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

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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

Опубликовано:

14 янв 2017

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Комментарии : 614

@TheOrganicChemistryTutor 6 месяцев назад

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

@komartiketmusa8447 3 месяца назад

splendid!!

@gamingresumed1788 3 года назад

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 3 года назад

my hero

@whyareyougae6839 3 года назад

You dropped this king 👑

@pikatothechu4737 3 года назад

You're the MVP

3 года назад

love how gaming also has to do homework

@maitemookamedi1700 2 года назад

Thank you

@m.miller8011 5 лет назад

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

@rudyj8948 4 года назад

Literally same

@memes4themasses365 3 года назад

I’m with ya rn

@quinive9812 3 года назад

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

@No-dy3zk 3 года назад

I got to do this for Algebra 2.

@Jackripz 3 года назад

@@No-dy3zk same

@lunam11 3 года назад

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 3 года назад

How did you do??

@ashwinanand1465 2 года назад

@@Stunz L

@dissociating1703 2 года назад

@@ashwinanand1465 💀💀

@declanrodgers8004 2 года назад

orc

@maryyou556 Год назад

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

@ign0tium539 Год назад

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

@xrzenel_8072 Год назад

I feel that

@shanepotter6348 Год назад

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

@princewillanyagagligbo6890 10 месяцев назад

glazing

@MZZ745 9 месяцев назад

@@shanepotter6348I got 1 day💀

@kiriuzi7959 7 месяцев назад

lmao try a day or approx one hour @@shanepotter6348

@wormonastring8934 3 года назад

anyone else crying in math class? :)

@Fishfriend001 3 года назад

Yes🥲

@sondersiya 3 года назад

@@Fishfriend001 yes 😢

@yunosogasii6200 3 года назад

Yes🥲

@official_kea_rsa 3 года назад

Every day

@bruh-cb9dc 3 года назад

yes ma’am

@krappa1234 4 года назад

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 2 года назад

This is what I've been looking for thanks bro

@vladimirsheydorov3776 Год назад

thank you!

@juaquiqui-kun4333 Год назад

@@jeeves4490 and I've been looking for you

@WeirdJeans Месяц назад

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

@draglonconx7771 5 лет назад

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!

@skandasringari2370 4 месяца назад

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

@squareeyes5942 2 месяца назад

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

@skandasringari2370 2 месяца 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 Месяц назад

Me right now 🥲

@JacobMachenje Месяц назад

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

@BamlakMengistu-qf3zx 10 дней назад

Same here 😭

@ilovesquishys1 5 лет назад

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

@mannydefour4838 2 года назад

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 2 года назад

046

@liezlkho7179 5 лет назад

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 3 года назад

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

@iglo1209 4 года назад

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

@safteyhazard 4 года назад

what about 2020?

@iamgroot7684 3 года назад

This aged pretty well.

@iamgroot7684 3 года назад

But also not too well

@samisiddiqi5411 3 года назад

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

@frankiecott 3 года назад

@@samisiddiqi5411 that it did

@mehakahuja9372 Год назад

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 10 месяцев назад

Me too It should X not equal 1

@drowzZzy_ 10 месяцев назад

same thoughts

@superiorjr154 8 месяцев назад

You’re right.

@nerimaken482 6 месяцев назад

ok good i was confused 😭

@JoeSwick41 5 месяцев назад

thank you, i was thinking the same..

@isaiahwhitney8168 4 года назад

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 Год назад

how did that go?

@lolmetyuri 7 месяцев назад

@@aryanrayana8065he didn't make it😢😢

@alt_entwined5252 4 года назад

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.

@slowmusical1749 3 года назад

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

@chooju6149 3 года назад

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

@brownie7535 3 года назад

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

@ET_AM Год 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. 🙏🙏🙏🙏

@sink6874 9 месяцев назад

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

@jasonbourne7843 2 года назад

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 Год назад

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

@WeirdJeans Месяц назад

@@sanopann1896 12th ?

