Horizontal Asymptotes and Slant Asymptotes of Rational Functions

This algebra video tutorial explains how to identify the horizontal asymptotes and slant asymptotes of rational functions by comparing the degree of the numerator with the degree of the denominator of the rational expression. The equation of the slant asymptote can be determine using long division if the degree of the numerator exceeds the degree of the denominator by exactly 1. This algebra video tutorial contains plenty of examples and practice problems.
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: 248

  • @TheOrganicChemistryTutor
    @TheOrganicChemistryTutor Жыл бұрын

    Final Exams and Video Playlists: www.video-tutor.net/ Next Video: kzread.info/dash/bejne/lIuKytmSlLbUls4.html

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    @haji-koto9765

    Жыл бұрын

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    @Gregory-the-small4 жыл бұрын

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    @SeanElliottH

    3 жыл бұрын

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    3 жыл бұрын

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    3 жыл бұрын

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    @The_jezeb3l

    3 жыл бұрын

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    @taysonm11

    3 жыл бұрын

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    @Kaininjagofan3 жыл бұрын

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    @nightandday7704

    2 жыл бұрын

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    @leviloverweirdo7713

    2 жыл бұрын

    @@nightandday7704 the go over it in pre-calc too

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    @brianjohnson7513

    Жыл бұрын

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    @im_diabetic2112

    Жыл бұрын

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    @urmomma3646

    Жыл бұрын

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    @handleDeezNu...3 жыл бұрын

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    @donphillips1276

    3 жыл бұрын

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    @The_jezeb3l

    3 жыл бұрын

    tenure this is when school sign contracts with teacher pretty much guarantees them a job for life no matter what. That's why when you get a bad teacher most of the time they get away with it. Even if they are so bad and the school decides to fire them the school has to go through a complicated process that can last at least a year or longer. Chances of a teacher getting fired is 1 in 2000 compared to a doctor which is 1 in 57. The American public school system sucks. We need more teachers like this dude.

  • @yoshy5651

    @yoshy5651

    2 жыл бұрын

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  • @vincentkouros5305

    @vincentkouros5305

    2 жыл бұрын

    @@yoshy5651 Idk where you live, but in NY, where the teachers union is strong, tenure is pretty common.

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    @yoshy5651

    2 жыл бұрын

    @@vincentkouros5305 CT

  • @ConservativeHippie001
    @ConservativeHippie0012 жыл бұрын

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    @danishmobeen73964 жыл бұрын

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  • @pigsonwings
    @pigsonwings3 жыл бұрын

    was gonna say i didn’t understand the long division part then i watched his video explaining how to do them and now this video is so easy to understand. guy’s a genius

  • @whipzy4301

    @whipzy4301

    4 ай бұрын

    very late reply but there is a quicker way called synthetic division, when you're dividing by those trinomials with a binomial it makes it so much easier.

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    @xenonmanaay11502 жыл бұрын

    you're the reason why I'm starting to love math☀️

  • @georgesadler7830
    @georgesadler78302 жыл бұрын

    MR. Organic Chemistry tutor ,thank you for a well explained and solid analysis of Horizontal and Slant Asymptotes in precalculus.

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    @daughtersofsparda4 жыл бұрын

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    @_empty_4945

    3 жыл бұрын

    Question of the century

  • @The_jezeb3l

    @The_jezeb3l

    3 жыл бұрын

    tenure this is when school sign contracts with teacher pretty much guarantees them a job for life no matter what. That's why when you get a bad teacher most of the time they get away with it. Even if they are so bad and the school decides to fire them the school has to go through a complicated process that can last at least a year or longer. Chances of a teacher getting fired is 1 in 2000 compared to a doctor which is 1 in 57. The American public school system sucks. We need more teachers like this dude.

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    @metiguda4733 жыл бұрын

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    @cecilion4909

    3 жыл бұрын

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    @metiguda473

    3 жыл бұрын

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    @ethanalbrecht8395

    10 ай бұрын

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    @dakshitakothari68352 жыл бұрын

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  • @nejcocepek8357
    @nejcocepek83575 ай бұрын

    in the first case of slant asymptote the asymptote does not exist since the remainder of long division is zero and if we cancel out the terms we see that we get linear function with equation y = x + 2 with a missing point at x = -3 which lies on the asymptote and that contradicts with the definition of an asymptote

  • @ad-np8ko

    @ad-np8ko

    Ай бұрын

    exactly i was confused on why he said it was slant

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    @fridamoreno96892 жыл бұрын

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    @yiktingcheuk99862 жыл бұрын

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    @EstherAhiableEyram2 ай бұрын

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  • @jackwilson4324
    @jackwilson43245 жыл бұрын

    I'm talking about: x^2+5x+6/X+3, but algebraic long division is probably something to get marks in the exam, rather than factoring, both ways are not that hard, after you explained them.

