Graphing Rational Functions Step-by-Step (Complete Guide 3 Examples)

Learn how to graph rational functions step-by-step in this video math tutorial by Mario's Math Tutoring. We go through 3 examples involving finding horizontal asymptotes, slant asymptotes, holes (removable discontinuities), x intercepts, y intercepts, as well as using sign analysis.
Related Videos to Help You Succeed!:
Sketching Rational Functions (6 Examples)
• Sketching Rational Fun...
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[@tacticalmistress]

Not many have the ability to carry over information and teach, but Mario has got it down. Brilliant.

[@rocks813]

This channel is criminally underrated! You teach very much clearly, Sir. Thank you so much for this! :>

[@camdenlippert3751]

you've taught me what my math teacher couldn't :)

[@metsielumeasso524]

Well that makes 2 of us😅

[@rustylarry7465]

You searched for this video which means you intend on actually listening, happens to the best of us.

[@mro7432]

I've seen this comment like a hundred times; You're not wrong tho

[@unskxjsixy]

Same I’m okay at understanding math but my teacher goes too fast for my little autistic brain

[@Lanoixsette]

@@unskxjsixy real

[@mercyokoth1852]

The way i understood everything without struggling you explain so well thanks alot Sir

[@Deangund]

You are genuinely saving my math grade single handedly

[@malcolm5132]

Love the sign method, I'd never heard of it before. Thank you!

[@via.jackson]

Thanks! You taught me everything I needed to know in 22 mins what my math teacher couldn’t in a week.

[@MariosMathTutoring]

Glad I could help!

[@comquatcash]

you are a national treasure Mario, the way you thoroughly go through every step is flawless in my opinion, you truly have a gift for teaching great work.

[@MariosMathTutoring]

Wow, thank you!

[@AnaiyahMalhotra]

You have saved me! I have a test tomorrow and before this, I was so confused but now I have got it! You are amazing!! Thank you so much

[@MariosMathTutoring]

Happy to help!

[@chanelvu1266]

Thank you so so much professor, you are so good at tutoring!

[@pedrogomez-jk2mm]

Thanks a lot Mario, great teaching

[@charityrotich3287]

Am greatful coz my tr did pay attention to these details...Thank u 😊

[@huzaifaali3969]

Thanks a bunch for giving me a new concept😃

[@SoryuJ]

Got my chapter 5 algebra 2 test tmr been binging your channel all day 😅

[@MariosMathTutoring]

You got this!

[@abdullahihilowle3117]

I don't understand what it is or how you do it but you just explained this better than my teacher congrats.

[@CaoMoloi]

You are such a geek Mario. Incredible stuff

[@renziz9541]

thank you!

[@peterczaja1669]

Thank you, I was falling behind in class but now I understand

[@preeze7335]

best of best tutors

[@michaeldiaz6642]

Can you please make a video about finding/writing rational functions
given the vertical asymptote, horizontal asymptote, and x-intercept?

[@Displ4c]

That is the cleanest board I’ve ever seen

[@agentduckduckgoosetr9800]

Thanks I was really struggling on this topic.😀

[@MariosMathTutoring]

You’re welcome!

[@clairez.6051]

i really don't know how to thank you sir, your video is exactly what I need for my final test, stay safe and good luck!

[@Mercy-x8o]

I Have A Test Tomorrow and i hope it's gonna help me in addition to God

[@nancydwyer4456]

Please check your long division on the third example. Should the slant asymptote be y = x + 1?

[@vaybrate]

You just show me that math is epic

[@shirazqasmi5090]

Thanks Mario! This is by far the best explanation of the subject I've seen to date. This helped me a lot.

[@laurandaver9112]

Ur an excellent teacher , wish u were my actual teacher 🙂

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you are such a spectacular math's teacher I have ever had keep it up .

[@yuvrajgrover1200]

You are awesome thanks for the help

[@chanian3908]

thankyou

[@slopcrusher3482]

Thank you so much for teaching about sign analysis. I've watched 3 videos so far, and while they may be okay for simple factors, when you get into multiple factors for the numerator or denomerator it takes a lot of calculations to find where the line goes for each "quadrant" or each side of a vertical asymptote, and not many of them have examples with multiple asymptotes.

[@apsara445]

Informative

[@ixchel8772]

just awesome

[@sallyfacefan321]

23:40 is it okay if the graph crossed the Oblique asymptote?

[@namankhajuria4058]

Brilliant teaching skills.
From India

[@thedeathofbirth0763]

Asha, Mario has great videos on graphing polynomial functions. Review them and I am sure your question will look very simple afterwards.

[@itzzkundan]

Very nice step by step explained. I think you must make a list of all the types of functions in sequence. It will be very useful here for IIT JEE exam in India.👍

[@sujathakiran4212]

Your explanation is too good and easy to understand. Thank you sir.

[@zoewood3601]

Saved me the night before my math test! Thank you!

[@btxtboys]

this helped me alot during online classes, thank you sir!

