louie
    @marcui_louie Жыл бұрын

    Thank you very much!

  • @jmarvinarnigo4w
    @jmarvinarnigo4w3 жыл бұрын

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

  • @MuhammadRafi-yh4xo
    @MuhammadRafi-yh4xo Жыл бұрын

    Thanks a lot sir❤

  • @girummogos
    @girummogos8 ай бұрын

    Thank you every much!

  • @plm.agsikapin2025
    @plm.agsikapin20253 жыл бұрын

    on 4:18, it should be n

  • @ProfessorDaveExplains

    @ProfessorDaveExplains

    3 жыл бұрын

    n refers to the denominator

  • @plm.agsikapin2025

    @plm.agsikapin2025

    3 жыл бұрын

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

  • @wingsoffreedom7138

    @wingsoffreedom7138

    2 жыл бұрын

    I thought so WHEN N LESS THAN M IT SHOULD 0

  • @jenanali5919
    @jenanali59193 жыл бұрын

    Thank you so much

  • @inuwagaming
    @inuwagaming4 жыл бұрын

    How do you pick the points tho

  • @twinkelry2410

    @twinkelry2410

    3 жыл бұрын

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

  • @sorryihaverehearsal5764
    @sorryihaverehearsal57643 жыл бұрын

    Thank you!

  • @umibrahimkebir4159
    @umibrahimkebir41599 ай бұрын

    A real hero 👏

  • @s.m.h.m8804
    @s.m.h.m8804 Жыл бұрын

    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

  • @jamikemichelohia2615
    @jamikemichelohia26153 жыл бұрын

    I always had time but you explained it explicitlu

  • @kholoudmohmed4083
    @kholoudmohmed40833 жыл бұрын

    many thanks

  • @upholdjustice372
    @upholdjustice372 Жыл бұрын

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

  • @Bandicoot1982z
    @Bandicoot1982zАй бұрын

    Thanks!

  • @RaffaelloLorenzusSayde
    @RaffaelloLorenzusSayde2 жыл бұрын

    What about oblique asymptotes and holes?

  • @carultch

    @carultch

    5 ай бұрын

    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.

  • @Arushaaaa
    @Arushaaaa3 жыл бұрын

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

  • @carultch

    @carultch

    5 ай бұрын

    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.

  • @jmslr
    @jmslr3 жыл бұрын

    Thank you po

  • @frommytravels
    @frommytravels3 ай бұрын

    Are you doing this in Powerpoint?

  • @sawankumar1450
    @sawankumar1450 Жыл бұрын

    Thanks sir

  • @lapatria100
    @lapatria100 Жыл бұрын

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

  • @dildobaggins2759
    @dildobaggins27594 жыл бұрын

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

  • @nandini2040

    @nandini2040

    4 жыл бұрын

    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

    @radia4752

    3 жыл бұрын

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

  • @Trynnagetmydegree__

    @Trynnagetmydegree__

    3 жыл бұрын

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

  • @alexiadd636
    @alexiadd6364 жыл бұрын

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

  • @YLprime

    @YLprime

    4 жыл бұрын

    u should have learnt these in high school

  • @alexiadd636

    @alexiadd636

    4 жыл бұрын

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

  • @Juuqe

    @Juuqe

    3 жыл бұрын

    ​@@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.

  • @HellooDae
    @HellooDae4 ай бұрын

    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

  • @lpsrosekitty2114
    @lpsrosekitty2114 Жыл бұрын

    Your saving my math grade

  • @ashauna3916
    @ashauna39163 жыл бұрын

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

  • @ahmedbaashi8872
    @ahmedbaashi88724 жыл бұрын

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

  • @a.henderson22
    @a.henderson224 жыл бұрын

    thanks

  • @michaelhawkingphd
    @michaelhawkingphd4 ай бұрын

    we stan professor dave

  • @mirahamdan7369
    @mirahamdan73694 жыл бұрын

    ur amazingggg

  • @marykinfe6127
    @marykinfe61272 жыл бұрын

    Add more explanation professor Dave

  • @xtremesssss
    @xtremesssss3 жыл бұрын

    i love your intro

  • @navedabbasi163
    @navedabbasi1636 жыл бұрын

    What if there is a mod

  • @jadeluigitaniii2416
    @jadeluigitaniii24162 жыл бұрын

    Hello! What website was used in graphing the function?

