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

This algebra 2 / precalculus video tutorial explains how to graph rational functions with asymptotes and holes. It shows you how to identify the vertical asymptotes by setting the denominator equal to zero and solving for x. It shows you how to find the equation of the horizontal asymptote by comparing the degree of the numerator with that of the denominator. In addition, it shows you how to find and graph the slant asymptote / oblique asymptote using long division. This video also shows you how to identify the x and y coordinate of any holes in the graph. This video contains plenty of examples and practice problems including those in which factoring quadratic expressions and equations are involved. This video also discusses the transformations that occur when graphing rational functions. Horizontal and Vertical shifts are covered as well as reflection over the y axis and the origin. In addition, this video shows you how to the coordinates of the x intercept and y intercept. Finally, this tutorial shows you how to write the domain and range of a rational function using interval notation. It mentions when parentheses and brackets should be use. Whenever you need to write the domain of a rational function, you need to take into account the vertical asymptote and the x coordinate of any holes in the graph. For the range, you need to remove the horizontal asymptote and the y coordinate of any holes in the curve. This video might be useful for students taking calculus.
Fundamental Theorem of Algebra:
• Fundamental Theorem of...
Rational Expressions - Basic Intro:
• Rational Expressions -...
Simplifying Rational Expressions:
• Simplifying Rational E...
Multiplying Rational Expressions:
• Multiplying Rational E...
Dividing Rational Expressions:
• Dividing Rational Expr...
______________________________________
Adding & Subtracting Rational Expressions:
• Adding and Subtracting...
Rational Expressions - Unlike Denominators:
• Adding and Subtracting...
Simplifying Complex Rational Expressions:
• Simplifying Complex Ra...
How To Solve Rational Equations:
• Solving Rational Equat...
Rational Equations - Extraneous Solutions:
• Extraneous Solutions o...
_____________________________________
Horizontal and Slant Asymptotes:
• Horizontal Asymptotes ...
Finding Rational Functions Given 2 Points:
• How To Find a Rational...
Rational Functions - X and Y Intercepts:
• How To Find The X and ...
Graphing Advanced Rational Functions:
• Graphing Advanced Rati...
Rational Inequalities:
• Rational Inequalities
________________________________________
Final Exams and Video Playlists:
www.video-tutor.net/
Full-Length Videos and Worksheets:
/ collections

Пікірлер: 620

  • @TheOrganicChemistryTutor
    @TheOrganicChemistryTutor7 ай бұрын

    Final Exams and Video Playlists: www.video-tutor.net/ Full-Length Videos & Worksheets: www.patreon.com/MathScienceTutor/collections

  • @komartiketmusa8447

    @komartiketmusa8447

    4 ай бұрын

    splendid!!

  • @gamingresumed1788
    @gamingresumed17883 жыл бұрын

    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)

  • @blockydogy1188

    @blockydogy1188

    3 жыл бұрын

    my hero

  • @whyareyougae6839

    @whyareyougae6839

    3 жыл бұрын

    You dropped this king 👑

  • @pikatothechu4737

    @pikatothechu4737

    3 жыл бұрын

    You're the MVP

  • 3 жыл бұрын

    love how gaming also has to do homework

  • @maitemookamedi1700

    @maitemookamedi1700

    2 жыл бұрын

    Thank you

  • @wormonastring8934
    @wormonastring89343 жыл бұрын

    anyone else crying in math class? :)

  • @Fishfriend001

    @Fishfriend001

    3 жыл бұрын

    Yes🥲

  • @sondersiya

    @sondersiya

    3 жыл бұрын

    @@Fishfriend001 yes 😢

  • @yunosogasii6200

    @yunosogasii6200

    3 жыл бұрын

    Yes🥲

  • @official_kea_rsa

    @official_kea_rsa

    3 жыл бұрын

    Every day

  • @bruh-cb9dc

    @bruh-cb9dc

    3 жыл бұрын

    yes ma’am

  • @m.miller8011
    @m.miller80115 жыл бұрын

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

  • @rudyj8948

    @rudyj8948

    4 жыл бұрын

    Literally same

  • @memes4themasses365

    @memes4themasses365

    3 жыл бұрын

    I’m with ya rn

  • @quinive9812

    @quinive9812

    3 жыл бұрын

    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

    3 жыл бұрын

    I got to do this for Algebra 2.

