Graphing Rational Functions Part 2

[@profrobbob]

And students writing comments like this are why I LOVE teaching...it made my wife cry when I showed her your comment! Teaching certainly isn't the highest paying job but if you are passionate about your career, enjoy what you do 95% of the time, and have a hand in touching so many lives the rewards are "PRICELESS" Thank you for making this another one of those "priceless" moments!

[@darshilpatel9112]

As a college student who is studying and reviewing for precalc final in less then 24 hrs, your videos are really helpful. I have been watching your videos since my first semester of college. Your videos are really helpful. I have also told my friends and classmates about your channel and it has also helped them a lot. I have learn a lot from your videos and will continue to do so. All of your lessons are really easy to understand, you make even hardest of the topic really easy to understand, and you also make learning fun.Thank you for being such an awesome teacher, You would make a great professor. My friends and i really appreciate all the help we get from your channel and if there is any way we can contribute to your channel, please let us know and we will try to do what we could to help your channel grow.

[@profrobbob]

+Darshil Patel since you asked... If you and all your supportive friends and fellow classmates would reach out to all forms of social medias you can think of and ask them to SUBSCRIBE to this channel (liking, sharing and supporting the ads really helps too)...our goal again this year is to reach 100,000 subscribers before the end of the year and we are still about 7,000 subscriber short:( I made a Merry Christmas 2015 video asking for help but so far it's only added about 1,000 subscribers....here is the link if you want to share it too kzbin.info/www/bejne/rKq1fnyKeJyog5I Otherwise...THANK YOU for taking the time to share this grateful and appreciative comment with us...students like you inspire us and are why we continue to work so hard to keep this channel growing! BAM!!! Enjoy your holiday break and thanks for all the continued support...Rob & Cheryl Tarrou

[@profrobbob]

And thank you for choosing to seek out extra help and chose my channel! Glad I could help!

[@profrobbob]

Almost "Gangnam Style" huh?!...LOL Thanks for watching and sending a comment. It's easy to do because of viewers like you:))

[@profrobbob]

And THANK YOU for posting such a complimentary comment! Thanks for liking my videos and I'm happy to hear they were beneficial & provided the extra help you were looking for to help you pass that class. I hope you will remember where to find me if you need extra help in the future:)

[@cportobanco]

Dea Professor, Your videos are extremely explicit, and your dedication is admirable. Thanks to your audiovisuals, I am able to acquire a clear understanding. Sincerely, C. P.

[@profrobbob]

+cportobanco and thanks for choosing my channel to share your appreciation, like, sub and study with! Please keep telling others to watch and do the same to help us keep growing:D

[@ganoosh6996]

I have a test on this next Tuesday and you just saved my life! You really clear things up! I find myself watching your videos more than just forking through a textbook. You're a wonderful teacher Mr.Tarrou!

[@profrobbob]

Hope you pass that test like BAM!!! Then after you do...please sub and share this free study resource with your teacher so all current and future students might benefit like you did...BAM!!!

[@profrobbob]

You are welcome...and thank you too for subscribing!...I hope my channel continues to be helpful to you and your friends:))...thanks again for watching.

[@georgesadler7830]

Professor RobBob, thank you for another tremendous video/lecture on Graphing Rational Functions Part Two. These graphing methods/breakdowns are always helpful especially when it comes to complex functions. The hole in a graph is something that I never pay attention to when graphing functions/rational functions, however this video solves that long lasting problem.

[@Janewt00]

I have a pre-calc final tomorrow and i have been studying like crazy all week due to a really bad teacher. I learned nothing all semester. I have been watching your videos for about half an hour and i already know more then what i've learned all semester. Thank you so much. I think you may have saved my grade.

[@jewelmeegarcia2614]

this is the most helpful lesson i've ever acquired so far. ghad, sir, you saved my grades!