  • @erikahazy6369
    @erikahazy63694 жыл бұрын

    your mother must be very proud of you. :)

  • @timber9440
    @timber94408 ай бұрын

    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

  • @takki9238
    @takki92384 жыл бұрын

    😊intro

  • @scarletblue8685
    @scarletblue86853 жыл бұрын

    Thankyouu

  • @user-xd1sc5ti4o
    @user-xd1sc5ti4o8 ай бұрын

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

  • @Chakamatics

    @Chakamatics

    3 ай бұрын

    Faxxx😂

  • @soumapriyamondal3808
    @soumapriyamondal38084 жыл бұрын

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

  • @ProfessorDaveExplains

    @ProfessorDaveExplains

    4 жыл бұрын

    hmm, hyperbolas come to mind

  • @jennifer_3683
    @jennifer_3683 Жыл бұрын

    Thanks for the video

  • @ridmicmeena4123

    @ridmicmeena4123

    Жыл бұрын

    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

    @jennifer_3683

    Жыл бұрын

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

  • @ridmicmeena4123

    @ridmicmeena4123

    Жыл бұрын

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

  • @club6525
    @club6525 Жыл бұрын

    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)

  • @thedestrolled
    @thedestrolled2 жыл бұрын

    moist critical in a parallel universe

  • @Sir_Drakarius
    @Sir_Drakarius2 жыл бұрын

    Thank you math Jesus!

  • @thecosmos7671
    @thecosmos76713 жыл бұрын

    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

  • @RafaelTNSG1245
    @RafaelTNSG12458 ай бұрын

    thank you math jesus

  • @nailach2039
    @nailach2039 Жыл бұрын

    Thanks

  • @ridmicmeena4123

    @ridmicmeena4123

    Жыл бұрын

    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

  • @froopi2
    @froopi25 ай бұрын

    ohmygod thanks

  • @hidden_fear4166
    @hidden_fear41663 жыл бұрын

    Doesn't show how to graph slants. Ugh

  • @giovannasimon7083
    @giovannasimon7083 Жыл бұрын

    i love you

  • @johnlark8995
    @johnlark89957 ай бұрын

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

  • @CardinalPopia
    @CardinalPopia8 ай бұрын

    Thank you Dave Grohl

  • @buggsguide6978
    @buggsguide69783 жыл бұрын

    THANX FOR MORE CONFUSION

  • @sadbear01
    @sadbear012 жыл бұрын

    Ty Jesus 🙏😀

  • @elainegracebanday9321
    @elainegracebanday93212 жыл бұрын

    Wala akong naiintindihan lord

  • @LegendaryLimeYT
    @LegendaryLimeYT3 жыл бұрын

    Thank you Jesus

  • @mickstone7380
    @mickstone73807 ай бұрын

    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

  • @davidliketogame2120
    @davidliketogame21202 жыл бұрын

    Mind giving me a shoutout homie?

  • @mahmoudaboheif4814
    @mahmoudaboheif4814 Жыл бұрын

    thx jesus

  • @manjumishra1896
    @manjumishra18962 жыл бұрын

    Being an indian villagers watch this video

  • @hisokageyming4990
    @hisokageyming49902 жыл бұрын

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

  • @sani8365
    @sani8365 Жыл бұрын

    he aamhi kelay ;(

  • @zkskakksis1514
    @zkskakksis15142 жыл бұрын

    math jesus thx

  • @ronachico7449
    @ronachico74498 ай бұрын

    Wala parin akong maintindihan 😍

  • @martinezjhoncedrickd.7901
    @martinezjhoncedrickd.79013 жыл бұрын

    u look like jesus

  • @nyinanajulu4905
    @nyinanajulu49053 ай бұрын

    That is not a nice name to call him.

  • @averynye
    @averynye2 ай бұрын

    This doesnt help at all

  • @sahilafnan427
    @sahilafnan427 Жыл бұрын

    Thanks sir