Horizontal Asymptotes of Rational Equations

[@persied8670]

As a 9th-grade student, reading this in my textbook was very confusing, but this video made it very easy to understand.

[@profrobbob]

I am so happy to know this lesson helped. There are over 660 more math lessons to watch organized by subject and chapter at www.profrobbob.com Together we will earn that A! BAM💥

[@Jeffreyfrmn]

You are the best math teacher I have ever had... You are helping me through college and I cant thank you enough!

[@profrobbob]

You're very welcome and THANK YOU for the compliment Jeffrey Freeman and thanks for liking, subbing and choosing #ProfRobBob to be your KZbin math teacher...I'm glad you are finding my channel so helpful! I also hope that means you are sharing my channel and your learning experience with EVERYONE you meet at college, even the teachers:D And please remind them to like, SUBSCRIBE, share thru social media and keep spreading the word to help this free educational channel continue to groW and remain free to help more students like you...BAM!!! We can't groW without the support of our subscribers:(

[@rache1sc123]

Your algebra and limits explanation of the three rules for horizontal asymptotes finally helped me understand how the rules were derived. Thank you!

[@profrobbob]

+Rachel C. glad I could help! ...and thanks for choosing my channel to learn from, like and sub to. Please keep spreading the word:D

[@profrobbob]

You're welcome!! And thank you for subscribing and taking the time to let me know how helpful you found my videos. They take alot of time in addition to my full time teaching job and its nice to hear that my time is well spent:) Good luck with your precalc class...now BAM!...let me know when you pass with that "A"!

[@xSazakura]

Mr Tarrou, I've been struggling in math every morning in my precal 12 class and ever since i've stumbled upon your channel, math has gotten easier because of your thorough and clear explanations! Thank you so much!!

[@GabrielaaCOLOMBIANA]

Thank you so much! Your method of teaching , makes me love mathematics even more! Fantastic Job, your students should be happy & proud to have a teacher like yourself!

[@profrobbob]

The limit as x approaches 3 equally infinity says that you have a vertical asymptote at 3. You just need to do a t-table to fill in any additional points you need to sketch the graph:)

[@profrobbob]

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[@profrobbob]

First, THANK YOU Jonathan Soto for serving our country and secondly, you're welcome and thanks for the awesome testimonial and taking the time to "thank the teacher"! I'm glad you have found my channel so helpful and hope you will continue to share your experience with other students looking for FREE math help...BAM!!!

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You are so welcome...and thank you for seeking out extra help and choosing my video to watch! I hope you will continue to choose my channel first when you need that extra help:)...and please share:D

[@paakwesi1750]

Mr.Tarrou you make math very easy to understand...I had no idea what was going on in my class since we got to this chapter but after I watched your video everything makes sense.... Thank you so much

[@profrobbob]

Thank you for your continued support and taking the time to send a comment. My writing skills come from learning calligraphy and enjoying what you do for a living because of students like yourself make my job worth it and taking the time to do these videos as well:) Thanks again.

[@yousuf53dx]

you're entire series of asymptotes is amazing! I was dumbfounded by them, but you're explanation and no nonsense videos are a blessing!

[@profrobbob]

Thanks for taking the time to study! Please sub and share this free resource with your teacher and classmates too:D

[@profrobbob]

If the degree of the numerator is one larger than the denominator you do long division to find the slant asymptote.

[@ericnelson2679]

you making mathematics very easy Prof,i hope the matric teachers learners can make use of your videos to improve the standard of the subject in our country. Thank you once again

[@profrobbob]

eric nelson you're welcome. Thanks for watching and please share my channel with all those teachers, and friends and remind everyone to like, subscribe, support the ads and keep sharing with others to help keep these free educational channels growing and remain free:D

[@profrobbob]

That is AWESOME! I am glad I could help, but you did all the work. GREAT JOB...and thanks for letting me know how great you did:D

[@shaniyawordsworth7800]

I just watched your vertical asym. Video also. And I have to say OMG THANK YOU SO MUCH! I had no idea what was going on in class. And I couldn't understand our homework. Watching the two videos helped me soooo much! Thank you!

[@profrobbob]

I have a video Determining Domain of Functions. As far as Range, I believe it is best to graph the function before determining the Range. I apologize for the very late response.

