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

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  • เผยแพร่เมื่อ 21 ธ.ค. 2024

ความคิดเห็น • 657

  • @TheOrganicChemistryTutor
    @TheOrganicChemistryTutor  ปีที่แล้ว +24

    Domain & Range - Free Formula Sheet: bit.ly/4eheN2W
    Final Exams and Video Playlists: www.video-tutor.net/
    Full-Length Videos & Worksheets: www.patreon.com/MathScienceTutor/collections

  • @gamingresumed1788
    @gamingresumed1788 4 ปีที่แล้ว +861

    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 ปีที่แล้ว +1376

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

    • @rudyj8948
      @rudyj8948 4 ปีที่แล้ว +11

      Literally same

    • @memes4themasses365
      @memes4themasses365 4 ปีที่แล้ว +7

      I’m with ya rn

    • @quinive9812
      @quinive9812 4 ปีที่แล้ว +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 ปีที่แล้ว +24

      I got to do this for Algebra 2.

    • @Jackripz
      @Jackripz 3 ปีที่แล้ว +4

      @@No-dy3zk same

  • @ign0tium539
    @ign0tium539 ปีที่แล้ว +341

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

    • @xrzenel_8072
      @xrzenel_8072 ปีที่แล้ว +5

      I feel that

    • @shanepotter6348
      @shanepotter6348 ปีที่แล้ว +23

      You got 2 weeks to learn this? I got 2 days 😭

    • @princewillanyagagligbo6890
      @princewillanyagagligbo6890 ปีที่แล้ว +2

      glazing

    • @MZZ745
      @MZZ745 ปีที่แล้ว

      @@shanepotter6348I got 1 day💀

    • @kiriuzi7959
      @kiriuzi7959 ปีที่แล้ว

      lmao try a day or approx one hour @@shanepotter6348

  • @lunam11
    @lunam11 4 ปีที่แล้ว +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!!

    • @Stunz
      @Stunz 3 ปีที่แล้ว +7

      How did you do??

    • @ashwinanand1465
      @ashwinanand1465 2 ปีที่แล้ว +1

      @@Stunz L

    • @dissociating1703
      @dissociating1703 2 ปีที่แล้ว +1

      @@ashwinanand1465 💀💀

    • @declanrodgers8004
      @declanrodgers8004 2 ปีที่แล้ว

      orc

    • @maryyou556
      @maryyou556 2 ปีที่แล้ว +1

      Do u have a Playlist for all the videos u watched ?

  • @ArpitaDebnath-fp8fg
    @ArpitaDebnath-fp8fg 5 หลายเดือนก่อน +7

    TH-cam is gold when such videos exists.
    Thanks a million man

  • @draglonconx7771
    @draglonconx7771 5 ปีที่แล้ว +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!

  • @iglo1209
    @iglo1209 5 ปีที่แล้ว +174

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

    • @safteyhazard
      @safteyhazard 4 ปีที่แล้ว +8

      what about 2020?

    • @iamgroot7684
      @iamgroot7684 4 ปีที่แล้ว +23

      This aged pretty well.

    • @iamgroot7684
      @iamgroot7684 4 ปีที่แล้ว +8

      But also not too well

    • @samisiddiqi5411
      @samisiddiqi5411 4 ปีที่แล้ว +3

      This aged like fine cheese. But blue cheese that is.

    • @jessivonfilm
      @jessivonfilm 4 ปีที่แล้ว

      @@samisiddiqi5411 that it did

  • @isaiahwhitney8168
    @isaiahwhitney8168 4 ปีที่แล้ว +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

    • @aryanrayana8065
      @aryanrayana8065 ปีที่แล้ว +4

      how did that go?

