Horizontal and Vertical Asymptotes - Slant / Oblique - Holes - Rational Function - Domain & Range

This math video tutorial shows you how to find the horizontal, vertical and slant / oblique asymptote of a rational function. This video is for students who might be taking algebra 1 or 2, precalculus or calculus in high school or those who might be taking college algebra in an university. This video contains plenty of notes, examples, and practice problems for you to master the concepts.
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

[@TheOrganicChemistryTutor]

Final Exams and Video Playlists: www.video-tutor.net/
Full-Length Videos & Worksheets: www.patreon.com/MathScienceTutor/collections
Functions and Graphs: th-cam.com/video/ZTEv8OnGaxo/w-d-xo.html
Transformations of Functions: th-cam.com/video/tyQLp6x-GoU/w-d-xo.html
Graphing Polynomial Functions: th-cam.com/video/rOOefdqMvtA/w-d-xo.html

[@ianraulguevara5446]

the fact that this was posted 10 days ago>> thanks for the dedication

[@Beanies-tf1sn]

Thank you❤

[@jin_cotl]

@@ianraulguevara5446bruh

[@swag-xn4rk]

how does this man know like every topic

[@swag-xn4rk]

NICHOLAS DZIEDZIC yea prob

[@jaleelbarnes7142]

I was thinking the same shit lmaoooo

[@RayxaxD]

med school probably

[@w00gedyb00gedy]

Being knowledgeable in many topic comes with hard work. But being able to explain it all as clearly and succinctly as he does, that’s a gift.

[@thatmst5791]

I think he takes extra tuitions after school 😂

[@phoebe9194]

dude you have a video for literally everything youre the reason im passing math and physics and passed chem last year

[@mathswithjosh8104]

hi you can learn more in this channel: th-cam.com/video/6veKRuZlKQo/w-d-xo.html

[@schrodingersgunna6390]

Chem tank

[@d.ori19]

Quite frankly you are the only reason I’m passing college

[@ath9558]

@George Godson we are learning it again and it comes up alot so :)

[@chufengxilin9869]

@George Godson when you reach college, your teacher will recall everything you learn

[@chufengxilin9869]

@George Godson its called applying what you learn or application.

[@carefull8365]

George Godson if u forget....

[@trevorbaker7168]

George Godson you relearn it in college bud

[@azoz8sultan]

whaat still searching youtube for math help.....

[@chrisashe9976]

Are the videos from 2006 really helping?

[@EtherealWorlds49]

Arent you tired of finding videos that arent getting you anywhere in math class

[@a6-stringsand4eyes51]

Does this day sound familiar? You go to a confusing lecture......

[@BookishAlexis]

Some teachers/professors suck at teaching.....

[@nilepluss644]

They dont know most math are one thousand year old and same

[@adamarzate1533]

I had to take a break to say that you are single-handedly the reason that I have hope that I can actually understand math now. sincerely thank you for your service!

[@dengosodawg]

25:18 for those just looking for help with slanted asymptotes. Also thanks for making this!

[@SameerKhan-zu2kj]

Thanks so much

[@alexzepeda6471]

ur a god for this lol tysm

[@patatespuresi1591]

king

[@arathi2501]

Thank you

[@pinecsne]

ty!!

[@anongamercatlover2196]

my dude you taught me more about algebra than any of my math teachers throughout high school combined, and u are the only reason I'm barely passing my college math class. I'm going to leave you everything in my will.

[@ronin4300]

Can I get some of that

[@cooper3220]

At 8:05 you stated that -1 + 7 = -6. You graphed it correctly but it should have been positive 6.

[@seanwells1672]

OHH thank god for clarifying - busting an all nighter trying to learn all this and that part made me thought I should sleep instead... Nonetheless, knocking that quiz out tomorrow thanks to this video.

[@saedisaga7860]

u are right, but thnks to the lecturer after Allah,

[@ibrahimshafi2064]

Ye however the graph would basically be the same sketch as positive 6 still below the horizontal asymptote (7)

[@myleneencina3045]

yah you're right

[@vanezzasutit5114]

I almost questioned everything I've ever known

[@antiquarian1773]

lol you cover every thing I do in class, and you teach it better than my professor who has a masters degree.

[@ahmadsa5601]

Joshua The Science god Trueee

[@TheDaniellouis]

Doesn't it bother you guys that professors don't need to have PhD's or be PhD candidates at the very least?