  • @Jackripz

    @Jackripz

    3 жыл бұрын

    @@No-dy3zk same

  • @ign0tium539
    @ign0tium539 Жыл бұрын

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

  • @xrzenel_8072

    @xrzenel_8072

    Жыл бұрын

    I feel that

  • @shanepotter6348

    @shanepotter6348

    Жыл бұрын

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

  • @princewillanyagagligbo6890

    @princewillanyagagligbo6890

    11 ай бұрын

    glazing

  • @MZZ745

    @MZZ745

    9 ай бұрын

    @@shanepotter6348I got 1 day💀

  • @kiriuzi7959

    @kiriuzi7959

    8 ай бұрын

    lmao try a day or approx one hour @@shanepotter6348

  • @lunam11
    @lunam113 жыл бұрын

    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 жыл бұрын

    How did you do??

  • @ashwinanand1465

    @ashwinanand1465

    2 жыл бұрын

    @@Stunz L

  • @dissociating1703

    @dissociating1703

    2 жыл бұрын

    @@ashwinanand1465 💀💀

  • @declanrodgers8004

    @declanrodgers8004

    2 жыл бұрын

    orc

  • @maryyou556

    @maryyou556

    2 жыл бұрын

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

  • @skandasringari2370
    @skandasringari23704 ай бұрын

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

  • @squareeyes5942

    @squareeyes5942

    3 ай бұрын

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

  • @skandasringari2370

    @skandasringari2370

    2 ай бұрын

    @@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

    2 ай бұрын

    Me right now 🥲

  • @JacobMachenje

    @JacobMachenje

    2 ай бұрын

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

  • @BamlakMengistu-qf3zx

    @BamlakMengistu-qf3zx

    Ай бұрын

    Same here 😭

  • @krappa1234
    @krappa12344 жыл бұрын

    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.

  • @jeeves4490

    @jeeves4490

    2 жыл бұрын

    This is what I've been looking for thanks bro

  • @vladimirsheydorov3776

    @vladimirsheydorov3776

    Жыл бұрын

    thank you!

  • @juaquiqui-kun4333

    @juaquiqui-kun4333

    Жыл бұрын

    @@jeeves4490 and I've been looking for you

  • @WeirdJeans

    @WeirdJeans

    2 ай бұрын

    ​@@jeeves4490 andddd I've been lookin for you all over the internet

  • @draglonconx7771
    @draglonconx77715 жыл бұрын

    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
    @iglo12094 жыл бұрын

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

  • @safteyhazard

    @safteyhazard

    4 жыл бұрын

    what about 2020?

  • @iamgroot7684

    @iamgroot7684

    3 жыл бұрын

    This aged pretty well.

  • @iamgroot7684

    @iamgroot7684

    3 жыл бұрын

    But also not too well

  • @samisiddiqi5411

    @samisiddiqi5411

    3 жыл бұрын

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

  • @frankiecott

    @frankiecott

    3 жыл бұрын

    @@samisiddiqi5411 that it did

  • @ArpitaDebnath-fp8fg
    @ArpitaDebnath-fp8fg21 күн бұрын

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

  • @chooju6149
    @chooju61493 жыл бұрын

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

  • @mannydefour4838
    @mannydefour48382 жыл бұрын

    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!