[@profrobbob]

You are taking the initiative to find extra resources to understand your homework. You deserve the credit, and i am glad I could be here to help you 😁👨‍🏫 I have hundreds of lessons organized here, www.profrobbob.com , if you ever need more help. Please like, subscribe, and share. I am confident you will be very successful in your math studies 😁👨‍🏫💯💥

[@thedumbaccountxxx]

You're incredible! Simply amazing! I'm going to share all of your videos with my friends who too are having trouble with math. You make it so easy, interesting, and FUN! I actually ENJOY watching your videos, thanks again!

[@profrobbob]

You're welcome! And thanks for taking time to "thank the teacher" and send such an awesome comment! Please be sure to remind all those friends you will be sharing with to SUBSCRIBE and support all educational channels like mine to help keep them FREE for everyone:)

[@profrobbob]

Thanks for liking my teaching style and for watching my videos. Please share my channel with others who may find it helpful:D...thanks!

[@josephcampbell640]

THANK YOU, THANK YOU, THANK YOU!!! You have been extremely helpful in preparing me for my Unit Assessment test tomorrow. Your time and effort for these videos have most definitely not been useless!

[@profrobbob]

Thank you for your very kind words. I am happy I can help through my videos.

[@legolepsy5265]

12 years later and this video is still tremendously helpful!! Thank you sir!

[@theleagueOFCOMEDIANS]

I kid you not, you've taught me a semesters worth of lessons. You're a legend.

[@profrobbob]

Glad I could help and I hope that earned me a new subscriber..BAM!!!

[@coldstopdrop]

thanks for the help. I love your enthusiasm with these videos. My pre-calc professor can hardly speak English and I find myself reteaching myself the lessons based on your videos and others. Keep up the good work.

[@profrobbob]

+Evan Brown you're welcome and thanks for liking and learning from my channel...please subscribe and share my channel with the rest of your class and teachers as an additional study reference for after class help:D We help you learn and you help us groW! BAM!!!

[@TalosAT]

Thank you so much for making these videos! I love the energy and enthusiasm you have in your videos; a lot of math videos I've watched were so dry they made it hard to stay focused. You saved me from having to take an extra year of college! My future classes require calculus, and I have to get through pre-calc 1 and 2 before this fall or I can't take calculus during my AA degree. With your help, I tested out of pre-calc 1 today, and can take pre-calc 2 this summer.

[@lie888]

Thank you so much for doing what other teachers can't seem to do and explaining everything so well. You make math understandable and even exciting with that great personality of yours. Thanks so much!

[@profrobbob]

You're welcome Elias Rodriguez thanks for watching and sharing your experience! Please like, subscribe and share my channel with everyone and please remind them to do the same to help us keep growing and remain FREE :D

[@profrobbob]

You can set the equation equal to the y value of the horizontal asymptote and solve for x to see if there is a solution. Or, you will see that crossing when you make a t-table to finish the graph after learning as much about the graph as you can.

[@profrobbob]

You are very welcome:) Thanks for watching.

[@profrobbob]

You're welcome and thanks for watching all the way from Turkey! Sorry I do not have anything on differential equations at this time:(

[@drisil7997]

THANK YOU THANK YOU THANK YOU! I have a pre-calc test tomorrow and this cleared everything up perfectly! watched your first video as well! Please continue with these videos :) ! Love the positive energy gets me pumped for math! WOOOHHH!

[@profrobbob]

You're welcome!!! Thanks for choosing Tarrou's Chalk Talk to learn from and subscribe to adri sil and I hope you pass that test like BAM!!! and will continue to learn, stay pumped about math and share my channel with all your friends and classmates:D

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Thanks:) And thank you for supporting by watching, liking and subscribing! Don't forget to tell your friends to do the same:D

[@profrobbob]

Somedays it's just alot harder to think, talk, write and teach all at the same time:)....it's nice to see that you were paying such close attention though...we teachers love that!

[@Kar76060]

Thank you a million times, I thought I lost hope in math until I found your channel. I'm currently in pre calculus, this helped a lot, thanks again!

[@profrobbob]

+Karim Fakhoury your a million times welcome and thanks for choosing this channel to learn from and sub to! I hope you continue to find it helpful thru more of your math journey and that you are sharing this channel with everyone along the way:D

[@podolskipodolski8783]

Thank you for taking the time to make these educational videos, it helps a whole lot. You make these subjects concise, precise and fun. Cheers professor.