    • @lolmetyuri
      @lolmetyuri ปีที่แล้ว +2

      ​@@aryanrayana8065he didn't make it😢😢

  • @wormonastring8934
    @wormonastring8934 4 ปีที่แล้ว +2767

    anyone else crying in math class? :)

  • @mannydefour4838
    @mannydefour4838 3 ปีที่แล้ว +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 9 หลายเดือนก่อน +102

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

    • @squareeyes5942
      @squareeyes5942 8 หลายเดือนก่อน +3

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

    • @skandasringari2370
      @skandasringari2370 7 หลายเดือนก่อน

      @@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 7 หลายเดือนก่อน +2

      Me right now 🥲

    • @JacobMachenje
      @JacobMachenje 7 หลายเดือนก่อน +3

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

    • @BamlakMengistu-qf3zx
      @BamlakMengistu-qf3zx 6 หลายเดือนก่อน +2

      Same here 😭

  • @ilovesquishys1
    @ilovesquishys1 5 ปีที่แล้ว +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 🙏🏼🙏🏼

  • @jasonbourne7843
    @jasonbourne7843 2 ปีที่แล้ว +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 ปีที่แล้ว

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

    • @Fishylocker
      @Fishylocker 7 หลายเดือนก่อน

      ​@@sanopann1896 12th ?

  • @mehakahuja9372
    @mehakahuja9372 ปีที่แล้ว +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

    • @MainulWasTaken
      @MainulWasTaken ปีที่แล้ว +3

      Me too
      It should X not equal 1

    • @drowzZzy_
      @drowzZzy_ ปีที่แล้ว +2

      same thoughts

    • @superiorjr154
      @superiorjr154 ปีที่แล้ว +3

      You’re right.

    • @nerimaken482
      @nerimaken482 ปีที่แล้ว +7

      ok good i was confused 😭

    • @JoeSwick41
      @JoeSwick41 11 หลายเดือนก่อน +2

      thank you, i was thinking the same..

  • @jaineilsart1528
    @jaineilsart1528 ปีที่แล้ว +3

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

  • @liezlkho7179
    @liezlkho7179 5 ปีที่แล้ว +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

  • @slowmusical1749
    @slowmusical1749 3 ปีที่แล้ว +8

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

  • @tgssabri
    @tgssabri 4 ปีที่แล้ว +7

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

  • @chooju6149
    @chooju6149 4 ปีที่แล้ว +54

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

  • @wilsonvinas5906
    @wilsonvinas5906 7 ปีที่แล้ว +257

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

    • @nboris31
      @nboris31 7 ปีที่แล้ว +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 ปีที่แล้ว +3

      Yeah, I noticed that too

    • @Edgylime6797lowl
      @Edgylime6797lowl 5 ปีที่แล้ว +2

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

    • @pranavm.9513
      @pranavm.9513 4 ปีที่แล้ว +11

      he does it for free calm down

    • @fryPS
      @fryPS 4 ปีที่แล้ว +16

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

  • @betterlsun4068
    @betterlsun4068 3 ปีที่แล้ว +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 ปีที่แล้ว +11

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

    • @cotyb5028
      @cotyb5028 2 ปีที่แล้ว +10

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

    • @timeelapse619
      @timeelapse619 2 ปีที่แล้ว +5

      Phew I thought I missed something

    • @soramin7926
      @soramin7926 2 ปีที่แล้ว +3

      Thx it confused me a little bit lol

    • @paulmaggiar8274
      @paulmaggiar8274 2 ปีที่แล้ว +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.

  • @sink6874
    @sink6874 ปีที่แล้ว

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

  • @alt_entwined5252
    @alt_entwined5252 4 ปีที่แล้ว +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.

  • @marsextras9172
    @marsextras9172 3 ปีที่แล้ว +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 😀💔

  • @mescalormavideos7767
    @mescalormavideos7767 10 หลายเดือนก่อน +1

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

  • @kasuyp
    @kasuyp 5 ปีที่แล้ว +15

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

  • @furaha7737
    @furaha7737 9 หลายเดือนก่อน +1

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

  • @robroineodingal5921
    @robroineodingal5921 4 ปีที่แล้ว +5

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

  • @IWApost
    @IWApost 3 ปีที่แล้ว +1

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

  • @saimaali843
    @saimaali843 5 ปีที่แล้ว +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 ปีที่แล้ว +1

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

    • @Fishylocker
      @Fishylocker 7 หลายเดือนก่อน

      ​@@youtubeweb3009use force

  • @WhatAMessJada
    @WhatAMessJada 5 ปีที่แล้ว +23

    thank u so much my math teacher could never

  • @beyondhumanity7025
    @beyondhumanity7025 10 หลายเดือนก่อน +1

    This guy saved my math grade!!!