[@swellingbeats8876]

Daniel Louis why need a PhD if that’s what there doing

[@yenaju6309]

why is his voice soothing like it doesnt annoy me that im doing math bc his voice is really nice and calm to listen to

[@mya8254]

Litterally thirty minutes before a test I found this, dude this was so helpful

[@harmanjotsingh4230]

Same here studying half hour b4 midterms

[@garybuttherissilent5896]

fools

[@Cartoonandanimelove1]

Thank you SO much. The only reason I'm passing my STEM classes. Professors in college can't teach for their life lol. You make things so simple and straight forward. And you speak clearly too. I've been watching all your videos.

[@bjap1563]

Faculty nowadays are like your typical company employee. No difference like you should figure it out on your own. And then they will take credit on your good performance.

[@frosting_flakes]

sound slike you have a littke bit of a freaking crush lol big nerd momemnt coming freom you lamo lmfao idiottt!!!!!!!!!!!!!!!!!!!

[@aseeljust7886]

I don’t know why I have to pay to college🙃
You are the greatest teacher I have ever know god bless you ❤️😍

[@arjunb.singhal7308]

I love how you teach by doing increasingly challenging examples. Keep up the great videos!

[@Chris-ni6pv]

The best, most concise teacher on youtube. Thank you for your service 100

[@Chris-ni6pv]

no cap

[@khaniesmakeuptutorials8649]

I love how you go through with unique examples not the easy ones so we can truly understand! I love your videos I will donate to you when i have money thank you for educating everyone ❤

[@gracemelanson5271]

you just made me understand 2 weeks of work in 30 minutes. that’s insane!! thank you!

[@mylesken6122]

Explanations to find vertical and horizontal asymptotes as well as slant asymptotes are clear and understandable. Thank you.

[@andrewmanzano4792]

I'm taking my pre-calculus final today for my first college class ever! You have been SO helpful! I'm going to find a way to support you. You are simply amazing. Thank you so so much!!!

[@zunnurmaisarahshahzalli5000]

Thanks Sir ! You have helped lots of students from all around the world!
Learning this in the 2nd chapter of Further Pure Maths 1 ALevel.

[@panutdachasombat4599]

I'm a third year accounting student in Thailand , don't know why but i have to enrol the General Mathemetics1 subject. I had drop this subject at second year but to graduate I have to pass this subject anyway. Im so stupid at Math and don't have a good basic unlike other student in the class, they all so good. On the other hand I have no idea what the teacher talk about especially Asymtote things so i go to ask teacher but he explain me like I'm a genius of mathematics so i decided to learn by myself, i search video youtube that teaching about the asymtote things in Thai but still don't get it, so I have last choice it is your video which is in English. I'm afraid that I might not get it but amazingly I get it because you taught so clear and so easy to understand. THANK YOU SO MUCH FOR UPLOADING you can (my goal is to don't get F)
p.s. I will update the exam score later.

[@hannahhighway2368]

Panutda Chasombat I want to know how your exam went:)

[@prequelanimations539]

@@hannahhighway2368 same

[@therichestgamer9033]

I love you so much man! you explain what my calc teacher can't and you do in in less then an hour, you are so awesome!

[@obl.aep_]

Ur legit the man. Thank you sooo much for helping me with this stuff. U clear up all of my questions and u help me sleep knowing that if i ever fail to remember this ull be there. So once again i thank u.

[@gwynethegomez7805]

I just learned 2 weeks worth of college lecture in 30 minutes. This guy saved me :') Thank you

[@layeng251]

dude same

[@quasarki8917]

I'm doing this in 11th grade😭😭

[@randommonkey4900]

@@quasarki8917 same

[@doctorcrew2388]

@@quasarki8917 10th for me!

[@sorfina2001]

Im taking Maths HL approaches and application for IB. This is really helpful thank youuu

[@progodspeed2311]

You are the master! You have earned a new follower; nay, a new disciple! Thanks JG!

[@mooshuthefatcat3217]

Currently you sir are carrying me through my college pre calc class. I can’t understand math when it’s explained in words on a paper for some reason. So thanks!

[@andrewsmanifest9201]

YESTERDAY my lecturer was teaching it like it was quantum physics but man you made it look like binary operations

[@madz3405]

it makes so much sense now!! Thank you for this!

[@knifewifeTM]

without fail, i always end up at your channel to try to make sense of my math, and without fail, you explain it. thanks so much!