[@profrobbob]

Podolski Podolski you're welcome and thanks for taking the time to learn from them and subscribe and for taking the time to "thank the teacher" :) Please keep spreading the word about this channel from sunny Florida :D

[@podolskipodolski8783]

I most definitely will.

[@profrobbob]

Podolski Podolski thanks!!!

[@profrobbob]

Thanks for watching and appreciating my teaching style!

[@profrobbob]

Thanks for watching, commenting and supporting by subscribing!

[@profrobbob]

LOL...thank you for watching, liking and subscribing & keeping your comment suitable for everyone to read!

[@miaricciardi-kling9582]

Am I the only one loving that he uses a chalkboard?! I love this man for his help!

[@profrobbob]

I don't know if has a use really...it is just a point where the function is undefined. In Calculus it will be called a removable discontinuity and you will be able to find the limit of the function at that point because it approaches the same y value from the left and right of the undefined x-value. Limits are extremely useful in Calculus, it is actually of the key concepts in Calculus.

[@americanbluediamonds]

You have made these concepts fun and so much easier to remember! Thank you.

[@profrobbob]

Thanks again...please share this free study resource with your teacher too, so the rest of the current and future students can benefit too...BAM!!!

[@hilaryyang3821]

omg THE HOLE explains a lot!! Thank you prof! The best math youtuber so far!

[@profrobbob]

THANK YOU!!! I really appreciate your kind words:) Please spread the word.

[@danielyusupov8507]

Finals week for me! Just refreshing my memory even though I've watched your videos all semester long. Never gets old... your passion for what you do really motivates me and inspires me to keep going. I love calculus just from watching your videos. People always bitch about math and say "We are never going to use this so why even learn about it, blah blah blah.." but one thing I learned from math is that there isn't always an answer to a problem just like in life. Sometimes, our problems are undefined and have no real solution to them. That is what I took out of my math classes over and over again and applied it to life. People overlook that part of math that you might use in your life from time to time.

[@profrobbob]

+Daniel Yusupov that was quite the deep thought you just shared and students like you are what motivates us to work harder to keep this channel growing! Keep that positive outlook on life and a world of opportunity will await you!!! Thanks for choosing my channel to study with and sub to and we ask that you remind everyone how important it is to like, sub, support the ads, share thru social medias and with friends, classmates and teachers to keep these free educational channels growing and remain free for everyone!

[@mynameisdelanie]

these videos are so informational and great and your way of teaching these things is great and you're so funny and why can't you be my teacher AND THANK YOU FOR TAKING TIME OUT OF YOUR DAY TO MAKE THESE. I REALLY APPRECIATE IT.

[@kunalbhattacharjee8659]

This guy saved my math grade...thank you!!!

[@profrobbob]

Actually in most of my videos I jump in and yell BAM!!! I am so happy you like my videos:):):) Thanks for watching.

[@joycebean]

ROB BOB YOU ARE MY HERO!!!!!!!!!!!!!

[@profrobbob]

+wilddaisyforever SUPERMATHMAN to the rescue...BAM!!! Please like, sub and share this channel with everyone:D

[@grahambest5712]

your a great teacher. clear and you help a lot with some of your comments like that an asymptote can some times go over. and the T table. I've started to learn to trust them and make a graph for that. it makes something really hard mindless. thanks.

[@profrobbob]

The rules you are referring to are for polynomial functions. Rational functions are different with there many types of possible asymptotes are different.

[@profrobbob]

You can ask questions here or send me a personal message through my facebook fan page. I am really really busy this year because I am teaching four different subjects at once. So I might get to your question right away or it might be days. I have always tried to answer my KZbin viewer's math questions since starting this channel but that is getting very difficult this year:(

[@dcristancho02]

Can't thank you enough! you explain so well, step by step! your videos are saving my grade!!! BAAAM Thanks!!!