[@profrobbob]

Well, THANK YOU loyal subscriber for continuing to watch and comment! This is like a second job for me now but the rewards from viewers like yourself remind me daily why I continue...to help others (and the coolest part is that I'm helping them all over the world:) I really appreciate your continued support and please don't forget, "you" can help me grow by sharing my channel with others:D

[@georgesadler7830]

Professor RobBob ,thank you for an awesome introduction to Horizontal Asymptotes of Rational Equations. This material is very helpful for students moving on to Calculus One and beyond.

[@profrobbob]

Thank you saying this is a Precalculus class. I like to give a complete introduction, and not just do some examples, like I do for my actually classes. This makes many on my videos long, but hopefully leave you fully understanding the concepts.

[@aulani41ja]

Much Mahalo! I have been stuck in figuring out my homework in MathLab. You have been helping me along the way. I am so grateful!!!!

[@profrobbob]

I am very grateful you are watching!!! I am honored I can help you understand your math homework better. I hope you pass your class with flying colors:)

[@profrobbob]

THANKS...and I appreciate the support of watching, liking and subscribing! I'm your KZbin teacher now...and you can choose any one of my 435 videos to watch whenever you feel like learning more math:) It's the next best thing to being there:D

[@profrobbob]

I've succeeded...math and fun in the same sentence...one of my goals is to share with students that math doesn't have to be such a dreaded subject to learn, and that you "can" have fun while learning:) THANKS for sharing, liking & subscribing and please tell all your friends to do the same!

[@NextLevelTrickShots304]

Wow, not sure what my pre-calc teacher was trying to teach me but your videos helped me understand the concept in a simplistic way. Thanks Rob!

[@profrobbob]

You're welcome...sounds like the perfect time to share this channel with your teacher when school starts again and don't forget to like and subscribe to help us keep growing and helping others!!!

[@bongwizard666]

It is amazing to me that I have learned so much in watching a few of your 13-15 minute videos when my professor fails to do such in weeks of 2 hour classes... I almost want to show her these, not out of disrespect but because she needs it.

[@profrobbob]

Thank you Taylor for taking the time to "Thank a Teacher" and watch my channel. As a teacher myself, I am always open to learn new ways to teach a lesson or hear another teachers point of view. Maybe you could share with her that while studying you found a channel that is supplementing her teaching and how hearing things taught differently has been helpful. Then you could share the channel with her in case she has other students looking for after hours help. I already have a lot of teachers using my channel for just that:)

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woah no one explains math better than you! you just earned a subscriber :) thank you for the videos

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you have the nicest writing skills for a math teacher! thanks for taking your time to make these vids :)

[@profrobbob]

Limits are a PreCalc concept and are the basis of much of Calculus. I actually made this video for my PreCalc class and put it in my Algebra 2 playlist. So now you know why the shortcuts work in your Algebra 2 book:) I doubt you will need the limit process for your algebra 2 class...just impress your teacher with the fact that you do know it:D

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Electric Engineer...Impressive. You will do great:) Thanks again.

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@HotRodStart Can you give me a more specific question to answer? Like where in the video you got confused?

[@profrobbob]

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YOU MY FRIEND IS A LIFE SAVER, YOU SHOULD BE MY PRE CAL TEACHER, KEEP UP THE GREAT WORK 👏👏👏👏, KEEP POSTING VIDEOS.

[@profrobbob]

THANK YOU Edgar Imguanzo glad you are learning so much from my lessons:) Since you're a subscriber remember that I can be your Pre Calc teacher anytime, 24/7 that you feel like learning more math...BAM!!! Does that mean you have shared my channel with the rest of your PreCalc class too?!

[@bcoll1082]

AWESOME! As always! Thanks again Mr. Tarrou. Precalc exam 2 in the a.m. Fingers crossed. Last one didn't go so well. Got an 84. Some of the problems on the exam weren't even the types of problems discussed in lecture. Oh well.

[@profrobbob]

THANKS! ..and you're always welcome! Don't be discouraged...you know and I know (after reading these 3 comments) that you certainly put in the study time:) Go pass that new exam like BAM!!! like I know you can!!!

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I must admit...you are the first one I have ever heard use that comparison...but it's defiantly an upgrade from Harry Potter!:)

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[@profrobbob]

Thanks for the feedback. I hope you do great in your Calc class:)

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Thats FANTASTIC! Great job...and thank you very much:)

[@profrobbob]

Now Closed Captioned:)

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Thank you (a million) you have no idea how your teaching is helping me :) God bless youuuuuuuuu

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[@alehax27]

Thank you! I was having problems understanding why you needed to multiply everything by 1/x^highest power and why you needed to replace things with 0.