  • @sanopann1896
    @sanopann1896 2 ปีที่แล้ว +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.

  • @sczscz6021
    @sczscz6021 5 ปีที่แล้ว +9

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

  • @nathaniel7813
    @nathaniel7813 9 หลายเดือนก่อน +1

    helped me pass my unit exam with this thanks bro👍

  • @sadijemelenica1575
    @sadijemelenica1575 6 หลายเดือนก่อน

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

  • @GabrielSanchez-rh6lv
    @GabrielSanchez-rh6lv 2 ปีที่แล้ว

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

    • @sanopann1896
      @sanopann1896 2 ปีที่แล้ว

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

    • @GabrielSanchez-rh6lv
      @GabrielSanchez-rh6lv 2 ปีที่แล้ว

      @@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.

  • @niburu4427
    @niburu4427 4 ปีที่แล้ว +6

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

  • @BrawlBearYT
    @BrawlBearYT 9 หลายเดือนก่อน

    This man has saved many lives

  • @brownie7535
    @brownie7535 3 ปีที่แล้ว +5

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

  • @CouncilOfBadDecisions
    @CouncilOfBadDecisions หลายเดือนก่อน +2

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

  • @sanraii
    @sanraii 9 หลายเดือนก่อน

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

  • @mariahtrizzy4166
    @mariahtrizzy4166 ปีที่แล้ว

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

  • @princekangwa3232
    @princekangwa3232 3 ปีที่แล้ว +1

    this guy deserves a medal

  • @ToTiredToDealWithThis
    @ToTiredToDealWithThis 3 ปีที่แล้ว +1

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

  • @cazandralopez7580
    @cazandralopez7580 4 ปีที่แล้ว +3

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

  • @joeyopes6064
    @joeyopes6064 3 ปีที่แล้ว +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😫

  • @earlhaywood4372
    @earlhaywood4372 3 ปีที่แล้ว +2

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

    • @sanopann1896
      @sanopann1896 2 ปีที่แล้ว

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

  • @CanIBeFrankWithYou81
    @CanIBeFrankWithYou81 2 ปีที่แล้ว

    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 🙌🙌🙌

  • @alanarcherman7946
    @alanarcherman7946 ปีที่แล้ว

    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

  • @ianjustus324
    @ianjustus324 3 ปีที่แล้ว

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

  • @Celeste21yt
    @Celeste21yt 4 ปีที่แล้ว +1

    You are the best thing that has ever happened to us

  • @mrpee2482
    @mrpee2482 5 ปีที่แล้ว +73

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

    • @sweetener2535
      @sweetener2535 4 ปีที่แล้ว +8

      Romeo Poomore Jshdjej that was adorable 😂

  • @admoto04
    @admoto04 3 ปีที่แล้ว +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

  • @zhanss-j2x
    @zhanss-j2x 2 ปีที่แล้ว +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! :)

  • @rowalynkeith.rilloraza
    @rowalynkeith.rilloraza 2 ปีที่แล้ว +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

  • @yasirabdifetah5739
    @yasirabdifetah5739 3 ปีที่แล้ว

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

  • @sahiliqbal4447
    @sahiliqbal4447 11 หลายเดือนก่อน +1

    Relearning everything thanks for these videos!