[@rockyflavaa]

this guy is an amazing teacher, unlike mine who doesnt even allow calculators in the classroom 😭

[@cameronkrewer1127]

thank you Mario math tutoring, your video is very easy to understand and you are the reason I will pass the test. You explain things much better than my teacher. Thank you sir and keep up the good work. :^)

[@ashakirdak4897]

Please answer of this question
Y=(x-2)/(x²+3x+2)
I have problem in positive side of x -axis

[@julianblacksmith8539]

omg u just saved me real hero

[@yashaswikulshreshtha1588]

I love it because it literally covers entire graphing rationals

[@blakebramford129]

thank you so much Mario

[@yonasbiloye4346]

thanks

[@dayanaraguzman4797]

please teach my teacher

[@Saad-up7lr]

Hahaha! That's so depressing to say..

[@1nonlytorres757]

Thank you so much, sir! keep safe and God bless!

[@boblobster5126]

This man is a god. In just a 22 minute video, he was able to teach me everything my teacher couldn't in an entire week. Not only did he teach me everything, he also explained why, like at the 12 minute mark when he explained why you use the starting coefficient, instead of my teacher just saying it as fact. I went into this video fully thinking that I would fail my test tomorrow, and came out 100% certain that I would get a good score, thank you so much Mario.

[@MariosMathTutoring]

You’re welcome! Glad the video helped you. Good luck on your exam.

[@boblobster5126]

@@MariosMathTutoring I got a 98, that you so much man.

[@CaptainTass]

It's all confusing as hell. I guess I'm just a dumbass.

[@migs_frias]

great!

[@hamzebeshir6406]

hey, teacher mario first thanks of all but i have a question when your'e ploting additional points or using the sign analysis in the first example, you've used the plot additional points method so when taking values you took -0.9 and 2.9 and that's where i couldn't understand how are you taking these values???????

[@inaayabintislam2590]

I don't know why our teacher can't teach like u

[@ericdotcom99]

Good tutor

[@MariosMathTutoring]

Thanks Eric! Glad my videos are helping you!

[@ericdotcom99]

@@MariosMathTutoring yes sir, can you kindly do this one for me |3x+1|-2 is less than or equal to zero

[@jonathana9236]

Thanks Mario very helpful!
Any video where I know how to graph.......... F(x) = 3x^4 -10 ???

[@_justchill777]

Thank you so much for these tutorials, they have saved my life over and over again

[@MariosMathTutoring]

Great to hear!

[@KingShark-rh3nk]

Thank you for the help. I was struggling a bit with this section, but this video was very informative and helpful. God bless

[@MariosMathTutoring]

Glad it was helpful!

[@apsara445]

Done

[@saachiyadav4739]

you are better than my professor

[@Shixye21]

This video helped out a lot!!

[@menandrolapada1340]

Good day sir. Very easy and crystal clear to understand your presentation. Can you please re-check the answer on the long method division (y=x-2)? Will it affect the graph, sir? Thanks again, sir.

[@jwmonkey0483]

You make this easy, but how do I find things like the x-intercept and graph it when the numerator is -4? There’s no variable for me to get one
The problem is -4/x2-4

[@hellohi1722]

I love you ur amazing

[@yabaliyu3418]

Why it is always simple?

[@epoch_ag]

You're a legend

[@aupatrick]

Thank you very much. What a great explanation.

[@MariosMathTutoring]

Glad it was helpful!

[@menbiWelde]

keep it up

[@simonyheyis821]

Wow 👌

[@VIDHIjj14]

Thanks

[@akachanfukuro1747]

is it ok to use synthetic division instead of long division?

[@Anythin09010]

Thank you sir for helping me through my class

[@MariosMathTutoring]

You’re welcome. Glad to hear my videos have helped you.

[@rezescat780]

12:40

[@theTSAguy]

NOW....i finally get it

[@MariosMathTutoring]

Glad my video was able to help!

[@elisiemartinchirwa9397]

Thank you so very much this really helped

[@MariosMathTutoring]

Glad it helped!

[@GiftMlinde]

Thenks sir u have helped me alottt!!

[@MariosMathTutoring]

You're welcome!

[@gisellejung3567]

THANK U, YOU ARE AMAZING MAN

[@aidanl3105]

best video on this topic by far

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[@Bamenglish5798]

This is so helpful! Thanks a lot!

[@MrMossadiq]

❤❤❤

[@justachildofGod]

Thanks so much

[@liaver3148]

HOW DO I FIND THE POINTS ?!!

[@neutronzz3543]

Chose random points usually to the right and left so use like 2 and the opposite-2

[@efrataanteneh4763]

Tank you so much

[@elizabethmutale6331]

Thank you😊😊😊

[@caseatt1e975]

thank you!!!

[@MariosMathTutoring]

You're welcome!

[@nwzz2916]

Thank you!

[@angelc5066]

i really didn't get it😭

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The best maths teacher ever
Sir i also watched ur capacitor series
Awesome 🙂🙂🙂🙂🙂🙂🙂

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Lifesaver

[@IM_RAPIST]

man, I love u. Life saver