Graphing Rational Functions With Vertical, Horizontal & Slant Asymptotes, Holes, Domain & Range

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  • Опубликовано: 5 янв 2025

Комментарии • 659

  • @TheOrganicChemistryTutor
    @TheOrganicChemistryTutor  Год назад +24

    Domain & Range - Free Formula Sheet: bit.ly/4eheN2W
    Rational Functions - More Lessons: www.video-tutor.net/rational-functions.html

  • @gamingresumed1788
    @gamingresumed1788 4 года назад +863

    0:10 y=1/x --
    2:10 y=1/x^2
    4:30 y=1/x-1
    11:36 y=(1/x+2)-3
    16:30 Graphs of y=1/x
    17:54 y=(-1/x+2)+3
    22:13 y=(1/(x-2)^2)+1
    24:44 y=(-1/(x+1)^2)+2
    28:00 HA OF same degree functions
    30:44 HA of bottom heavy
    31:47 y=((2(x-2))/(x-3)
    35:35 y=(3x^2+9x-12)/(x^2+x-2)
    44:40 Slant asymptote y=(2x^2+6x-8)/(x-2)

  • @m.miller8011
    @m.miller8011 6 лет назад +1377

    I wouldn't be passing precal if it wasn't for you, really appreciate the videos

    • @rudyj8948
      @rudyj8948 4 года назад +11

      Literally same

    • @memes4themasses365
      @memes4themasses365 4 года назад +7

      I’m with ya rn

    • @quinive9812
      @quinive9812 4 года назад +10

      no matter what i do i still fail pre cal. would it help me pass if i watched all pf his vid?

    • @No-dy3zk
      @No-dy3zk 4 года назад +24

      I got to do this for Algebra 2.

    • @Jackripz
      @Jackripz 3 года назад +4

      @@No-dy3zk same

  • @lunam11
    @lunam11 4 года назад +476

    I started at 2 am and now it's 6 am ...
    This whole time I was studying graphs and all from your videos 😭♥
    Am really thankful for each and every video u made , you just don't know how much this meant to me !! You are a life saver
    May God bless you and your family
    My number one hero!!

  • @ign0tium539
    @ign0tium539 Год назад +341

    man really taught me a whole unit in an hour that my teacher couldn't explain in 2 weeks

  • @draglonconx7771
    @draglonconx7771 5 лет назад +92

    Im SOOOO glad you added that -3 at 11:43. I've been looking for an example that affects HA, now I know how to interpret it. Thanks a lot!

  • @ArpitaDebnath-fp8fg
    @ArpitaDebnath-fp8fg 6 месяцев назад +7

    RUclips is gold when such videos exists.
    Thanks a million man

  • @isaiahwhitney8168
    @isaiahwhitney8168 4 года назад +27

    I’ve been taking Algebra II all year. I just realized that I love physics and that I’ll need math in the future. So I’m deciding to learn all pre calc in the next 3 months and then take the final. You’re so much help

  • @wormonastring8934
    @wormonastring8934 4 года назад +2771

    anyone else crying in math class? :)

  • @mehakahuja9372
    @mehakahuja9372 Год назад +62

    Your videos to watch are always helpful. I always search you up for Math topic explanations. For a problem, time on the video (10:47 to 11:05), you mentioned the domain as (- ∞,-1) ∪(-1, ∞). However, I feel it should be 1 in the domain not -1

  • @iglo1209
    @iglo1209 5 лет назад +174

    This guy is a hero. I'm blessed to live in 2019 :)

  • @mannydefour4838
    @mannydefour4838 3 года назад +29

    Absolutely amazing, I was a little frustrated at the beginning but I stuck through to the end and I understand it entirely now. Thank you for your content!

  • @skandasringari2370
    @skandasringari2370 10 месяцев назад +103

    currently 3am, school in 3 hours, math test 1st period, im fucked.

    • @squareeyes5942
      @squareeyes5942 9 месяцев назад +3

      why do you get up so early to study?? how did the test go

    • @skandasringari2370
      @skandasringari2370 8 месяцев назад

      @@squareeyes5942 went swimmingly I got a 94, for me math is easy to understand but I wasn't there for the whole unit so I had to study, also forgot to mention I'm a huge procrastinator

    • @aaliyahg4
      @aaliyahg4 8 месяцев назад +2

      Me right now 🥲

    • @JacobMachenje
      @JacobMachenje 7 месяцев назад +3

      Don't worry bro u ain't alone, you're gonna push through ok, hv some faith

    • @BamlakMengistu-qf3zx
      @BamlakMengistu-qf3zx 6 месяцев назад +2

      Same here 😭

  • @jasonbourne7843
    @jasonbourne7843 2 года назад +4

    I have to say, I've watched about 50 of your videos, and a million times, thank you for what you do. I'm in precal and my class is tough for me. You really help me understand everything. Better than my professor explains it. seriously, you're the GOAT!!!!

