Graphing Rational Functions and Their Asymptotes
You might think we are all set with graphs, but you're wrong! We will learn about many other types of functions as well as how to graph them. First up is rational functions, which are quotients of polynomials. How can we graph these? We have to find their asymptotes. What's that? Sounds sexy. Well, it is, kind of.
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Пікірлер: 142
Bro why do teachers not teach like this. It actually pisses me off why they don’t teach so well and simple with patience. I’ve learned more in 7 minutes than my teacher did in a week
@user-mr7xw1mr9z
3 ай бұрын
probably graphics teachers don't have access to and you listened and he doesn't have to classroom manage.
@basketguitar9768
2 ай бұрын
Your teacher probably has poor public speaking skills, making it difficult to focus on what they're saying.
a video with 7.24 duration taught me better than 2 hours of pre-recorded lecture by a lecturer
This was my first time watching one of your videos, and the into alone made me smile.
Your lessons have helped me so much thanks once again
3:51 Great👍 There could be an asymptote if m>n by just 1. That's slanted asymptote
@RadoHudran
2 жыл бұрын
Yup On my exam they literally gave me such a problem where m>n and I couldn't do it. Lesson learned: Even if your source seems reliable, always check multiple sources to be sure
Thank you! I am currently using Aleks for my Precalculus course and the instructions and explanations were very unclear but this video answered every question I had.
I remember "Our asymptotic love story" :'
@jazzphetmacahig4578
3 жыл бұрын
awts gege
@scarletblue8685
3 жыл бұрын
@@jazzphetmacahig4578 HAHAHAHAHAHAHA gege
Thanks math jesus❤️
@yeetdelete2816
2 жыл бұрын
He's the mathiah! lol
@abellevanceryans.6775
2 жыл бұрын
Our Lord and Solver
@supcutiewannaride
2 жыл бұрын
Lmfao
@cindychilufya9220
Жыл бұрын
😂💀
@aramacabenlar4786
Жыл бұрын
No you did not 🤣🤣🤣
Im sick with covid and missing this portion of the class where my professor did not extend the time for homework for me to rest. Once more, she told me to reach out to tutoring to teach me this stuff when it is due tuesday and they are only open on the monday. You are a lifesaver, thank you so much! This video has cut through brain-fog more effectively than the textbook and exercises posed by my college algebra class.
*just the word thank you cant express my feelings and i cant seem to express in words just how much your lessons means to me*
I always get so excited watching his videos that I even start dancing when the iconic into starts 😂
Thank you so much for this tutorial. I am learning things I've never known before because I realize that there are so many things in life that I don't know about. The truth is, I'm learning Further Maths due to having some interest in mathematics and I wanted to know my true capabilities by learning things beyond what I'm supposed to cover because I'm only in year 9. I've done the same thing in some Oxford university maths lectures. I want to finish watching the ones on complex numbers and dynamics.
3:24 Does that mean there can never be more than one horizontal asymptote in ANY function? or just in the given function
*immaculate precise explanation* 💕
what is the video app change background the background? thank you
Correction sir on 3:49 you thought that when n > m then y = 0? and when m > n then y = NHA? But according to the books and some references it is not. The correct is: If n > m , then y = 0 If n n then y = No Horizontal Asymptote..
@ashauna3916
3 жыл бұрын
you said the same thing twice....
You make math seem so easy 😌
@lynx3953
Жыл бұрын
fr
Amazing ! Wonderful ! You cleared so many things in so efficiently!
this is amazing thank you
amazing stuff thanks
Really nice job explaining this!
This helped me a lot! Thanks!
how do we interpret the results gathered when testing selective x values? how do we know where the points are specifically?
Thanks a lot professor Dave!
is there any way to use transformations directly, like derive the graph of these polynomial functions directly from its parent function?
I swear you are making me love maths
My problem is that i cant just came up with random numbers strategically for drawing z graph
Great video and put me right on a few things there, thank you Professor Dave :-)
Thanks man ,I have an exam tomorrow and this really helped out
these stuffs are gold
I still don't get this 😂
@ErinRaciell
4 жыл бұрын
Its because instead of making a multistep process so its easy to digest he go straight to the the no intuitive part of the rational function.
@YLprime
4 жыл бұрын
maybe your are just not at that level yet to be able to understand it. I find it very easy to understand
@etzjunior_
3 жыл бұрын
@@YLprime i don't understand the graph. He was saying, "as we plug in numbers, we get closer and closer to 0", but as he was saying that, the dots that were appearing were moving away from 0. Tf
@jokersjoke1204
3 жыл бұрын
@@etzjunior_ lol bro I feel the same way tf
@makgabomashala4859
3 жыл бұрын
You are not alone I'm also lost in the asymptote😢
Thank you good sir
Thank you very much!
N>m is y=0, but the other teach as n
Thanks a lot sir❤
Thank you every much!
on 4:18, it should be n
@ProfessorDaveExplains
3 жыл бұрын
n refers to the denominator
@plm.agsikapin2025
3 жыл бұрын
@@ProfessorDaveExplains oh sorry in our school n refers to the numerator, but nevertheless thanks for helping me out prof dave! 🥰
@wingsoffreedom7138
2 жыл бұрын
I thought so WHEN N LESS THAN M IT SHOULD 0
Thank you so much
How do you pick the points tho
@twinkelry2410
3 жыл бұрын
Pretty sure you just pick some points on the graph to draw it, mostly the ‘x’es in which the graph would lie
Thank you!
