Graphing Rational Functions and Their Asymptotes

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  • เผยแพร่เมื่อ 21 พ.ย. 2017
  • 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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ความคิดเห็น • 142

  • @Nram10
    @Nram10 6 หลายเดือนก่อน +73

    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 4 หลายเดือนก่อน

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

    • @basketguitar9768
      @basketguitar9768 2 หลายเดือนก่อน

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

  • @rinofrancisxavier
    @rinofrancisxavier 3 ปีที่แล้ว +42

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

  • @jeremyfowler26
    @jeremyfowler26 3 ปีที่แล้ว +19

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

  • @tambuwalmathsclass
    @tambuwalmathsclass 2 ปีที่แล้ว +8

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

    • @RadoHudran
      @RadoHudran 2 ปีที่แล้ว +2

      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 ปีที่แล้ว +10

    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.

  • @festuslubinga6168
    @festuslubinga6168 6 ปีที่แล้ว +34

    Your lessons have helped me so much thanks once again

  • @leiwansue6024
    @leiwansue6024 3 ปีที่แล้ว +547

    Thanks math jesus❤️

  • @starangel951
    @starangel951 ปีที่แล้ว +1

    *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
    @justsomesaltyboi8716 5 หลายเดือนก่อน

    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.

  • @HDrea
    @HDrea 4 ปีที่แล้ว +81

    I remember "Our asymptotic love story" :'

  • @lushgreendesert3523
    @lushgreendesert3523 3 ปีที่แล้ว +5

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

  • @marufhossain6697
    @marufhossain6697 2 ปีที่แล้ว +29

    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.

  • @SamLuv07
    @SamLuv07 ปีที่แล้ว +2

    *immaculate precise explanation* 💕

  • @geolescano4695
    @geolescano4695 3 ปีที่แล้ว +2

    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
      @ashauna3916 3 ปีที่แล้ว +2

      you said the same thing twice....

  • @chrisc708
    @chrisc708 8 หลายเดือนก่อน

    Really nice job explaining this!

  • @elishagunasekara4038
    @elishagunasekara4038 3 ปีที่แล้ว

    This helped me a lot! Thanks!

  • @katiew912
    @katiew912 ปีที่แล้ว +1

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

  • @CJ-cy3mm
    @CJ-cy3mm 4 ปีที่แล้ว +4

    this is amazing thank you

  • @mtycoder
    @mtycoder 6 ปีที่แล้ว +4

    amazing stuff thanks

  • @lynjunemorbos6677
    @lynjunemorbos6677 4 ปีที่แล้ว +1

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

  • @__ICT__1288
    @__ICT__1288 9 หลายเดือนก่อน

    Thanks a lot professor Dave!

  • @mickodonnell890
    @mickodonnell890 4 ปีที่แล้ว +15

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

  • @Hadeeth_
    @Hadeeth_ 19 วันที่ผ่านมา

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

  • @Faisalmussa0
    @Faisalmussa0 3 ปีที่แล้ว +3

    I swear you are making me love maths

  • @wintanahabtu7259
    @wintanahabtu7259 3 ปีที่แล้ว +3

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

  • @denissemedina4619
    @denissemedina4619 3 ปีที่แล้ว +68

    You make math seem so easy 😌

  • @dellisandwich
    @dellisandwich หลายเดือนก่อน

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

  • @plm.agsikapin2025
    @plm.agsikapin2025 3 ปีที่แล้ว +1

    on 4:18, it should be n

    • @ProfessorDaveExplains
      @ProfessorDaveExplains  3 ปีที่แล้ว +2

      n refers to the denominator

    • @plm.agsikapin2025
      @plm.agsikapin2025 3 ปีที่แล้ว +2

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

    • @wingsoffreedom7138
      @wingsoffreedom7138 2 ปีที่แล้ว

      I thought so WHEN N LESS THAN M IT SHOULD 0

  • @lio9575
    @lio9575 7 หลายเดือนก่อน

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

  • @Bixcei
    @Bixcei 5 ปีที่แล้ว +129

    I still don't get this 😂

    • @ErinRaciell
      @ErinRaciell 4 ปีที่แล้ว +5

      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 ปีที่แล้ว +2

      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 ปีที่แล้ว +12

      @@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 ปีที่แล้ว

      @@etzjunior_ lol bro I feel the same way tf

    • @makgabomashala4859
      @makgabomashala4859 3 ปีที่แล้ว +1

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

  • @ayushsingh5517
    @ayushsingh5517 3 หลายเดือนก่อน

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

  • @jmarvinarnigo4w
    @jmarvinarnigo4w 3 ปีที่แล้ว

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

  • @MuhammadRafi-yh4xo
    @MuhammadRafi-yh4xo ปีที่แล้ว

    Thanks a lot sir❤

  • @marcui_louie
    @marcui_louie ปีที่แล้ว

    Thank you very much!