    • @sanopann1896
      @sanopann1896 2 года назад

      i just want to ask what grade you learning this stuffs mister

    • @Fishylocker
      @Fishylocker 7 месяцев назад

      ​@@sanopann1896 12th ?

  • @ilovesquishys1
    @ilovesquishys1 5 лет назад +25

    This video is blessing me right now 😩 my teacher taught us this with so little explanation and this video explains everything in such detail 🙏🏼🙏🏼

  • @jaineilsart1528
    @jaineilsart1528 Год назад +3

    Hey. This guy is basically a genius in everything. He probably need to get an reward for that.

  • @liezlkho7179
    @liezlkho7179 5 лет назад +18

    I've learned a lot from this video! Thouroughly explained how to graph rational functions with ease. The best math teacher in you tube!
    Thank you Sir! =D

  • @tgssabri
    @tgssabri 4 года назад +7

    You are a great help, straight forward videos, best on the internet. You are my main reference right now.

  • @slowmusical1749
    @slowmusical1749 3 года назад +8

    I would like to thank you for this amazing 58 minutes of incredible explanation that my teacher couldnt do within months

  • @chooju6149
    @chooju6149 4 года назад +54

    6:04 "now, if you have a piCkY teacher and you wanna draw a graph accurately..." YES I HAVE smh

  • @sink6874
    @sink6874 Год назад

    this man an khan academy are my go-tos
    endless examples and explains everything thorough. Thank god for this individual

  • @furaha7737
    @furaha7737 9 месяцев назад +1

    omg you are a life saver because i had no idea how to do the graphing part but you explained it so well

  • @alt_entwined5252
    @alt_entwined5252 5 лет назад +12

    I'm so grateful for this video. My math class is going a little too fast to keep up so you help me learn everything and have time to process it.

  • @wilsonvinas5906
    @wilsonvinas5906 7 лет назад +257

    at 11:15 the domain should be (-in,1) U (1,in) correct me if I'm wrong.

    • @nboris31
      @nboris31 7 лет назад +62

      yeah, HE actually meant (-inf,1) U (1,inf), it's just some human errors that may just slip in anyone's work

    • @itayikatiro3564
      @itayikatiro3564 5 лет назад +3

      Yeah, I noticed that too

    • @Edgylime6797lowl
      @Edgylime6797lowl 5 лет назад +2

      (-in, 1)U(1, in) is correct

    • @pranavm.9513
      @pranavm.9513 4 года назад +11

      he does it for free calm down

    • @fryPS
      @fryPS 4 года назад +16

      Your typical Indian Fisherman Literally no one is angry. Everyone is being cool about it.

  • @mescalormavideos7767
    @mescalormavideos7767 11 месяцев назад +1

    Thank you so much man, you explain things really clearly and a lot better than most school teachers

  • @sanopann1896
    @sanopann1896 2 года назад +4

    00:00 Degree of denominator is higher than the numerator.
    28:05 Degree of denominator is the same as the numerator.
    30:50 Degree of numerator is greater than the denominator.

  • @marsextras9172
    @marsextras9172 3 года назад +41

    i'm gonna be honest, i have to do an online test today and i'm just binging all rational functions and equation videos 😀💔

  • @kasuyp
    @kasuyp 5 лет назад +15

    Nice presentation very easy to understand... Math teachers should be precise in their explanations like you do...

  • @sadijemelenica1575
    @sadijemelenica1575 7 месяцев назад

    I am very thankful for such a meaningful asymptote video. It's explained in detail carefully considering most possible cases of rational functions.

  • @IWApost
    @IWApost 3 года назад +1

    Omfg I’m literally crying 😭 I’ve been struggling to understand and now I do!!!!!! THANK YOUU

  • @betterlsun4068
    @betterlsun4068 3 года назад +53

    Hi! Mr.chemistry tutor, I think the domain of the function in 11:26 is 1 not -1. The Vertical asymptote is x=1.

    • @EldanaG
      @EldanaG 3 года назад +11

      Exactly what i thought... i was like Huh??

    • @cotyb5028
      @cotyb5028 3 года назад +10

      That's why I started reading the comments ha. Thanks!