@marsextras9172 3 года назад

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

@sadijemelenica1575 Месяц назад

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

@deputy1968 2 года назад

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

@mescalormavideos7767 4 месяца назад

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

@mariahtrizzy4166 Год назад

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

@farmachook Год 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 🙌🙌🙌

@estajabartoskova2057 2 года назад

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

@jaineilsart1528 Год назад

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

@sczscz6021 4 года назад

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

@furaha7737 3 месяца назад

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

@earlhaywood4372 2 года назад

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

@sanopann1896 Год назад

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

@kasuyp 5 лет назад

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

@declanrodgers8004 2 года назад

@wilsonvinas5906 7 лет назад

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

@nboris31 6 лет назад

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

@itayikatiro3564 4 года назад

Yeah, I noticed that too

@Edgylime6797lowl 4 года назад

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

@pranavm.9513 4 года назад

he does it for free calm down

@fryPS 4 года назад

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

@sahiliqbal4447 5 месяцев назад

Relearning everything thanks for these videos!

@cazandralopez7580 3 года назад

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

@yasirabdifetah5739 2 года назад

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

@mohsenamini3297 4 года назад

Very great work JG, Always thank you.

@WhatAMessJada 4 года назад

thank u so much my math teacher could never

@meritu985 3 года назад

You are the best thing that has ever happened to us

@IWApost 2 года назад

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

@saarazart1291 6 лет назад

Thank you so much!! You are the best.

@Bredkid96 3 месяца назад

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

@robroineodingal5921 3 года назад

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

@GabrielSanchez-rh6lv 2 года назад

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

@sanopann1896 Год назад

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

@GabrielSanchez-rh6lv Год 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.

@sanya5538 6 лет назад

Thank you for taking your time to explain this wonderful video

@betterlsun4068 2 года назад

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 2 года назад

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

@cotyb5028 2 года назад

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

@timeelapse619 2 года назад

Phew I thought I missed something

@soramin7926 2 года назад

Thx it confused me a little bit lol

@paulmaggiar8274 Год назад

@@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.

@betterlsun4068 2 года назад

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

@modesterdeene2428 4 года назад

I really appreciate you. I'm learning a lot

@caylylikessweets8594 3 года назад

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

@niburu4427 3 года назад

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

@nathaniel7813 3 месяца назад

helped me pass my unit exam with this thanks bro👍

@user-tj9qz5ec1f 2 года назад

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! :)

@ianjustus324 2 года назад

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

@kylieb4722 5 лет назад

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

@princekangwa3232 3 года назад

this guy deserves a medal

@BrawlBearYT 3 месяца назад

This man has saved many lives

@Study-ASMR 2 года назад

Thank you so much for saving my grade!!

@she2787 2 года назад

You are saving the world!!!

@joeyopes6064 2 года назад

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😫

@saimaali843 5 лет назад

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

@youtubeweb3009 3 года назад

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

@WeirdJeans Месяц назад

@@youtubeweb3009use force

@beyondhumanity7025 5 месяцев назад

This guy saved my math grade!!!

@sanraii 3 месяца назад

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

@hiwotwesenseged6057 2 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 Год назад

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

@danielperezrosales8392 5 лет назад

thank you very much for making this video

@user-ny3dl1ju4e 4 года назад

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

@user-ny3dl1ju4e 4 года назад

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

@franklinchacon1824 5 лет назад

Thank you!!!! really helped.

@ToTiredToDealWithThis 2 года назад

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

@wesamzamzam8461 3 года назад

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

@poelow2178 4 года назад

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

@tristanorarson3069 4 года назад

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

@admoto04 3 года назад

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

@alexalopez4904 2 года назад

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

@sanopann1896 Год назад

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

@thebakingsquad9924 6 месяцев назад

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

@stickmanbattle997 3 года назад

Thank you sm , my self study pre cal is consistent

@kyleliebenberg7169 2 года назад

I genuinely love you

@JohnsonMaths Год назад

Really clarifies all our doubts

@asif7240 3 года назад

This man is a legend

@dolimwaki6484 4 года назад

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

@enickerson5 4 года назад

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

@MoHeartVlogs 2 года назад

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

@user-sl3eo3xn1p 3 года назад

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.

@yehiamohamed140 4 года назад

Thanks for your effort

@ellibott._.2334 2 года назад

This helped so much thank you

@sereneblossom2951 2 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

@briannaorange9910 3 года назад

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

@rowalynkeith.rilloraza Год назад

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

@alanarcherman7946 7 месяцев 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

@levon2371 3 года назад

love your work

@gtgaming47 2 года назад

god bless you . i have learned so much from you

@priscamwale9132 Год назад

You are awesome and genius 🔥🔥🔥

@terrer7567 Год назад

This video is amazing thank you

@minjekim7667 4 года назад

Thank you for helping me

@takeeoro2 2 месяца назад

Best teacher world thanks

@shame5669 2 года назад

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

@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 Год назад

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