  • @declanrodgers8004

    @declanrodgers8004

    2 жыл бұрын

    046

  • @ilovesquishys1
    @ilovesquishys15 жыл бұрын

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

  • @wilsonvinas5906
    @wilsonvinas59067 жыл бұрын

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

  • @nboris31

    @nboris31

    6 жыл бұрын

    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 жыл бұрын

    Yeah, I noticed that too

  • @Edgylime6797lowl

    @Edgylime6797lowl

    4 жыл бұрын

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

  • @pranavm.9513

    @pranavm.9513

    4 жыл бұрын

    he does it for free calm down

  • @fryPS

    @fryPS

    4 жыл бұрын

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

  • @liezlkho7179
    @liezlkho71795 жыл бұрын

    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

  • @isaiahwhitney8168
    @isaiahwhitney81684 жыл бұрын

    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

    Жыл бұрын

    how did that go?

  • @lolmetyuri

    @lolmetyuri

    8 ай бұрын

    ​@@aryanrayana8065he didn't make it😢😢

  • @tgssabri
    @tgssabri3 жыл бұрын

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

  • @slowmusical1749
    @slowmusical17493 жыл бұрын

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

  • @mehakahuja9372
    @mehakahuja9372 Жыл бұрын

    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

    11 ай бұрын

    Me too It should X not equal 1

  • @drowzZzy_

    @drowzZzy_

    10 ай бұрын

    same thoughts

  • @superiorjr154

    @superiorjr154

    9 ай бұрын

    You’re right.

  • @nerimaken482

    @nerimaken482

    7 ай бұрын

    ok good i was confused 😭

  • @JoeSwick41

    @JoeSwick41

    6 ай бұрын

    thank you, i was thinking the same..

  • @marsextras9172
    @marsextras91723 жыл бұрын

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

  • @alt_entwined5252
    @alt_entwined52524 жыл бұрын

    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.

  • @ET_AM
    @ET_AM2 жыл бұрын

    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
    @brownie75353 жыл бұрын

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

  • @betterlsun4068
    @betterlsun40682 жыл бұрын

    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

    2 жыл бұрын

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

  • @cotyb5028

    @cotyb5028

    2 жыл бұрын

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

  • @timeelapse619

    @timeelapse619

    2 жыл бұрын

    Phew I thought I missed something

  • @soramin7926

    @soramin7926

    2 жыл бұрын

    Thx it confused me a little bit lol

  • @paulmaggiar8274

    @paulmaggiar8274

    Жыл бұрын

    @@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.

  • @deputy1968
    @deputy19682 жыл бұрын

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

  • @jasonbourne7843
    @jasonbourne78432 жыл бұрын

    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

    Жыл бұрын

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

  • @WeirdJeans

    @WeirdJeans

    2 ай бұрын

    ​@@sanopann1896 12th ?

  • @jaineilsart1528
    @jaineilsart1528 Жыл бұрын

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

  • @estajabartoskova2057
    @estajabartoskova20572 жыл бұрын

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

  • @sczscz6021
    @sczscz60215 жыл бұрын

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

  • @sink6874
    @sink68749 ай бұрын

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

  • @mariahtrizzy4166
    @mariahtrizzy4166 Жыл бұрын

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

  • @WhatAMessJada
    @WhatAMessJada4 жыл бұрын

    thank u so much my math teacher could never

  • @robroineodingal5921
    @robroineodingal59213 жыл бұрын

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

  • @mescalormavideos7767
    @mescalormavideos77675 ай бұрын

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

  • @julialewis6843
    @julialewis68436 жыл бұрын

    How do I find a function when I have points? There is no x or y intercept, and only a horizontal asymptote.

  • @SM-qn7sr
    @SM-qn7sr3 жыл бұрын

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

  • @farmachook
    @farmachook Жыл бұрын

    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 🙌🙌🙌

  • @furaha7737
    @furaha77374 ай бұрын

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

  • @saimaali843
    @saimaali8435 жыл бұрын

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

  • @youtubeweb3009

    @youtubeweb3009

    3 жыл бұрын

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

  • @WeirdJeans

    @WeirdJeans

    2 ай бұрын

    ​@@youtubeweb3009use force

  • @sahiliqbal4447
    @sahiliqbal44476 ай бұрын

    Relearning everything thanks for these videos!

