Finding Vertical and Horizontal Asymptotes of Rational Functions

[@1twothree4]

I HAD NEVER UNDERSTOOD THIS EVER UNTIL NOW. THANK YOU.

[@sarahjanetanedo1100]

Hahahahhaha me too 😂😂

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OUR EXAM'S ARE TOMORROW. ITS 3AM AND I LOVE U

[@thanossmith1126]

Same

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I have a test tomorrow 😳

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Mine is in 30 minutes lol

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good thing it wasn't an english exam

[@t.9j_]

i am watching this video after 8 years and you explain everything in a perfect way that we can solve any similar problem thank you man

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Woah 8 days ago

[@zub4516]

YOU ARE ABSOLUTELY AMAZING!!!!!! after searching for hours I come across this masterpiece and it literally saved my life. I cannot thank you enough..

[@rayann.669]

u just explained that better than anyone on the internet and i love u for that

[@jortiz9475]

Dude you are amazing i didn't get it till i saw this. God Bless You sir.

[@ashain1463]

dude i love you for this no place has vertical and horizontal together thanks a lot

[@airicadaria1739]

You're the best! I've watched too many tutorials on this, they're all confusing af

[@jennifernarbonne3405]

Thank you. Every other source was explaining this so poorly. You nailed it.

[@siyam7401]

U have no clue how easy you made life for me. THANKYOUUU.

[@hsmathsolutions]

I'm glad I could help!! :-)

[@peiqi7787]

thnk you im gonna cry

[@theeargasmchannel]

Honest mood

[@maignanmclopez345]

Couldn’t explain it clearer, great job on demonstrating these examples, I was able to understand on mute due to my location at the time I couldn’t turn up the volume

[@sghand1218]

Just to add, I also enjoy your guitar picking and the songs in your videos!! Thank you!

[@misantrophic3580]

Dang he should earn 1m subscribers than 1k something. This dude teaches greaterthan my professor!

[@morningstar2728]

Thank you! James This will help me to get quickly V.A and H.A in MCQ without wasting time on differentiating....

[@varunjhamvar3600]

thank u!! Finally someone covered all the examples!

[@hsmathsolutions]

Glad it was helpful!

[@RBISmael]

Best explaination out of 100 vids

[@micamunoz4745]

Dude after so long I got a high score in my math worksheets thanks to youuu

[@hsmathsolutions]

Awesome! I'm glad I could help!

[@GabrielMariMan]

Thank you so much! Best tutorial on this topic I've found yet on youtube :)

[@karimspeleman2349]

my man saving my points at school.

[@hamasahmad8444]

Best video ever may you stay blessed bro✌🏻

[@mariamaleksanian]

You are my savior, thank you!!!

[@steph2Gee]

Thank you man. You save my life.

[@fatimaabdullah8224]

Thanks ... you taught this topic very well 👌

[@gannamohamedibrahimhelal6076]

It became too easy now really Thank you soooooooooooooo much ❤️❤️

[@sghand1218]

Thank you so much for showing this example of asymptotes. It made learning so much clearer. I am now looking to solve Oblique asymptotes, but cannot find your video for that? Do you have one? Also, I am so thankful you have the Vertex and other functions in your teaching videos. Your videos will get me through this college algebra!! Thank you again.

[@doohickey3710]

This video is simply very helpful for my homework

[@dummykotik9080]

Thank you for teaching this clearly! Really understood it better! 😊

[@ruchiradaluwatta9898]

Very clear explanation. Many thanks sir

[@drag0nh0rn]

Thanks so much for the video! Have my Maths exam in 2 days and I didn't understand this until now!

[@shohruxibragimov2411]

Thank you, James!

[@jenovaheskalion999]

thank you this helped me a lot in my calculus

[@ziyolamusic2066]

Yeah it's my summative exam tom and this is the Coverage for summative assessment. Gen. Math: asymptote problem solving involving rational equation(motion and number problem), exponential equation, exponential inequality, exponential function, logarithms and logarithmic properties. Pre cal: Systems of Non linear equation Series and sequence Sigma notation Fundamental identities

[@hsmathsolutions]

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[@johnrayballon6666]

DUDE YOU ARE AMAZING YOU JUST SAVED ME!