    • @timeelapse619
      @timeelapse619 2 года назад +5

      Phew I thought I missed something

    • @soramin7926
      @soramin7926 2 года назад +3

      Thx it confused me a little bit lol

    • @paulmaggiar8274
      @paulmaggiar8274 2 года назад +1

      @@maryyou556 1/x-1. x=1. 1 renders the denominator 0. 1 is the VA. What is throwing you off is that he got the domain wrong.

  • @nathaniel7813
    @nathaniel7813 9 месяцев назад +1

    helped me pass my unit exam with this thanks bro👍

  • @beyondhumanity7025
    @beyondhumanity7025 11 месяцев назад +1

    This guy saved my math grade!!!

  • @CanIBeFrankWithYou81
    @CanIBeFrankWithYou81 2 года назад

    I love you. I say it every time I watch one of your videos. You give me hope for our species, thank you for sharing your talents with the world 🙌🙌🙌

  • @mariahtrizzy4166
    @mariahtrizzy4166 Год назад

    I had really given up asymptotes but this video is a life saver thanks alot pal

  • @GabrielSanchez-rh6lv
    @GabrielSanchez-rh6lv 2 года назад

    This video was better than the last two weeks of reading about graphing rational functions. Thank you!

    • @sanopann1896
      @sanopann1896 2 года назад

      i just want to ask what grade you learning this stuffs mister

    • @GabrielSanchez-rh6lv
      @GabrielSanchez-rh6lv 2 года назад

      @@sanopann1896 i was taking a college algebra class. And believe me when I tell you this, math is not something I am good at. I struggle to have motivation to learn it and remember the formulas and understand why things are the way they are. But just apply yourself enough even if you may never do it again because learning is learning and you learn about yourself and ways that things make sense to you.

  • @robroineodingal5921
    @robroineodingal5921 4 года назад +5

    I think I've watched this video at least once a year during high school. It's a tradition now.

  • @saimaali843
    @saimaali843 5 лет назад +48

    Whoever made the video.. I will find you and I will marry you ..
    much needed video for my summer precalculus class

    • @youtubeweb3009
      @youtubeweb3009 4 года назад +1

      what if he doesn't want to marry you? haha just askin' though

    • @Fishylocker
      @Fishylocker 7 месяцев назад

      ​@@youtubeweb3009use force

  • @sczscz6021
    @sczscz6021 5 лет назад +9

    We need more people like you
    Thank you for your teaching.

  • @sahiliqbal4447
    @sahiliqbal4447 11 месяцев назад +1

    Relearning everything thanks for these videos!

  • @ET_AM
    @ET_AM 2 года назад

    Thanks for you're contribution! i have been using this channel for three years.and it helped me a lot. i belive that you wiil teach my field of study in the future. i have full confident that i will be surved by your channel again. 🙏🙏🙏🙏

  • @brownie7535
    @brownie7535 3 года назад +5

    Wow , your way of teaching is extremely wonderful ,I really really appreciate your work 👏👏👏👏

  • @joeyopes6064
    @joeyopes6064 3 года назад +1

    Dude this video saved me last minute! I got a 100 on the test… I literally can’t thank you enough I would of failed😫

  • @admoto04
    @admoto04 3 года назад +3

    I've been trying to figure out how to find the holes of a rational function for weeks and just figured it out 37:57

  • @niburu4427
    @niburu4427 4 года назад +6

    Thanks a lot this help me in guiding my son, Math is kinda hard now adays 😭😀

  • @earlhaywood4372
    @earlhaywood4372 3 года назад +2

    Thank You Sir, You are patient , articulate , and very thorough in your explanations . God Bless You ,and your parents

    • @sanopann1896
      @sanopann1896 2 года назад

      i just want to ask what grade you learning this stuffs mister

  • @cazandralopez7580
    @cazandralopez7580 4 года назад +3

    Thank you so much...you save me from this math for my grade 11 this 2020

  • @rowalynkeith.rilloraza
    @rowalynkeith.rilloraza 2 года назад +3

    the x-int at 39:36 is i believer +4, not -4 therefore when doing the line, it'll eventually touch the +4 as it goes down by the right side after th curve touches the P.O.D or the hole

  • @zhanss-j2x
    @zhanss-j2x 2 года назад +1

    thanks mate, I`m about to lose my scholarship, yet i hope that some staff that you taught me will help me to keep it! :)

  • @sanraii
    @sanraii 9 месяцев назад

    i literally fell asleep during class and saw random shit… ty😭😭 uve been saving my ass since algebra 1

  • @kylieb4722
    @kylieb4722 5 лет назад +1

    You’re a life saver omg thank u 😭😭 this is the first math video where I fully understood something.