  • @ET_AM
    @ET_AM 2 ปีที่แล้ว

    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. 🙏🙏🙏🙏

  • @thebakingsquad9924
    @thebakingsquad9924 ปีที่แล้ว

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

  • @kylieb4722
    @kylieb4722 5 ปีที่แล้ว +1

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

  • @shame5669
    @shame5669 3 ปีที่แล้ว

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

  • @deputy1968
    @deputy1968 3 ปีที่แล้ว +3

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

  • @dolimwaki6484
    @dolimwaki6484 4 ปีที่แล้ว +1

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

  • @Bredkid96
    @Bredkid96 9 หลายเดือนก่อน

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

  • @hiwotwesenseged6057
    @hiwotwesenseged6057 3 ปีที่แล้ว

    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 ปีที่แล้ว

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

  • @JP-wt4zr
    @JP-wt4zr 2 ปีที่แล้ว

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

    • @sanopann1896
      @sanopann1896 2 ปีที่แล้ว

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

    • @JP-wt4zr
      @JP-wt4zr 2 ปีที่แล้ว +2

      @@sanopann1896 Junior in high school

    • @LullabyBabyCar
      @LullabyBabyCar ปีที่แล้ว

      @@JP-wt4zr im a sophmore

  • @SM-qn7sr
    @SM-qn7sr 3 ปีที่แล้ว +4

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

  • @sereneblossom2951
    @sereneblossom2951 3 ปีที่แล้ว

    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

  • @wesamzamzam8461
    @wesamzamzam8461 4 ปีที่แล้ว +1

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

  • @mariomends702
    @mariomends702 5 หลายเดือนก่อน +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.

  • @modesterdeene2428
    @modesterdeene2428 5 ปีที่แล้ว +9

    I really appreciate you. I'm learning a lot

  • @alexalopez4904
    @alexalopez4904 2 ปีที่แล้ว

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

    • @sanopann1896
      @sanopann1896 2 ปีที่แล้ว

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

  • @estajabartoskova2057
    @estajabartoskova2057 2 ปีที่แล้ว

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

  • @enickerson5
    @enickerson5 4 ปีที่แล้ว +6

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

  • @she2787
    @she2787 2 ปีที่แล้ว

    You are saving the world!!!

  • @Study-ASMR
    @Study-ASMR 2 ปีที่แล้ว

    Thank you so much for saving my grade!!

  • @anshakrajdehl9391
    @anshakrajdehl9391 2 ปีที่แล้ว

    Excellent Explanation Sir!!

    • @sanopann1896
      @sanopann1896 2 ปีที่แล้ว

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

  • @asif7240
    @asif7240 4 ปีที่แล้ว

    This man is a legend

  • @briannaorange9910
    @briannaorange9910 4 ปีที่แล้ว +1

    thank you, I don't learn from my assigned teacher, I learn from you lol

  • @MrYoenny
    @MrYoenny ปีที่แล้ว +2

    after 6 years i find this to study for myself

  • @potafish5107
    @potafish5107 2 ปีที่แล้ว

    he is better than my math teacher. why isn't he teaching in my school

  • @KelvinHarawa-uj4ik
    @KelvinHarawa-uj4ik ปีที่แล้ว +1

    This video saved me, but I still don't get the point of learning this in medical school🤣

  • @mohsenamini3297
    @mohsenamini3297 4 ปีที่แล้ว +1

    Very great work JG, Always thank you.

  • @betterlsun4068
    @betterlsun4068 3 ปีที่แล้ว +1

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

  • @tylerdelatorre8230
    @tylerdelatorre8230 4 ปีที่แล้ว +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?

  • @scottpalmer829
    @scottpalmer829 2 ปีที่แล้ว

    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 ปีที่แล้ว

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

  • @caylylikessweets8594
    @caylylikessweets8594 4 ปีที่แล้ว

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

  • @JohnsonMaths
    @JohnsonMaths ปีที่แล้ว

    Really clarifies all our doubts

  • @Wonu1
    @Wonu1 ปีที่แล้ว

    Mamatay na ako sa Gen Math 😊😊

  • @jazminegarcia9910
    @jazminegarcia9910 2 ปีที่แล้ว +1

    At 11:12, wouldn't the domain be positive 1 rather than negative?

  • @kyleliebenberg7169
    @kyleliebenberg7169 3 ปีที่แล้ว +1

    I genuinely love you

  • @TomakoDela
    @TomakoDela 3 ปีที่แล้ว +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.

  • @priscamwale9132
    @priscamwale9132 ปีที่แล้ว +1

    You are awesome and genius 🔥🔥🔥

  • @sovitbista1770
    @sovitbista1770 3 ปีที่แล้ว +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

  • @dennisrayrosas3175
    @dennisrayrosas3175 4 ปีที่แล้ว +1

    Is it always the numerator to be used when finding x and y intercept?

  • @emperorvladimir4479
    @emperorvladimir4479 4 ปีที่แล้ว +2

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

  • @tristanorarson3069
    @tristanorarson3069 4 ปีที่แล้ว

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

  • @stickmanbattle997
    @stickmanbattle997 3 ปีที่แล้ว

    Thank you sm , my self study pre cal is consistent