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    @nirvanakitty10073 жыл бұрын

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  • @brakk7117
    @brakk71172 жыл бұрын

    its amazing how you didnt stretch this into an 80 minute lesson for absolutely no reason!

  • @tmthyaj
    @tmthyaj5 жыл бұрын

    10:01 lmao i thought it was (7x-y) + y but the y was actually 4 😂 anyways great video man!

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    @dr.jenkem75742 жыл бұрын

    Exactly what I was looking for!

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    @user-uj9hf8ht5q Жыл бұрын

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    @lackability60005 ай бұрын

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    @mlh69972 жыл бұрын

    Thank you soo muuch for the beatiful meaningful explanation! We love you.

  • @AceOfHearts001
    @AceOfHearts001 Жыл бұрын

    Really useful, thank you so much!

  • @qazwad2772
    @qazwad27724 ай бұрын

    thank you, TheOrganicChemistryTutor for making my and millions of others lives easier when it comes to our studies.

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    @abdullahalajeel4801 Жыл бұрын

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    @brandenvlogs1018 ай бұрын

    Thank you so much I have an exam coming up for pre calc and this low key confused me until u explained

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    @mantuli_ka1 Жыл бұрын

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  • @jaytzy9858
    @jaytzy985811 ай бұрын

    Straight to the point Btw thanks bro

  • @jackwilson4324
    @jackwilson43245 жыл бұрын

    Great videos, and for the question with the O.A you could have factored.

  • @honeymnkrl
    @honeymnkrl2 жыл бұрын

    Dudeeeee this is so easy with youuu

  • @villanueva778
    @villanueva7784 жыл бұрын

    I wish we learnED this!

  • @barrym5310
    @barrym5310 Жыл бұрын

    By the way, synthetic division can be used to find the asymptote, although it might be easier to use polynomial long division in certain situations.

  • @daniaalsadi7208

    @daniaalsadi7208

    11 ай бұрын

    Is synthetic devision the same as long division?

  • @sauffle

    @sauffle

    10 ай бұрын

    @@daniaalsadi7208 you end up getting the same answer in both but the way you get that answer is little different.

  • @qarashuaq

    @qarashuaq

    10 ай бұрын

    imo synthetic division is more convenient to use

  • @rohanmarde9303
    @rohanmarde93033 жыл бұрын

    thank you very much for this video man.

  • @taiedy
    @taiedy4 жыл бұрын

    Sorry, how can there be a slant asymptote if the equation at 5:20 factors cleanly into [x+2] without a remainder? Shouldn't there be a slant asymptote only if it leaves a remainder?

  • @headyshotta5777

    @headyshotta5777

    4 жыл бұрын

    yes i think youre right, he made a mistake

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    @user-qu4qc5dt2u Жыл бұрын

    Favorite teacher

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    @sonoresmore3 жыл бұрын

    this dude is the only real math teacher

  • @hanifqureshi823
    @hanifqureshi8234 жыл бұрын

    Very good explanation.

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    @marrymemyeonginlee31172 жыл бұрын

    The only teacher who literally use a BLACKBOARD thank youuu you helped me a lot 😭❤️

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    @mccadewaite6057 Жыл бұрын

    I will protect you at all costs, thank you for getting me through class

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    @rafiulislamatanu1472 жыл бұрын

    Amazing explain...

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    @yvettehernandez9038 Жыл бұрын

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  • @jamesforteza5142
    @jamesforteza51422 жыл бұрын

    Y=(x²-3x+4)/(x²-6x+8) Y=1 is the horizontal asymptote but when you graph it it is only applicable on the right side of the graph but when you extend the line y=1 to the left it will intersect the graph of the given rational equation.

  • @fundamentalsofphysicsnmath4306
    @fundamentalsofphysicsnmath43062 жыл бұрын

    Thanks for such a nice explanation. Love you from India......

  • @tlhomotsemoteme2423
    @tlhomotsemoteme24235 жыл бұрын

    Thank you... again.

  • @frankketzman7245
    @frankketzman72454 жыл бұрын

    Great lessons sir, I learn a lot of you ! Thank you very mutch

  • @noahmiller794
    @noahmiller7942 жыл бұрын

    you have taught me more math in 6 minutes than my entire last semester of school

  • @danichang2700
    @danichang27003 жыл бұрын

    THANK YOU 💚👀✨ I didn't understand how to find Slant asymptote, but I'll understand I watched this video twice, and now I better understand how to find slant asymptote :з)

  • @EstherAhiableEyram
    @EstherAhiableEyram2 ай бұрын

    I really like watching math videos by this man

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    @pankajamin24210 ай бұрын

    Bro thank you so much u saved my exam 💯

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    @syntax19718 ай бұрын

    Ingl you are saving my life every single day i have precalc class

  • @noeldiaz1354
    @noeldiaz13543 жыл бұрын

    its easy to remember if u think like this... Think the rational expression as a building if its top heavy just by one it will collapse but not desintagrate resulting in a oblique line if its top heavy by more than one it will collapse and desintagrate, theres no line! if its bottom heavy well the building its on the floor as it should be, y=0 if top and bottom are equally heavy, then divide those bad boys

  • @urmom8565

    @urmom8565

    3 жыл бұрын

    omg... this is genius thank you

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    @narphaloe6465

    3 жыл бұрын

    This is actually so smart thanks!