  • @jenanali5919
    @jenanali5919 3 ปีที่แล้ว

    Thank you so much

  • @s.m.h.m8804
    @s.m.h.m8804 ปีที่แล้ว

    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

  • @spacecadet3779
    @spacecadet3779 2 ปีที่แล้ว +1

    Thank you good sir

  • @girummogos
    @girummogos 9 หลายเดือนก่อน

    Thank you every much!

  • @upholdjustice372
    @upholdjustice372 ปีที่แล้ว +2

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

  • @manpierre571
    @manpierre571 2 ปีที่แล้ว

    these stuffs are gold

  • @Arushaaaa
    @Arushaaaa 3 ปีที่แล้ว +1

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

    • @carultch
      @carultch 6 หลายเดือนก่อน

      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.

  • @sorryihaverehearsal5764
    @sorryihaverehearsal5764 3 ปีที่แล้ว

    Thank you!

  • @jamikemichelohia2615
    @jamikemichelohia2615 3 ปีที่แล้ว +1

    I always had time but you explained it explicitlu

  • @ahmedbaashi8872
    @ahmedbaashi8872 4 ปีที่แล้ว +4

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

  • @ashauna3916
    @ashauna3916 3 ปีที่แล้ว +1

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

  • @kholoudmohmed4083
    @kholoudmohmed4083 3 ปีที่แล้ว

    many thanks

  • @jmslr
    @jmslr 3 ปีที่แล้ว

    Thank you po

  • @lapatria100
    @lapatria100 ปีที่แล้ว

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

  • @inuwagaming
    @inuwagaming 4 ปีที่แล้ว +5

    How do you pick the points tho

    • @twinkelry2410
      @twinkelry2410 3 ปีที่แล้ว

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

  • @navedabbasi163
    @navedabbasi163 6 ปีที่แล้ว +2

    What if there is a mod

  • @Bandicoot1982z
    @Bandicoot1982z 2 หลายเดือนก่อน

    Thanks!

  • @RaffaelloLorenzusSayde
    @RaffaelloLorenzusSayde 2 ปีที่แล้ว +3

    What about oblique asymptotes and holes?

    • @carultch
      @carultch 6 หลายเดือนก่อน +1

      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.

  • @sawankumar1450
    @sawankumar1450 ปีที่แล้ว

    Thanks sir

  • @umibrahimkebir4159
    @umibrahimkebir4159 10 หลายเดือนก่อน

    A real hero 👏

  • @dildobaggins2759
    @dildobaggins2759 4 ปีที่แล้ว +18

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

    • @nandini2040
      @nandini2040 4 ปีที่แล้ว +8

      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 ปีที่แล้ว +3

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

    • @Trynnagetmydegree__
      @Trynnagetmydegree__ 3 ปีที่แล้ว +1

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

  • @frommytravels
    @frommytravels 3 หลายเดือนก่อน

    Are you doing this in Powerpoint?

  • @soumapriyamondal3808
    @soumapriyamondal3808 4 ปีที่แล้ว +1

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

  • @alexiadd636
    @alexiadd636 4 ปีที่แล้ว +17

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

    • @YLprime
      @YLprime 4 ปีที่แล้ว +2

      u should have learnt these in high school

    • @alexiadd636
      @alexiadd636 4 ปีที่แล้ว +2

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

    • @Juuqe
      @Juuqe 3 ปีที่แล้ว

      ​@@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.

  • @a.henderson22
    @a.henderson22 4 ปีที่แล้ว

    thanks

  • @timber9440
    @timber9440 9 หลายเดือนก่อน

    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

  • @marykinfe6127
    @marykinfe6127 2 ปีที่แล้ว +1

    Add more explanation professor Dave

  • @club6525
    @club6525 ปีที่แล้ว

    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)

  • @lpsrosekitty2114
    @lpsrosekitty2114 ปีที่แล้ว

    Your saving my math grade

  • @scarletblue8685
    @scarletblue8685 3 ปีที่แล้ว

    Thankyouu

  • @erikahazy6369
    @erikahazy6369 4 ปีที่แล้ว +3

    your mother must be very proud of you. :)

  • @jadeluigitaniii2416
    @jadeluigitaniii2416 2 ปีที่แล้ว

    Hello! What website was used in graphing the function?