[@profrobbob]

AWESOME! I am so glad I could help. Thank you for watching and please spread the word about my math channel. I hope you do great in your class.

[@profrobbob]

You need to watch my video horizontal asymptote of irrational functions. Your denominator is not a simple polynomial so this video is not what you need. If you divided by the highest power then the numerator would have been multiplied by 1/x^2 and the denominator 1/sqrt(x^4). Irrational functions can also have 2 horizontal asymptotes and you need to account for x approaching infinity and negative infinity so you actually need to divide by highest power of denominator & account for sign change

[@alooooshm]

thanks a lot.so helpful, I love using algebra and idea of limits to explain the horizontal asymptotes

[@profrobbob]

+‫علي مصطفی الموسی‬‎ you're welcome and THANKS for choosing my channel to study with:D

[@fclaisabellagutierrez3170]

You are a great teacher!!! Thank you !!

[@profrobbob]

Your'e welcome new subscriber from the youtube student universe:)

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Thank you so much for putting in time and effort to help me through High School :D Thank you Thank you, you are very thorough with your explanation, Im learning heaps from you :D

[@profrobbob]

And THANK YOU Alice M for taking the time to "thank the teacher" , for liking & subbing, for putting in the time to find additional help, choosing my channel and then to study! Students like you are the reason teachers love to teach...BAM!!! Please keep sharing your learning experience and my channel with your friends, class and teachers too, while you remind them to like, sub, support the ads and keep spreading the word :D

[@profrobbob]

And here we are...2013...and I still make my videos on a chalkboard! I LOVE my chalkboards, in fact I still have chalkboards in my classroom:)...I'm saving the planet, one whit board at a time!!! THANK YOU for watching:D

[@markbrant6955]

Thank you for the very informative video! I owe a big part of my education to you. I have never had an opportunity to learn mathematics from someone who taught the concepts well. The public education I have received is substandard. I have gone through almost all your algebra 2 videos and I plan on going through your trig and calculus videos as well. I was watching through this video and I noticed you made a minor calculation error. 1 divided by 1000 would equal .001. You said it was .0001.

[@profrobbob]

If the degree of the denominator is larger the horizontal asymptote is y=0.

[@profrobbob]

Back then I couldn't slow down. KZbin limits you to 15 minutes when you first start making videos. At least you can pause and replay my videos which you couldn't do in high school. If anything, I hope you see that I over explain most of the concepts...especially in later videos. I hope you got or get the help you need.

[@MrRockyracerm]

Oh my gosh. As a nerd who is taking pre calculus. I must say this made me so happy that it's that easy.

[@profrobbob]

AWESOME! Thanks for choosing my channel to learn from and please Like, SUBSCRIBE and share it with others to help me groW! I'm happy you found that math is so easy for you MrRockyracerm...could be a future teacher inside:)

[@손일영-j9k]

What a perfect lecture is!

[@profrobbob]

BAM!!! 손일영 Thanks!

[@rajdeepchakraborty9533]

Is that the Project IGI alarm going off in the background? Well done on condensing the topic in such a short video.

[@sheet-son]

Hey mr tarouu, I don't see the vertical asymptote's video in the playlist? If it still exists can you add it to the playlist? I looked through the upload list and couldn't find it, thanks :)

[@margar1231]

TY for acing my exam for me! YOUR A GENIUS!

[@profrobbob]

I start summarizing the rules around minute 13:00

[@profrobbob]

@TheComputergeek365 Thank you:)

[@andrewmichaels6955]

keep up the good job Professor!

[@profrobbob]

You keep watching and spreading the word and I'll keep making videos:)

[@NiceWatchMiss]

Thanks a lot for taking time out and making precalc less complicated and suck less.

[@sugin7184]

Awesome video! I have been stuck on lim(x->infinity) of x^2/sqrt(x+1)...I got 1 for the horizontal asymptote as the answer but I understand that when I substitute 1 into the equation, i get a value of 1/sqrt(2) which means this is not a horizontal asymptote. My question now is why did i still get 1 when i divided the equation by the highest power?

[@strangehobbit]

you are amazing sir!!!! I wish you were my math teacher

[@al-muntazar3137]

ProfRobBob Thank you for your answer :) I do understand the horizontal asymptotes now after that I've seen this video about 20 times. Thanks :)

[@profrobbob]

You're welcome…some things just take a little longer:( Good job on not giving up!

[@therussell8836]

props man.. your videos helped me alot

[@profrobbob]

AWESOME!...thanks for watching.