[@ridewithkay]

You r a live saver man u reminded me how to do long division, synthetic, partial fractions etc tq so much man

[@idc20627]

Crazy how these videos are already 7 years old, and I find myself going back after changing majors, wowserz

[@babynaturallia7678]

Your a great teacher. I understand the topics better when I come here but tbh I also think I'm addicted to your voice. Very soothing.

[@butterbear934]

I am reviewing for my entrance exam for college and you are helping me a lot. Thank you so much for existing

[@hannahhighway2368]

BLESS YOUR SOUL. Gots a quiz tmrw and my teacher was busy talking bout video games when I needed help.

[@renewd]

For the 2nd example, y = 1/(x + 2) + 7, I had never tried to graph a rational expression with a constant added to it. I went ahead and rewrote it as y = (7x + 15)/(x + 2) using a common denominator, and then found the horizontal asymptote to be 7x/x = 7/1 = 7, so y = 7. It was interesting to know that it is the same as y = 0 shifted up 7.

[@amanchoudhary756]

Ya it's quite beautiful

[@carterbaldwin4091]

This saved my ass it's my teachers first year teaching this in high school and hes still getting the hang of teaching this stuff

[@marcui_louie]

Ok, I finally understood this theme. I'll try practice problems on my own later, but I think I understood.
Thank you very much!

[@caseyemory5211]

thank you so much for all your videos and expertise!

[@JamesBrodski]

Great video once again! Thank you for making it.

[@kidusbahiru4369]

Thank you. This helped me to prepare my lesson plan

[@dearbrandee]

Excellent video! I learned a lot

[@areejkadhem9234]

Hello, I would like to thank you a lot for your great educational vedios. You can not imagine the amount of help that you offer to us everyday. To whom are seeking knowledge. Wish you all the best.

[@areejkadhem9234]

I have a question, if you kindly answer it, that would be much appreciated.
Q, A circle is divided into 12 equal triangles. Each triangle has same size, the diameter=16 inches. Find the coordinate of a point E on the circle.

[@bruhmomentum9884]

thank you! you have no idea how much this helped me

[@biseraciric454]

Thank you so much for your work.. You helped many, including me. Bravo 👏🏻👏🏻

[@joestunna4887]

I appreciate for your lectures dude I always depend on you 🙏

[@princesspeach8728]

Thank you for a this! You’re awesome!

[@lynhartmoon1914]

Thank you very much
Thank you for the video, easily understandable and would recommend it as teaching material for those who wants to understand the topic.

[@user-xc8rv5vy8n]

Thank you. These videos helped me to pass Maths and Chemistry in my varsity. You explain it simple and that is really helping because after the end of the video, I can relate my notes to your videos easily.

[@princeali4080]

We owe you a lot! Amazing teacher! At 8:05 you stated that -1 + 7 = -6. You graphed it correctly but it should have been positive 6.

[@bethelmesfin5301]

correct.1/-1+7+6,its like a/b+c/d=ad+bc/bd.we use it to make the denominator the same inorder to - or +.I know 🤯 but,try to use some numbers,

[@mark760]

@@bethelmesfin5301 so thats how it works

[@AL-xg8vx]

You are an actual god send, thank you! Your videos make so much sense

[@Triadow]

Thank you so much oh my gosh it's like 11 at night and I just wanna go to bed and this is sooo helpful I can't thank you enough these kind of tutorials save my sanity

[@Hdhugeo234]

great video but you should consider when the graph is able to cross the HA since the graph of a rational function can have a hole but it does not have to pass through it.

[@rizkimaulana7331]

this video really helps me. thanks!

[@nathaliebarrera9213]

this man has saved my life , mad respect for you !

[@swiggityswoner4281]

you're the best i have a final tomorrow you saved my life

[@user-qb7nh9up3s]

Very good,,
I never knew if I could find anyone to explain like that .

[@GabrielRodriguez-fp5gw]

Your videos are the best, thanks to you I didnt fail AP Physics and understading AP Calculus is easy

[@adeenaM6816]

You just know everything. You are the only teacher who is very very talented! I only watch your lecture

[@randommonkey4900]

not even done watching this but this has helped already a ton tysm for all these videos their life savers

[@jackal3578]

Such a great review!

[@shihaburrahmansamrat9453]

Thanks, helped me a lot.

[@melanieann4614]

This helped me so much!!

[@geovanyl.3354]

You are a serious great teacher man.

[@lemuelcastillano7913]

Hi! can i attach the
youtube link of your video to the self-learning modules of our department in
order for the students to learn more from the contents of this video aside from
the modules that will be distributed to them? Thanks a lot.