  • @sadijemelenica1575
    @sadijemelenica1575Ай бұрын

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

  • @earlhaywood4372
    @earlhaywood43722 жыл бұрын

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

  • @sanopann1896

    @sanopann1896

    Жыл бұрын

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

  • @kasuyp
    @kasuyp5 жыл бұрын

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

  • @declanrodgers8004

    @declanrodgers8004

    2 жыл бұрын

    9

  • @mohsenamini3297
    @mohsenamini32974 жыл бұрын

    Very great work JG, Always thank you.

  • @saarazart1291
    @saarazart12916 жыл бұрын

    Thank you so much!! You are the best.

  • @GabrielSanchez-rh6lv
    @GabrielSanchez-rh6lv2 жыл бұрын

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

  • @sanopann1896

    @sanopann1896

    Жыл бұрын

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

  • @GabrielSanchez-rh6lv

    @GabrielSanchez-rh6lv

    Жыл бұрын

    @@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.

  • @meritu985
    @meritu9853 жыл бұрын

    You are the best thing that has ever happened to us

  • @betterlsun4068
    @betterlsun40682 жыл бұрын

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

  • @caylylikessweets8594
    @caylylikessweets85943 жыл бұрын

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

  • @cazandralopez7580
    @cazandralopez75803 жыл бұрын

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

  • @IWApost
    @IWApost2 жыл бұрын

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

  • @yasirabdifetah5739
    @yasirabdifetah57392 жыл бұрын

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

  • @modesterdeene2428
    @modesterdeene24284 жыл бұрын

    I really appreciate you. I'm learning a lot

  • @princekangwa3232
    @princekangwa32323 жыл бұрын

    this guy deserves a medal

  • @kentrader2489
    @kentrader24894 жыл бұрын

    On the last rational : How do you know that (3, 23.8) is the vertex for that parabola?

  • @sanya5538
    @sanya55386 жыл бұрын

    Thank you for taking your time to explain this wonderful video

  • @danielperezrosales8392
    @danielperezrosales83925 жыл бұрын

    thank you very much for making this video

  • @user-ny3dl1ju4e
    @user-ny3dl1ju4e4 жыл бұрын

    Super helpful, awesome! A big thank you to you!

  • @user-ny3dl1ju4e

    @user-ny3dl1ju4e

    4 жыл бұрын

    And also you can use demos to find points as well.

  • @franklinchacon1824
    @franklinchacon18245 жыл бұрын

    Thank you!!!! really helped.

  • @niburu4427
    @niburu44273 жыл бұрын

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

  • @lachlanedwards05
    @lachlanedwards054 жыл бұрын

    whats domain and range of the graph f(x) =2/x, i dont know what changes from this trandformation

  • @BrawlBearYT
    @BrawlBearYT4 ай бұрын

    This man has saved many lives

  • @ianjustus324
    @ianjustus3242 жыл бұрын

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

  • @prinzecesartonares9332
    @prinzecesartonares93325 жыл бұрын

    Can you please elaborate. Why is it the value of range/horizontal asymptote must be ax/bx, if y=ax+c/bx+e. For ex. The vertical asymptote must equate to 0 since having a 0 denominator is undefined.

  • @dennisrayrosas3175
    @dennisrayrosas31753 жыл бұрын

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

  • @mrpee2482
    @mrpee24824 жыл бұрын

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

  • @sweetener2535

    @sweetener2535

    4 жыл бұрын

    Romeo Poomore Jshdjej that was adorable 😂

  • @ToTiredToDealWithThis
    @ToTiredToDealWithThis2 жыл бұрын

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

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    @kyleliebenberg71692 жыл бұрын

    I genuinely love you

  • @tristanorarson3069
    @tristanorarson30694 жыл бұрын

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

  • @Bredkid96
    @Bredkid964 ай бұрын

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

  • @admoto04
    @admoto043 жыл бұрын

    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

  • @MoHeartVlogs
    @MoHeartVlogs2 жыл бұрын

    Thanks you soo much for your help :) Your video really helped me

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    @asif72403 жыл бұрын

    This man is a legend

  • @she2787
    @she27872 жыл бұрын

    You are saving the world!!!