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    @heleenghafour78472 жыл бұрын

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  • @SarwatSherazi
    @SarwatSherazi8 ай бұрын

    Amazing sir❤

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    @Sarah-ih1pj3 жыл бұрын

    super expensive college textbooks are pretty much useless when free youtube is here. thank you.

  • @Life_forms
    @Life_forms7 ай бұрын

    My appreciation sir❤

  • @fatsow3639
    @fatsow36394 жыл бұрын

    I humbly thank you.

  • @sonjahenderson1390
    @sonjahenderson139011 ай бұрын

    Im confused about if these rules ALWAYS apply. For instance take (5x + 1) / (x^2 - x - 1) and graph it in the graphing calculator. There appears to be a horizontal asymptote at y = 0. However there is a vertical like that strikes through y = 0 in between 2 other lines in the function. Does the horizontal asymptote still apply?? Do these set of rules apply no matter what? If anyone could help that would be wonderful!! Thank you

  • @tanujakumar3411
    @tanujakumar34117 ай бұрын

    I hv exam of calculus on 21 dec, well this sir is gonna help me so much, u teach so well , i only have watched 2videos of yours and i feel like i will pass onlye because of you sir ,thank you 🤞✨

  • @silverdove9911
    @silverdove99113 жыл бұрын

    This man is saving me in precalc

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    @haleighgrace806

    3 жыл бұрын

    SAME

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    @barbarawrakonei7354 Жыл бұрын

    So helpful to me

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    @mirzafarhan99322 жыл бұрын

    Broooo he made it look so easy

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    @joaquinvargas97026 жыл бұрын

    You came through brother! Thanks!

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    @mtycoder

    6 жыл бұрын

    he was sick or something?

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    @mim0735 жыл бұрын

    Link to previous video please

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    @coreyhaimeditz95974 жыл бұрын

    You teach this way better than my math teacher😂

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    @shadon_official25105 жыл бұрын

    Thank you so much

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    @calisthenicsguy05183 жыл бұрын

    Damn,U helped me alot bro

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    @farihaislamefa42633 жыл бұрын

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    @yonathanabuhay1977 ай бұрын

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    @LS-dx9gu3 жыл бұрын

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    @unknownman15923 жыл бұрын

    You are a legend

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    @ahmedmansaray-sz8eu Жыл бұрын

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    @suhailasaupi45055 жыл бұрын

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    @maxinem4423 жыл бұрын

    Thank you so much good sir

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    @kcpahuyo457 Жыл бұрын

    thankyou very much

  • @mr.9754
    @mr.97544 жыл бұрын

    The other oblique asymptote is good, but I think it's best to write out the full answer (kind of like a mixed number). The rational function, after long division, equals 2x + (-16x+6)/(xx+4). Then analyze as x approaches infinity....(-16x+6)/(xx+4) will approach zero....ie leaving y=2x as the oblique asymptote.

  • @migzwrld909
    @migzwrld9093 жыл бұрын

    Thank you!

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    @joseflores2893 жыл бұрын

    The best right here for a fact

  • @bobu5213
    @bobu52132 жыл бұрын

    is there a way to rationally calculate these without knowing any tricks like "If the degree is the same devide the coefficients". I want to know how to look at a function and see in my head where the asymptotes would be

  • @Dee_alh
    @Dee_alh4 жыл бұрын

    Thank you 👍🏼👍🏼👍🏼👍🏼

  • @user-zr1li2ni4v
    @user-zr1li2ni4v9 ай бұрын

    Thank you

  • @the_br0wnie294
    @the_br0wnie2948 күн бұрын

    Comment for engagement You’re better than my college professor Appreciate it homie

  • @idkwhysojustcallmeshiro1147
    @idkwhysojustcallmeshiro11478 ай бұрын

    THANKYOU

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    @raprap04catahay602 жыл бұрын

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    @archangbriel3 жыл бұрын

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    @kennedylynn21123 жыл бұрын

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    @mickanton72852 жыл бұрын

    come and teach our university professors please, they definitely need you

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    @xoreh15372 жыл бұрын

    I really fucking love man, you have no idea how much help and hope you give people like me!

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    @annieshikupa41453 жыл бұрын

    Thank you😄😄