[@cupcakes4100]

I'm gonna be a champion some day if I keep watching you videos🤔
Thank you😂🎁 you don't know how much you're helping us

[@oliviab8275]

Life saver. Thank you.

[@CNM3]

You're a great teacher!

[@YousefHaidary]

Great work, thank you

[@emilytruax3487]

I love you. Thank you so much for all of this information

[@lamedev1342]

If anyone got confused at 13:30 you can just do -18/4 and you will still get -4.5, he just broke the fraction down.

[@nicolel9587]

god this saved my damn life!!!thank you so much for uploading the videos

[@Bubber_Bear]

It took you 3 minutes of video to explain what a textbook couldn't do in 2 hours of reading. Thank god for you.

[@rexrender4095]

THANK YOU A VERY SMALL PORTION OF THIS WAS REQUIRED TO DO SOME OF THE TRICKY GRAPH QUESTIONS ON THE SAT

[@huiyenlo2461]

at the time 22:51 -- I calculated the zeros x= -1/2 however you plot the curve touching around 1.5 as a zero. I just wanted to check if you were doing the rough sketch or I was calculating it wrong on Zeros for this problem. Thanks advance.

[@zenikbeatz8373]

you are the best tutor ever GOD bless you

[@tony43934]

Man I just want you to know that I love your vids. You explained in 30 minutes what my professor took 2 hours to fail to explain.

[@LU-dm7kj]

great tutorial. thank you very much :)

[@foursquin]

this was so helpful. thx

[@jett6865]

EXAM TODAY; thanks for the help 💯👍

[@giemar8307]

thank you so much Sir... you help a lot of students

[@Aldream]

This is my whole lesson in my math lol, thanks

[@kifter4254]

Thank you so much

[@hey_there_tigger3736]

You just helped me out more then me actual teacher

[@ariaahmed3130]

Assalamualaikum. For 15:42 how should we know when to get the x and y intercept or just take x as -1 like the previous questions ?
thank you

[@garybuttherissilent5896]

AssalamualaikumAssalamualaikumAssalamualaikumAssalamualaikumAssalamualaikumAssalamualaikumAssalamualaikumAssalamualaikumAssalamualaikumAssalamualaikumAssalamualaikumAssalamualaikumAssalamualaikumAssalamualaikumAssalamualaikumAssalamualaikumAssalamualaikumAssalamualaikumAssalamualaikumAssalamualaikumAssalamualaikumAssalamualaikumAssalamualaikumAssalamualaikumAssalamualaikumAssalamualaikumAssalamualaikumAssalamualaikumAssalamualaikumAssalamualaikumAssalamualaikumAssalamualaikumAssalamualaikumAssalamualaikumAssalamualaikumAssalamualaikumAssalamualaikumAssalamualaikumAssalamualaikumAssalamualaikumAssalamualaikumAssalamualaikumAssalamualaikumAssalamualaikumAssalamualaikumAssalamualaikumAssalamualaikumAssalamualaikumAssalamualaikumAssalamualaikumAssalamualaikumAssalamualaikumAssalamualaikumAssalamualaikumAssalamualaikumAssalamualaikum

[@teamjuanelias]

My man! Makes perfect sense !

[@leenjundi3811]

i literally love u ty for everything

[@leonardbairagee2849]

Awesome vid, really helped me understand better than my teacher

[@user-bv8my1op6f]

This guy literally knows everything

[@Marv-Cow]

❤❤❤❤ i am learning a lot in your videos. Very imformative

[@harmanjotsingh4230]

Last hour studying before precalc midterms in social distances learning.

[@astrobear1236]

Im taking precal soon and brushing up with his videos

[@sarujanrupan4831]

You're actually such a great teacher.

[@etienne7930]

He is indeed

[@annasnotabanana]

I’m so grateful for these tutorials, I’d be doing soo much worse in college algebra right now if it weren’t for you 🙏🏼

[@danaomarkjhonm.3308]

this is helpful especially today where students can' go to school due to this pandemic

[@mrgatogris8863]

Dude you are the best !

[@ruhamabehailu4483]

you are a life savior thank you

[@fuego786]

question, if i have a polynomial, not in a fraction, how should i do this? denominator 1? example: -2x(x+3)^2

[@milknight5181]

this saved me, thank you

[@mirahamdan7369]

thank youuuuu i already know this is gold :)))