[@kevinjacobavediangonzalez1354]

amazing video! super clear and easy to follow

[@bonbonpony]

05:41 Actually, there's one more asymptote in this example: y = x² + x + 1. If you add it to your graph, you will see that the branches of the curve approach this parabola as `x` increases/decreases without bounds. 06:18 Well, at least not in the plane of the graph ;>

[@AadityaChawla-bc4ic]

I don’t understand can you please elaborate.

[@bonbonpony]

@@AadityaChawla-bc4ic Start with the rational function from the video: `y = (x³+2) / (x-1)`. Divide out the numerator `x³+2` through the denominator `x-1` (e.g. using polynomial long division) to get the polynomial part `x² + x + 1` and the remainder (which is still rational) part `3/(x-1)`. In other words, you get the following decomposition: y = (x³+2) / (x-1) = x² + x + 1 + 3/(x-1) Now observe what happens when `x` increases (or, for that matter, decreases) without bound: the denominator `x-1` in the last term (which is still rational) gets bigger and bigger, which means that you divide the numerator `3` into more and more parts, so each such part gets smaller and smaller, i.e. the entire fraction shrinks to 0, leaving just the polynomial part `y = x² + x + 1`, which is a formula of a parabola. This means that as `x` gets bigger and bigger (either positive or negative), the graph of this function starts looking more and more like a parabola `y = x² + x + 1`. Here's a graph that demonstrates it: www.desmos.com/calculator/kjs0e3ivya Notice how the blue curve approaches the red parabola as `x` gets more and more negative. But when `x` becomes more and more positive, approaching `x=1`, the curve gets farther from the parabola and starts approaching the vertical asymptote (which is a straight line) instead, `y` going towards `-∞`. Then it returns on the other side from `+∞` and starts diverging from the vertical asymptote and getting closer and closer to the parabola again as `x` increases even further (as well as `y`, going towards `+∞` again). You can also turn the green graph on or off to verify that these two formulas, `y = (x³+2) / (x-1)`, and `y = x² + x + 1 + 3/(x-1)`, are indeed the same function. Also try zooming the graph in/out with your mouse wheel to observe how the graph approaches the straight vertical line as well as the parabola as `x` gets bigger (disregarding its sign) without bounds.

[@himlolo]

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[@bonbonpony]

@@himlolo Oh yeah? Then try me.

[@salmofn]

THIS VIDEO SAVED ME

[@hernestinedjakou3285]

wow the only video i understood. thank you

[@lockedgaming6549]

Thank you James!

[@anushkamalik7522]

Amazing explanation

[@christianlee7824]

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[@krave1324]

Great explanation!!!!!

[@riyadulislam9832]

thanks so much. That was very helpful. ✌

[@Radeo12]

Thank you so much! Much more helpful.

[@floridaboi217]

Easy, well explained and a nice variety, thanks man!

[@crislyngerolao9686]

On 1:55 why is the curve on the upper right corner? Cant it be facing the left? And the other one to its right???

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lexine potter 🗿

[@TheGates7]

Thank you soo much for this video dude. Really helpful

[@mahalfatah7783]

Not me getting ready for my.exam on the bus

[@crislyngerolao9686]

I mean in 1:55 why is the curve on the Quadrant 1 and not on Q2? Then the curve on Q3 not on Q4??????

[@judiemoody5321]

Thanks I’m so grateful!!

[@limsolalin4419]

Thanks, this actually HELP a lot

[@ritsk2074]

Thanks man!!Finally got it

[@RDFspaniard]

Fyi x^2+1 can be factored, but it's factors are not on a real number graph.

[@spaz3216]

Thanks for you video! Great explanation ! I understood everything thanks to you!🙏

[@Biswajit_G]

Well explained 👍👍

[@hsmathsolutions]

I'm glad it was helpful! :-)

[@Biswajit_G]

@@hsmathsolutions sir I just checked most of your video all are very well explained.❤️❤️ Love you Sir from India ❤️

[@hsmathsolutions]

I'm glad you are watching my videos and finding them helpful! Be sure to share them with your classmates!!

[@aliwaleed7053]

Thanks, I finally got it, thank you sooooo much!!!

[@joycexie8537]

4:48 I have a question, if shouldn't you factor out the numerator and the denominator first and cancel out (x+2), which would be a hole?