  • @xtremesssss
    @xtremesssss 4 ปีที่แล้ว

    i love your intro

  • @mirahamdan7369
    @mirahamdan7369 4 ปีที่แล้ว

    ur amazingggg

  • @jennifer_3683
    @jennifer_3683 ปีที่แล้ว

    Thanks for the video

    • @ridmicmeena4123
      @ridmicmeena4123 ปีที่แล้ว

      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 ปีที่แล้ว +1

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

    • @ridmicmeena4123
      @ridmicmeena4123 ปีที่แล้ว +1

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

  • @takki9238
    @takki9238 4 ปีที่แล้ว +2

    😊intro

  • @michaelhawkingphd
    @michaelhawkingphd 5 หลายเดือนก่อน

    we stan professor dave

  • @thecosmos7671
    @thecosmos7671 3 ปีที่แล้ว

    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

  • @HellooDae
    @HellooDae 5 หลายเดือนก่อน

    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

  • @nailach2039
    @nailach2039 ปีที่แล้ว

    Thanks

    • @ridmicmeena4123
      @ridmicmeena4123 ปีที่แล้ว

      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

  • @hidden_fear4166
    @hidden_fear4166 3 ปีที่แล้ว +1

    Doesn't show how to graph slants. Ugh

  • @Sir_Drakarius
    @Sir_Drakarius 2 ปีที่แล้ว +1

    Thank you math Jesus!

  • @johnlark8995
    @johnlark8995 7 หลายเดือนก่อน

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

  • @thedestrolled
    @thedestrolled 2 ปีที่แล้ว +1

    moist critical in a parallel universe

  • @user-xd1sc5ti4o
    @user-xd1sc5ti4o 8 หลายเดือนก่อน +5

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

    • @Chakamatics
      @Chakamatics 4 หลายเดือนก่อน

      Faxxx😂

  • @RafaelTNSG1245
    @RafaelTNSG1245 9 หลายเดือนก่อน

    thank you math jesus

  • @froopi2
    @froopi2 5 หลายเดือนก่อน

    ohmygod thanks

  • @CardinalPopia
    @CardinalPopia 9 หลายเดือนก่อน

    Thank you Dave Grohl

  • @giovannasimon7083
    @giovannasimon7083 ปีที่แล้ว

    i love you

  • @elainegracebanday9321
    @elainegracebanday9321 2 ปีที่แล้ว +1

    Wala akong naiintindihan lord

  • @sadbear01
    @sadbear01 2 ปีที่แล้ว +1

    Ty Jesus 🙏😀

  • @LegendaryLimeYT
    @LegendaryLimeYT 3 ปีที่แล้ว +1

    Thank you Jesus

  • @buggsguide6978
    @buggsguide6978 3 ปีที่แล้ว +1

    THANX FOR MORE CONFUSION

  • @davidliketogame2120
    @davidliketogame2120 2 ปีที่แล้ว +1

    Mind giving me a shoutout homie?

  • @manjumishra1896
    @manjumishra1896 3 ปีที่แล้ว

    Being an indian villagers watch this video

  • @hisokageyming4990
    @hisokageyming4990 2 ปีที่แล้ว

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

  • @mahmoudaboheif4814
    @mahmoudaboheif4814 ปีที่แล้ว

    thx jesus

  • @mickstone7380
    @mickstone7380 8 หลายเดือนก่อน

    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

  • @sani8365
    @sani8365 ปีที่แล้ว

    he aamhi kelay ;(

  • @ronachico7449
    @ronachico7449 8 หลายเดือนก่อน

    Wala parin akong maintindihan 😍

  • @nyinanajulu4905
    @nyinanajulu4905 4 หลายเดือนก่อน

    That is not a nice name to call him.

  • @martinezjhoncedrickd.7901
    @martinezjhoncedrickd.7901 3 ปีที่แล้ว +1

    u look like jesus

  • @zkskakksis1514
    @zkskakksis1514 2 ปีที่แล้ว

    math jesus thx

  • @averynye
    @averynye 2 หลายเดือนก่อน

    This doesnt help at all

  • @sahilafnan427
    @sahilafnan427 ปีที่แล้ว

    Thanks sir