[@nigel2014]

damn I swear this video helps me out a lot the usefulness of my precal teacher totally can't compare with this single vid.... love u my teacher,ur the only math teacher for me in the world

[@profrobbob]

Thanks for choosing my channel to learn from and sub to abdul muhammad and for taking the time to share your appreciation! Please tell all your friends, class and teachers to watch and do the same to help us keep growing and helping others...BAM!!!

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@@profrobbob HE IS FROM PAKISTAN. YOUR SUPPORT IS REALLY GOING FAR.

[@profrobbob]

@@aashsyed1277 Thank you Aash. You keep me motivated!

[@aashsyed1277]

@@profrobbob haha! i like your channel!

[@profrobbob]

Yes...and finding your x and y intercepts.

[@ballerv19]

You are the PURE REASON I am not failing out of precalculus! THANK YOU!!!!!!!!!!

[@profrobbob]

You're welcome…but if it were not for YOU seeking extra help on KZbin there would have been no ME to help YOU:) Thanks for taking the time to get extra help, watch my videos, subscribe and make the grade…you made this teacher proud!!!

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Thank you so much, I feel so much more confident for my test, wish I had teachers like this

[@profrobbob]

Hope you pass that test like BAM!!! Then return to sub and then I can at least be your KZbin teacher:)

[@folarin1998]

Dude your shirt is AWESOME! And you are a great math teacher! I love your vids!

[@TheBigbees]

Jesus, I find myself expecting (hoping) all videos I view now start with HYYYEEEELLOOOOO. Love these videos!

[@profrobbob]

Cool. Thanks for watching:)

[@profrobbob]

I always try to make sure that you will be paying attention at the beginning of my lesson...LOL:)) I hope you learned from it as well and will continue watching!

[@killerbigred]

Thank you so much. Even though I don't want to sound mean, but you are so much better than my Pre-Calc teacher. I really wish you were my teacher. BAM!

[@profrobbob]

You're welcome DieNoMight135 we all have our own teaching style and can always learn from each other, even teachers...I hope you will share my channel with yours as an additional study reference for teachers and students alike! Now that you've subscribed I can be your KZbin teacher anytime 24/7...BAM!!! SPREAD THE WORD :D

[@profrobbob]

:D Thank for letting me know how much my videos are helping you! Your awesome. Keep up the good work:)

[@tarotthephenomenon5185]

10:05 TI83/84 will show the hole at x = - 4 for the above graph. Type the function in the Y= EDITOR then press the ZOOM button then the 4:ZDECIMAL option. The rational function is then graphed with a hole - brilliant !

[@someoneOnYoutube001]

Just wanted to say thanks for the math videos! They're very helpful.

[@profrobbob]

You're welcome and thanks for studying and subbing Hazel! Please share the help with your friends, classmates and teacher too:D

[@profrobbob]

Thanks for watching until the end:D

[@profrobbob]

Now Closed Captioned #math

[@studywithankitadas]

Sir thank you so much...I have a paper tomorrow and since last 3 days I am trying to understand asymptotes and finally ur vedio brought a relief...Thank you so much for helping me..You are a great enthusiastic teacher.please keep uploading more vedios.😄

[@profrobbob]

You are so welcome Ankita! Thanks for not giving up until you found the help you needed...proves to me that you already have a great work ethic. Thanks for studying and please take the time to like, subscribe and share this free study resource with your teacher too.

[@profrobbob]

You have to look at the entire rational function and don't forget that -4 is going to make the denominator 0 making the rational function undefined. If the factor of x+4 did not cancel with the denominator there would be an x intercept of -4.

[@xpaigexpaigex]

Watching your videos doesn't even feel like work!

[@profrobbob]

BAM!!! That's what a teacher like to hear:) Thanks for watching, learning, liking and subbing paigegibbons ! Please share my channel and your experience with all your friends, class and teachers and remind them to like, sub and support the ads to help us keep growing and helping others:D

[@waleedhk1]

BAMM!! that always brings a smile to my face for some reason. and Thank You for doing these math videos. :)

[@profrobbob]

You're welcome waleedhk1 THANK YOU for watching and learning! Please continue to share my channel with others and remind them to like, SUBSCRIBE and spread the word to help me help others...BAM!!!