  • @Study-ASMR
    @Study-ASMR2 жыл бұрын

    Thank you so much for saving my grade!!

  • @user-tj9qz5ec1f
    @user-tj9qz5ec1f2 жыл бұрын

    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! :)

  • @ellibott._.2334
    @ellibott._.23342 жыл бұрын

    This helped so much thank you

  • @stickmanbattle997
    @stickmanbattle9973 жыл бұрын

    Thank you sm , my self study pre cal is consistent

  • @poelow2178
    @poelow21784 жыл бұрын

    Again, thank you very much. I really appreciate the videos you’re making. It really helped a lot😄.

  • @alexalopez4904
    @alexalopez49042 жыл бұрын

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

  • @sanopann1896

    @sanopann1896

    Жыл бұрын

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

  • @yehiamohamed140
    @yehiamohamed1404 жыл бұрын

    Thanks for your effort

  • @beyondhumanity7025
    @beyondhumanity70255 ай бұрын

    This guy saved my math grade!!!

  • @JohnsonMaths
    @JohnsonMaths Жыл бұрын

    Really clarifies all our doubts

  • @nathaniel7813
    @nathaniel78134 ай бұрын

    helped me pass my unit exam with this thanks bro👍

  • @hiwotwesenseged6057
    @hiwotwesenseged60572 жыл бұрын

    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

    Жыл бұрын

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

  • @kylieb4722
    @kylieb47225 жыл бұрын

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

  • @minjekim7667
    @minjekim76674 жыл бұрын

    Thank you for helping me

  • @terrer7567
    @terrer7567 Жыл бұрын

    This video is amazing thank you

  • @mckennasuorsa6455
    @mckennasuorsa64555 жыл бұрын

    at 53:16 , shouldn't there be a bracket on 4.2 because it's touching? so it's be (-infi, 4,2]

  • @pa_u_los

    @pa_u_los

    4 жыл бұрын

    Yeah, and also it should be a bracket in the 23.8 i guess, as it where it's the last point until the limit with the asymptote. It would be R (-\infty, 4.2] U [23.8, \infty] The thing is that this guy obviously is not going to read the comments, and good comments like this one get dissapear behind all the shit comments like Oh my god tysm! or whatever other shit. So yeah. I hope I'm right; if not tell me so. Edit: I'm right, you can try yourself with WA (WolframAlpha) that's what I did.

  • @sanraii
    @sanraii4 ай бұрын

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

  • @Coreyahno
    @Coreyahno4 жыл бұрын

    Does anyone know if he has calculus 1 2 and 3 videos as well? I’m going to need those over the coming year!

  • @rowalynkeith.rilloraza
    @rowalynkeith.rilloraza Жыл бұрын

    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

  • @briannaorange9910
    @briannaorange99103 жыл бұрын

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

  • @levon2371
    @levon23714 жыл бұрын

    love your work

  • @aarushisaha5016
    @aarushisaha50162 жыл бұрын

    Thank you so muchhh!!!

  • @sanopann1896
    @sanopann1896 Жыл бұрын

    44:10 how about the y-intercept of the range should it be included

  • @tylerdelatorre8230
    @tylerdelatorre82303 жыл бұрын

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

  • @Johnsonhzs

    @Johnsonhzs

    Жыл бұрын

    Yup he didn't

  • @gtgaming47
    @gtgaming472 жыл бұрын

    god bless you . i have learned so much from you

  • @GolDVYT
    @GolDVYT3 жыл бұрын

    Urgent! How do I know if a graf has extremepoints? For example: x/(x-2)? If in supposed to draw this graph, how should I know not to waste time on derivating x/(x-2) and setting it equal to 0?

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