  • @ianjustus324
    @ianjustus324 3 года назад

    This man literally saved me I have no clue about anything in pre calc 😭

  • @BrawlBearYT
    @BrawlBearYT 10 месяцев назад

    This man has saved many lives

  • @alanarcherman7946
    @alanarcherman7946 Год назад

    YASSSSS!!!! QUEEEEENNNNN!!! THANK YOU!!!!! LALALALA! I"M 12! I didn't understand a part of math class. I would be failing my homework if not for thisSSSSSS!!! AHHHHH THANK! YOUU! THX

  • @Celeste21yt
    @Celeste21yt 4 года назад +1

    You are the best thing that has ever happened to us

  • @CouncilOfBadDecisions
    @CouncilOfBadDecisions Месяц назад +2

    Bro is using ms paint and a bad mic and is still 1000x better than my teacher

  • @ToTiredToDealWithThis
    @ToTiredToDealWithThis 3 года назад +1

    When this 60min video teaches you more and better than 4 2h precalculus classes

  • @yasirabdifetah5739
    @yasirabdifetah5739 3 года назад

    you are the only one i listen to. You are a hero and understandable one. I thank you alot

  • @Bredkid96
    @Bredkid96 10 месяцев назад

    THANK YOU i have a math test today and this really helped me!!

  • @thebakingsquad9924
    @thebakingsquad9924 Год назад

    I got two days till test day and you just saved my life

  • @afridi501
    @afridi501 Год назад +1

    This is a mistake in time 11:20 1/(x-1) the domain is (-infinity, +1)u(+1, +infinity). I hope you dont mind

  • @SM-qn7sr
    @SM-qn7sr 3 года назад +4

    Hi at 11:20, isn’t the domain (-infinity, 1)U(1, infinity)?

  • @princekangwa3232
    @princekangwa3232 3 года назад +1

    this guy deserves a medal

  • @sereneblossom2951
    @sereneblossom2951 3 года назад

    bro my school puts this on the end of every module of our school website and i just skip thru the written ones and go straight to ur video cause i understand urs better lmao

  • @WhatAMessJada
    @WhatAMessJada 5 лет назад +23

    thank u so much my math teacher could never

  • @hiwotwesenseged6057
    @hiwotwesenseged6057 3 года назад

    I appreciate u a lot I have understood all thing rational graph within this 58 minutes than my teacher trying to get me into rational graph well for an hours

    • @sanopann1896
      @sanopann1896 2 года назад

      hi miss monaliza i just want to ask what grade you learning this stuffs

  • @mariomends702
    @mariomends702 5 месяцев назад +1

    Correct me If I'm wrong but at 10:50 you said the domain is -infinity to -1 when it should be to positive 1.

  • @shame5669
    @shame5669 3 года назад

    studying for a quiz rn literally this is saving me so much praise allah

  • @JP-wt4zr
    @JP-wt4zr 2 года назад

    An entire chapter in less than an hour? That's dope🔥🔥🔥👍

    • @sanopann1896
      @sanopann1896 2 года назад

      i just want to ask what grade you learning this stuffs mister

    • @JP-wt4zr
      @JP-wt4zr 2 года назад +2

      @@sanopann1896 Junior in high school

    • @LullabyBabyCar
      @LullabyBabyCar Год назад

      @@JP-wt4zr im a sophmore

  • @dolimwaki6484
    @dolimwaki6484 4 года назад +1

    I'm from Africa continentTanzania is my country seriously God sent You to make me understand 😍

  • @deputy1968
    @deputy1968 3 года назад +3

    Thank you very much for taking your time to make these video's!! They are extremely helpful!

  • @enickerson5
    @enickerson5 5 лет назад +6

    Thank you for being so clear and easy to follow! This helped my daughter for a test last night!

  • @mrpee2482
    @mrpee2482 5 лет назад +73

    13:20 "Oh Wow That's Terrible 🤣😂🥺"

    • @sweetener2535
      @sweetener2535 5 лет назад +8

      Romeo Poomore Jshdjej that was adorable 😂

  • @priscamwale9132
    @priscamwale9132 Год назад +1

    You are awesome and genius 🔥🔥🔥

  • @TomakoDela
    @TomakoDela 3 года назад +1

    thank you so much for the tutorial video, your tutorial is one of the best in my opinion, I only watch the one you updated and Khan Academy TvT The others are just not on the point.