A real hero 👏
I'm watching many of your series. Fantastic teaching. I Always stop your videos at any important hint and look for it on other videos or search google bard etc to complete my tutorial. Thank you
I always had time but you explained it explicitlu
many thanks
Thank You Professor Dave, but you did not talk about Curvilinear Asymptotes.
Thanks!
What about oblique asymptotes and holes?
@carultch
5 ай бұрын
Oblique asymptotes are asymptotes that aren't parallel to either of the two coordinate axes, but instead approach a diagonal line. You'll see this for rational functions, when the numerator has a higher degree than the denominator. As an example, y = x^2/(x + 4) has a behavior, where in the long run, it approaches the line y = x - 1. This occurs both as x approaches infinity, and as x approaches -infinity.
Really good please guide if the numerator leading degree power is higher than denominator leading degree power
@carultch
5 ай бұрын
If the denominator has a higher degree, it will have vertical asymptotes at each pole, and horizontal asymptotes at y=0. If the two degrees are equal, it will also have a vertical asymptote at each pole, but its horizontal asymptotes will be shifted to a different vertical position. If the numerator is of a higher degree than the denominator, it will have oblique asymptotes instead of horizontal asymptotes. The vertical asymptotes will still oxxur at the poles.
Thank you po
Are you doing this in Powerpoint?
Thanks sir
4:24..."we can test select values of ...y?
the plotting the points on the asympotes is too hard there must be an easier way...
@nandini2040
4 жыл бұрын
there is! for the horizontal asymptote, our teacher told us to calculate the value of the limit of x approaching infinity for the function. if you've done limits, it's pretty easy to get it right. for the vertical one, check for points where the denominator is zero. this is because the vertical asymptote is defined as the finite value of x where y approaches + or - infinity. hope that helps!
@radia4752
3 жыл бұрын
@@nandini2040 what? I dont fucking understand anything, goddayumn
@Trynnagetmydegree__
3 жыл бұрын
@@radia4752 lol, man I hate calc....I wish I had this guy as my teacher
thank you! my professor doesn't teach these things...
@YLprime
4 жыл бұрын
u should have learnt these in high school
@alexiadd636
4 жыл бұрын
@@YLprime "learned " and no unfortunately not i was a slacker and only took up to algebra 2 in highschool then accounting
@Juuqe
3 жыл бұрын
@@alexiadd636 learnt* Americanised English only makes up a small percentage of all english speech, grammar and spelling. To correct someones spelling when they are a part of a larger, more popular group is probably incorrect. Know your place woman.
I have been watching this series since December. Now I can solve math equations I never thought I was ever able to even comprehend. I am forever grateful
Your saving my math grade
at 0:41 seconds you mentioned the denominator cant be 0 but during checking comprehension answers your denominator came out to be 0.
Thnks prof but we need more examples in order to understand thnksr again and again
thanks
we stan professor dave
ur amazingggg
Add more explanation professor Dave
i love your intro
What if there is a mod
Hello! What website was used in graphing the function?
your mother must be very proud of you. :)
The solving of horizontal asymptote is wrong In the video its shown N>m means y=0 When in reality it means theres no horizontal asymptote
😊intro
Thankyouu
Why is he talking like he's at a gunpoint?
@Chakamatics
3 ай бұрын
Faxxx😂
thank you professor...but can you pls tell me what kind of functions do have slant asymptotes...
@ProfessorDaveExplains
4 жыл бұрын
hmm, hyperbolas come to mind
Thanks for the video
@ridmicmeena4123
Жыл бұрын
hi it looks like you get everything in this video I have a doubt plz help me so in the first and last Q of Checking comprehension the y = 2 and y=3 so did we take 2/1 and just ignore the 1 and same in last one did we take 3/1 and ignored the 1 and wrote only 3 plz help me as soon as possible
@jennifer_3683
Жыл бұрын
@@ridmicmeena4123 hi there! It's been long since I watched this video... I will rewatch and revert u back soon!
@ridmicmeena4123
Жыл бұрын
@@jennifer_3683 thank you so much i really appreciate it 💜
The definition for asymptotes is incorrect. Asymptotes are not lines since lines are real object. Rather, they are boundaries. Second, the function can touch and even cross asymptotes such as in the case of (x-1)/(x^2 - x - 6)
moist critical in a parallel universe
Thank you math Jesus!
Professor,why the coordinates of 2/(X-1) are (2,1) at 5:30 when it should be( 2,2) I may be wrong please explain me
thank you math jesus
Thanks
@ridmicmeena4123
Жыл бұрын
hi it looks like you get everything in this video I have a doubt plz help me so in the first and last Q of Checking comprehension the y = 2 and y=3 so did we take 2/1 and just ignore the 1 and same in last one did we take 3/1 and ignored the 1 and wrote only 3 plz help me as soon as possible
ohmygod thanks
Doesn't show how to graph slants. Ugh
i love you
great video but its half knowledge , you didn't talk about x,y intercepts - those are key metrics for plotting,
Thank you Dave Grohl
THANX FOR MORE CONFUSION
Ty Jesus 🙏😀
Wala akong naiintindihan lord
Thank you Jesus
The Freddie Mercury Rule: If a rational equation is bottom heavy, its horizontal asymptote will be equal o zero. This is because of the fact that Fat Bottomed girls make the rockin' world go round, Zeroes are round. QED
Mind giving me a shoutout homie?
thx jesus
Being an indian villagers watch this video
I give 7mins of my life on learning things.. I still don't understand 🤦♂️🤦♂️
he aamhi kelay ;(
math jesus thx
Wala parin akong maintindihan 😍
u look like jesus
That is not a nice name to call him.
This doesnt help at all
Thanks sir