[@prissarpong]

thanks sir, you made math look much more fun.

[@profrobbob]

You are SOOOOOOOOOO Welcome!...ps - I had to google Jeremy Renner to see who I looked like after the last comment that said so...my wife told me to take it as a compliment!...so thank you:) Keep watching and sharing the channel with your friends:D

[@معاويةالجزائري]

fantastic ! ! ! ...... bravo dear bob Although I do not understand English well , But I took a good idea of the asymptotic horizontal and vertical Because your explanation ......respect from algeria

[@norhankhairy9368]

Thanks a lot ,It really helped me out .

[@THEQuantumPolkaDots]

Can you explain why we multiply by the highest degree (or would we say that is the reciprocal of the highest degree with the 1 over it?) anyways I am unclear as to why we do this and if there is another way as well.

[@profrobbob]

@yahya3563 I am always open to good advice and opinions:)

[@Jarlzdotorg]

So helpful; thanks again!

[@profrobbob]

Good to see your smiling face still learning from my videos Charles Henry and I hope you're telling everyone where to find my channel:D

[@wavemasterz1]

How do you determine if it approaches from Above or below if they both approach 0

[@coolrahul223516]

hi sir can u put video for domain and range of functions and their graphs please

[@profrobbob]

You are very welcome. I am glad I could help!!! You can return the favor by helping me spread the word about my new math channel...and doing awesome in your math class:D

[@edster210]

I have a question that i hope someone can answer before friday afternoon. How do i graph as the limit as x approaches -infinite f(x)= -3 and then the limit as x approches 3 f(x)= infinite? I got the H.A. and plotted the intercepts she gave me in the problem. I just need to know how to graph that above stuff. thanks.

[@YoshevElazarMikael]

Thank you very much sir!!!!! Always the good stuff!!!!!

[@profrobbob]

You're always welcome...your becoming one of my best students...BAM!!!

[@YoshevElazarMikael]

ProfRobBob Thanks sir, that means a lot to me.

[@profrobbob]

You're shares and support means a lot to us too...BAM!!!

[@profrobbob]

My goal is to "Make Math FUN"(while learning)...does this mean I have another believer?!

[@keekli9046]

Thank youuu!!!

[@profrobbob]

...watching another video already, THANK YOU!

[@profrobbob]

Happy to save a life in from the sea of math:)

[@dbella804]

Thank you so much!!! I finally understand

[@profrobbob]

haha...I have to make sure you are awake before the lesson!

[@profrobbob]

@thethug89 :)

[@al-muntazar3137]

Great video, but I'm not being able to solve this question: Identify the horizontal and vertical asymptotes for this function ; y= (2x)/(x+2) I understand the vertical asymptote, but not the horizontal.. :/ Please help me!

[@JoseCastillo-pu9cv]

Nice!!!! I am subscribed.

[@profrobbob]

+Jose Castillo THANKS!

[@sinistril]

Well played sir.

[@profrobbob]

use some test values.

[@cilva7able]

Can't you just take the numerator and set it = to zero? Would that give you the horizontal asymptote?

[@dlggnation]

great video

[@ThePond1]

my brain is non existent right now and just sitting here thinking, "Wtf am I looking at?"

[@profrobbob]

ps...thank you for subscribing!

[@profrobbob]

I hope that means you're busy doing your homework now?!...LOL

[@profrobbob]

okay...now BAM!...go get that "A":)

[@profrobbob]

Must have been the Old Spice Swagger!

[@suckonit555]

Give an example of a rational function that has a horizontal asymptote at y = 0 and a vertical asymptote at, x = 2 and x = 1.?

[@profrobbob]

Gods Child If you have not already studies vertical asymptotes you will find this lesson helpful kzbin.info/www/bejne/p5y4n4aloq2Nmsk For a horizontal asymptote of y=0, the degree of the denominator must be larger of the numerator. To have vertical asymptotes of x=2 and x=1, you need to have factors in the denominator that cannot cancel with any factor in the numerator that is equal to zero when x=2 and x=1 such as (x-2) and (x-1).

[@RemigiusKalimba]

Why does he all of a sudden have swag in this video??

[@TheComputergeek365]

Pure Awesome.

[@zoey1492]

awesome

[@profrobbob]

Thanks for watching...don't forget to like and SUBSCRIBE and share my channel too:D

[@moonshotm3387]

u are awesome

[@profrobbob]

...good to see you are already watching more videos:)