  • @TheRohanMan
    @TheRohanMan 5 лет назад +114

    WHEN YOU'RE TRYING TO STUDY FOR EXAM AND GRAMMARLY AD COMES UP EVERY 2 MINUTES
    IT'S SO ANNOYING!

    • @arjay_2002
      @arjay_2002 5 лет назад +9

      dont watch this then lmao no one is paying him to do this

    • @matheobrooks6450
      @matheobrooks6450 4 года назад +1

      @@arjay_2002 RUclips is you dimwit

    • @itsbeanslol
      @itsbeanslol 4 года назад +7

      There's something called an ad blocker

    • @rawandhwayyiz4302
      @rawandhwayyiz4302 4 года назад +2

      @@matheobrooks6450 yes, though ads dumass,

    • @tatiana1310
      @tatiana1310 4 года назад

      Same here

  • @alexalopez4904
    @alexalopez4904 2 года назад

    I have a huge test tomorrow, thank you so much for your help.

    • @sanopann1896
      @sanopann1896 2 года назад

      i just want to ask what grade you learning this stuffs miss

  • @wesamzamzam8461
    @wesamzamzam8461 4 года назад +1

    You teach better than my teacher, Thanks a lot man, really appreciate your hard work!

  • @she2787
    @she2787 2 года назад

    You are saving the world!!!

  • @sovitbista1770
    @sovitbista1770 3 года назад +2

    11:02 domain supposed to be (-∞,1)U(1,∞) not (-∞,-1)U(-1,∞). He said right but wrote wrong. If I am not wrong

  • @anshakrajdehl9391
    @anshakrajdehl9391 2 года назад

    Excellent Explanation Sir!!

    • @sanopann1896
      @sanopann1896 2 года назад

      i just want to ask what grade you learning this stuffs mister

  • @caylylikessweets8594
    @caylylikessweets8594 4 года назад

    Thank you so much, I really needed this video👏👏👏

  • @emperorvladimir4479
    @emperorvladimir4479 4 года назад +2

    The video is amazing but I just want to suggest increasing the volume of your voice. Aside that, Nice content!

  • @kyleliebenberg7169
    @kyleliebenberg7169 3 года назад +1

    I genuinely love you

  • @scottpalmer829
    @scottpalmer829 2 года назад

    Your explanation is excellent. It is clear and at a good pace. My one suggestion for improvement would be to have a pre-made grid like graph paper. Your sketches are a little crudely done. Your video is well-worth watching nonetheless.

    • @sanopann1896
      @sanopann1896 2 года назад

      i just want to ask what grade you learning this stuffs mister

  • @thelife8836
    @thelife8836 2 года назад

    You are a hero brother 😍😍😍😍

  • @modesterdeene2428
    @modesterdeene2428 5 лет назад +9

    I really appreciate you. I'm learning a lot

  • @Study-ASMR
    @Study-ASMR 2 года назад

    Thank you so much for saving my grade!!

  • @tylerdelatorre8230
    @tylerdelatorre8230 4 года назад +2

    In finding the x -intercept for the problem at 40:00 do you not distribute 3 to (x + 4) then equate it to 0?

  • @mohsenamini3297
    @mohsenamini3297 4 года назад +1

    Very great work JG, Always thank you.

  • @estajabartoskova2057
    @estajabartoskova2057 2 года назад

    You're a genius. Thank you. Couldn't survive without you.

  • @septicalwolf7361
    @septicalwolf7361 2 года назад

    11:00 the answer is actually negative infinite to one and from one to infinite. It’s not negative one because that is included in the graph

  • @zzaeris
    @zzaeris Год назад

    Dude i suck at math i dont even have the multiplication table memorized 😢 but i did really good in our exam and now my classmates think im good at the subject and made me one of the leaders ☠☠☠ here rn to educate myself

  • @takeeoro2
    @takeeoro2 9 месяцев назад

    Best teacher world thanks

  • @mathtutorph5718
    @mathtutorph5718 4 года назад

    At around 39:50 he solved for the y-intercept. Why is that? Is it because there is a hole? If there is a hole, will we need to solve for the y-intercept?

  • @tristanorarson3069
    @tristanorarson3069 4 года назад

    Awesome video, I didn't understand the last thing in but still awesome video

  • @betterlsun4068
    @betterlsun4068 3 года назад +1

    Thank you so much. I totally understand all the things!

  • @oops1088
    @oops1088 Год назад +1

    11:00 tiny mistake. Should be negative infinity to 1 not -1

  • @Wonu1
    @Wonu1 Год назад

    Mamatay na ako sa Gen Math 😊😊

  • @asif7240
    @asif7240 4 года назад

    This man is a legend