Graphing Rational Functions and Their Asymptotes
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- เผยแพร่เมื่อ 21 พ.ย. 2017
- 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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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
probably graphics teachers don't have access to and you listened and he doesn't have to classroom manage.
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.
3:51 Great👍
There could be an asymptote if m>n by just 1. That's slanted asymptote
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.
Your lessons have helped me so much thanks once again
Thanks math jesus❤️
He's the mathiah! lol
Our Lord and Solver
Lmfao
😂💀
No you did not 🤣🤣🤣
*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*
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.
I remember "Our asymptotic love story" :'
awts gege
@@jazzphetmacahig4578 HAHAHAHAHAHAHA gege
Amazing ! Wonderful ! You cleared so many things in so efficiently!
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.
*immaculate precise explanation* 💕
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 < m or m > n then y = No Horizontal Asymptote..
you said the same thing twice....
Really nice job explaining this!
This helped me a lot! Thanks!
3:24 Does that mean there can never be more than one horizontal asymptote in ANY function? or just in the given function
this is amazing thank you
amazing stuff thanks
what is the video app change background the background? thank you
Thanks a lot professor Dave!
Great video and put me right on a few things there, thank you Professor Dave :-)
I always get so excited watching his videos that I even start dancing when the iconic into starts
😂
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
You make math seem so easy 😌
fr
how do we interpret the results gathered when testing selective x values? how do we know where the points are specifically?
on 4:18, it should be n
n refers to the denominator
@@ProfessorDaveExplains oh sorry in our school n refers to the numerator, but nevertheless thanks for helping me out prof dave! 🥰
I thought so WHEN N LESS THAN M IT SHOULD 0
Thanks man ,I have an exam tomorrow and this really helped out
I still don't get this 😂
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.
maybe your are just not at that level yet to be able to understand it. I find it very easy to understand
@@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
@@etzjunior_ lol bro I feel the same way tf
You are not alone I'm also lost in the asymptote😢
is there any way to use transformations directly, like derive the graph of these polynomial functions directly from its parent function?
N>m is y=0, but the other teach as n
Thanks a lot sir❤
Thank you very much!
Thank you so much
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
Thank you good sir
Thank you every much!
Thank You Professor Dave, but you did not talk about Curvilinear Asymptotes.
these stuffs are gold
Really good please guide if the numerator leading degree power is higher than denominator leading degree power
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!
I always had time but you explained it explicitlu
Thnks prof but we need more examples in order to understand thnksr again and again
at 0:41 seconds you mentioned the denominator cant be 0 but during checking comprehension answers your denominator came out to be 0.
many thanks
Thank you po
4:24..."we can test select values of ...y?
How do you pick the points tho
Pretty sure you just pick some points on the graph to draw it, mostly the ‘x’es in which the graph would lie
What if there is a mod
Thanks!
What about oblique asymptotes and holes?
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.
Thanks sir
A real hero 👏
the plotting the points on the asympotes is too hard there must be an easier way...
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!
@@nandini2040 what? I dont fucking understand anything, goddayumn
@@radia4752 lol, man I hate calc....I wish I had this guy as my teacher
Are you doing this in Powerpoint?
thank you professor...but can you pls tell me what kind of functions do have slant asymptotes...
hmm, hyperbolas come to mind
thank you! my professor doesn't teach these things...
u should have learnt these in high school
@@YLprime "learned " and no unfortunately not i was a slacker and only took up to algebra 2 in highschool then accounting
@@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.
thanks
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
Add more explanation professor Dave
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)
Your saving my math grade
Thankyouu
your mother must be very proud of you. :)
Hello! What website was used in graphing the function?
i love your intro
ur amazingggg
Thanks for the video
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
@@ridmicmeena4123 hi there!
It's been long since I watched this video... I will rewatch and revert u back soon!
@@jennifer_3683 thank you so much i really appreciate it 💜
😊intro
we stan professor dave
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
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
Thanks
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
Doesn't show how to graph slants. Ugh
Thank you math Jesus!
great video but its half knowledge , you didn't talk about x,y intercepts - those are key metrics for plotting,
moist critical in a parallel universe
Why is he talking like he's at a gunpoint?
Faxxx😂
thank you math jesus
ohmygod thanks
Thank you Dave Grohl
i love you
Wala akong naiintindihan lord
Ty Jesus 🙏😀
Thank you Jesus
THANX FOR MORE CONFUSION
Mind giving me a shoutout homie?
Being an indian villagers watch this video
I give 7mins of my life on learning things.. I still don't understand 🤦♂️🤦♂️
thx 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
he aamhi kelay ;(
Wala parin akong maintindihan 😍
That is not a nice name to call him.
u look like jesus
math jesus thx
This doesnt help at all
Thanks sir