[@profrobbob]

You are doing great...you are just going to need to use a t-table to find some more points the graph goes through to finish.

[@profrobbob]

Yes...we will always need to use a t-table to fill in missing information to finish the graph.

[@nicmarin12]

love your videos! helping me get through higher level math

[@profrobbob]

THANKS Nicolas Marin ...please help "me" by Liking me on Facebook, sharing, supporting the ads, Liking and SUBSCRIBING to my channel...all these things help my channel groW to help others find FREE math help...BAM!!!

[@josephmontanti9119]

I go to sleep in math class, then the day before the test i watch your videos and get a 100. Thanks!

[@profrobbob]

You're welcome Joseph and thanks for watching! I appreciate that you are taking the time to learn the lessons and getting "A's" but as a classroom teacher myself, a lot of preparation goes into teaching and sleeping should be saved for your pillow:)

[@profrobbob]

I don't understand where from the video your question is coming from.

[@abdinassir4004]

I just can't thank you enough. You're a lifesaver

[@profrobbob]

+Abdi Nassir you're welcome...and you can thank me by sharing this channel with others as you remind them to like and subscribe as they continue to share:D

[@bcoll1082]

Excellent! What a huge help. Thanks you again Mr. Tarrou.

[@profrobbob]

WOW...I just realized from your comments that you've been studying since 10:30! Wish ALL my own students were that motivated...BAM!!!

[@bcoll1082]

Actually since much earlier than that. I hit the books hard. I have to. And I was up til about 2.

[@profrobbob]

like I said...wish all my students worked that hard:)

[@superluigi5757]

Thank you so much man this seriously helped. My Algebra II teacher is extremely confusing, this is a life-saver! :)

[@profrobbob]

Super Luigi you're welcome and thanks for choosing my channel to learn from! Please be sure to like, subscribe and share my channel and your experience with your friends, the rest of your class and your teacher as an additional study reference:D

[@profrobbob]

I don't understand the system error 404...the video worked for me. Thanks for the comment. I hope you can see the rest of the video:)

[@libreg]

Wow, you do a really good job at teaching. Thanks a lot for this.

[@CIE903]

loving your videos!!!! cant stop watching them :D

[@profrobbob]

BAM!!! That's what I like to hear:) Thanks for watching, liking and subbing too!

[@profrobbob]

That is awesome!!! I am glad I could help save you some time and money by helping you test out of Pre-Calc 1:) I hope my videos continue to help you do great in your summer pre-calc 2 class and Calculus next semester.

[@asfjbnsad]

great work prof! thank you so much by making this video, although there's one point during this video which i do not understand fully - when you try to find the x-interception, you used the simplified/factored form of the original numerator which is 5, therefore there's no x-intercept, but why can't you use the original numerator instead? if you do that, you will figure out the x-intercept is -4 cince 5*-4+20 is zero, and what is wrong with that? thanks again, this helps a lot!

[@calebtoyo]

Wow don't know what to say you are fantastic.... Math just got fun God bless you ........

[@profrobbob]

Thanks for choosing Tarrou's Chalk Talk to learn from! Math & Fun in the same sentence...that's one of my favorite things to hear:)

[@aytanmaster1459]

Thank you so much sir your videos are great. It really helped me. I might as well also recommend some of my friends.

[@profrobbob]

THANKS for subbing and sharing, we appreciate your support!! Don't forget to share with your teacher too, so ALL their students know where to find free math help after class...BAM!!!

[@chrismatthew8150]

Man... You make learning FUN!!! Great Teacher!!! THANKS!!!! :)

[@profrobbob]

+Chris Matthew BAM!!! Thanks for watching and learning:)

[@bobmarleykagan1]

Thanks a lot for your videos . do you have any work on differential equations? İt would be great with the intiuiton..

[@qwertkinz]

I love your energy and love for teaching :)

[@profrobbob]

Thanks for watching and liking...don't forget to SUBSCRIBE and share my channel and love of teaching with your friends too!

[@Bubblyone009]

You're a cool teacher. I actually understood it. The bam! Made me laugh lol

[@profrobbob]

THANKS for watching Bubblyone009 I hope you will return to like, subscribe and tell all your friends and classmates to watch and do the same!