[@hsmathsolutions]

Thank you for your question. In that example, the numerator is prime and will not factor; thus no terms will cancel out. But you are right, if it did cancel, there would be a hole instead of an asymptote. Also, you can take a look at the graph for confirmation.

[@joycexie8537]

Ohh.....I see it now! There would be a middle term if the numerator were to be factored into (x+2)(x+2) I was not looking carefully XD Thanks for replying.

[@RellianPagulong090]

May god bless you... Amen!!!

[@blessedlarissa452]

Thank youu soo much ♥️♥️

[@kwakei1424]

Thanks alot, brother!

[@hsmathsolutions]

You're welcome. Glad it helped!

[@tinaeden8317]

Excellent video. So helpful and succinct!

[@SylvesterSimukoko]

You're the best

[@MichaelPeters2004]

Very helpful, appreciate it.

[@toothyguardian6343]

Thank you for this sir!

[@christinesahakyan3609]

Thanks! U are the best

[@silentkid1003]

i hope u r our math teacher, cos we just finished midterm exam, and no one passed the examination ☹️

[@EnClix]

Very helpfull sir

[@丅〆]

Please Tell How to Plot this on Graph

[@丅〆]

We give values to hole equation or only x-3 for graph

[@EulersRoadTrippin]

How do you know how to graph these lines (functions) within the multiple vertical an horizontal asymptotes?

[@malikfatima3466]

thanks a lot sir

[@amielraphaelsalarda4923]

Thank you so much!

[@krazythekid]

We just not gonna talk about how he's doing all his math in pen?

[@jeaulrahaman4973]

Outstanding

[@debabrataghosh8971]

Thanks ❤️

[@shbhok6866]

Thank u sir

[@devendrautekar7305]

Why did you equate the denominator to zero in case of vertical asymptot?

[@akashdeepsingh4539]

Nice video

[@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.

[@hsmathsolutions]

Lemuel Castillano Yes. Sounds good.

[@ThomasFlanagan-vr7nz]

what makes the fraction rational?

[@LostInsan-fr3rc]

thanks so much sir

[@DemiseReturns]

Thank you I was so lost

[@siyam7401]

I LOVE YOU.

[@MuhammadSaadKhanIBAKAGY]

love u helped alot

[@youknownothingjonsnow2418]

what if the function doesn't have a denominator? fx= x+3x+7??

[@hsmathsolutions]

If the function doesn’t have a denominator, then there will be no asymptotes. Vertical asymptotes arise from division by zero. Without a denominator, there cannot be division by zero. Horizontal asymptotes arise from comparing the degrees of the numerator and denominator. Again, if there is no denominator, then there is no horizontal asymptote. Hope that helps!

[@farhakhan4288]

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Anyone watching from 2024

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Thank you so much

[@aeriee.__]

Thank youuuuu ♥️

[@DM-gw8zx]

THANK YOU

[@milesmandar5234]

What about vertical and horizontal shifts

[@hduque8153]

Professor, good morning. You no longer posted math classes. I haven't received notice of his posts in a long time. (Brazil-RJ)

[@Ahtohallan.]

Thanks xx thanks thank you X

[@angelicamaerequina7616]

what is the factor of x squared -2x? hope u can help me thank u

[@angelicamaerequina7616]

x squared -2x?

[@hsmathsolutions]

x^2-2x=x(x-2)

[@angelicamaerequina7616]

thank you so much

[@sa758]

i don''t understand one thing, my professor uses limits to find them and no matter how many videos i look up they all use this method, am i missing something?

[@selenadookaran4984]

thank you! I have a question like this 3x^2 + 17x + 10 / x^2 + 7x +10

[@hsmathsolutions]

The numerator (3x^2+17x+10) will factor as (3x+2)(x+5). The denominator (x^2+7x+10) will factor as (x+2)(x+5). The (x+5) factors will cancel between the numerator and denominator. However, the denominator still has the (x+2) factor. So there will be a vertical asymptote at x=-2 (x=-2 causes the denominator to be zero), and a hole in the graph at x=-5 because those factors canceled. Hope that helps!

[@elianaguerrero69]

Thank you

[@jask320]

The second graph is not correct, there is a max point for the right side at (8, 0.0625) if you take a first derivative and then it goes down to zero inf.