[@JK18BFF]

can i use a t-table on any type of rational function graph? As in can i use it all the time instead of setting the equation equal to y?

[@khalilhijazi4588]

Nice explanation of the difference between even and odd functions. Here's a similar explanation of the differences: If you can plug in either x or -x into a function and get the same y, then that's an even function. If you can plug in either -x into a function and get -y (basically the opposite of (x,y)), then that's an odd function.

[@profrobbob]

Thanks....not that is sounds like you need the lesson but I have one about Even and Odd functions here:) kzbin.info/www/bejne/jXvZqIiXh7aXn7s

[@khalilhijazi4588]

lol thanks, but I already learned about even and odd functions in Barron's SAT Math Level 2 Prep Book.

[@dahe1352]

RobBob is awesome as heck

[@profrobbob]

+Thedock Leesmile thanks! ...and thanks for watching, learning and liking...please sub and share too:D

[@KTMaths02]

You're such a good teacher :') thanks for this video

[@profrobbob]

You're welcome Khet Corpuz ...thanks for learning from #ProfRobBob ! Please Like, SUBSCRIBE and share my channel with all your friends too:D

[@misty348]

thanks for going step-by-step so im not stuck on what u did 5 steps ago lol ;D story of my life thanks for the great videos

[@profrobbob]

Thanks to you seeking out additional help our worlds collided...I hope you continue to benefit from my videos, and let me know how you did on that final...A..A...A...A...A! (that's positive chanting)..LOL

[@fatimaveras2637]

Great help with both videos. Although there's more my professor had wanted me to do. Can you please make a video on 1. Factoring the numerator and denominator. 2. Find the domain. Cancel any common factors and list any holes. 3. Determine if it has a verticals asymptote and decide is y-> infinity or y-> -infinity around the vertical asymptote. 4. Determine if the graph has horizontal or oblique asymptotes and decide if it intersects then look for intercepts. You explained most I just need help on finding the domain and finding out where the graph will intersect.

[@profrobbob]

+Fatima Veras The domain of rational functions are all real values except those x's where there is a hole or vertical asymptote. By intersect do you mean the x intercepts. If so then you set y=0 and the only way a rational function will equal zero is if the numerator is equal to zero.

[@Skevywoods]

Awesome lesson! You made it so easy!

[@profrobbob]

THANK YOU…BAM!!! …and Thanks for supporting by subscribing and watching:)

[@loganmoyer2998]

His laugh at 3:51 hahaha

[@GreggyAnt]

haha did anyone watch all the way to the ending? funny. I think if you where my math teacher I would actually pay attention haha Thank You!

[@NiceWatchMiss]

Which vertical asymptote would i graph if I have two of them? I.e. 6/(x-2)(x+3)?

[@darkflores5562]

omyg its been 5 years and sir im super thankfu,l representative of year 2021

[@profrobbob]

Thanks for watching and representing 2021...good thing math never goes out of style (just my clothes and hair:) since I made this video 10 years ago...BAM!!!

[@williamlabrit8987]

When you get the hole(-4), aren't you supposed to plug that value into the simple equation (5/x-3) so that you can have an ordered pair to graph as your hole? Or do you just graph the hole at f(-4)? Thank you!

[@emiichimira8466]

that ending HAHAHA TYSM this helped so much

[@profrobbob]

thanks for watching...please sub and share too:D

[@JK18BFF]

@profrobbob how do u know when it crosses the Horizontal Asy?

[@jessicaloraine]

Thank you so much! Such a helpful video. Keep it up!

[@maxdiamond4868]

Dear Prof Rob - When finding whether or not the function is even or odd, if you do not start with the reduced function then you get -5 +20/-x^2 +x -12, which factors to 5(-x+4)/(-x+4)(x+3), and you are left with 5/(x+3). Isn't this is the same as the original function making the function even? Or is the question whether or not the initial function (prior to factorization) is equal to f(-x)?

[@yousefmechanic9563]

thank you for your videos what about the vertical asymptote x not equal to -4