Graphing Rational Functions With Vertical, Horizontal & Slant Asymptotes, Holes, Domain & Range
This algebra 2 / precalculus video tutorial explains how to graph rational functions with asymptotes and holes. It shows you how to identify the vertical asymptotes by setting the denominator equal to zero and solving for x. It shows you how to find the equation of the horizontal asymptote by comparing the degree of the numerator with that of the denominator. In addition, it shows you how to find and graph the slant asymptote / oblique asymptote using long division. This video also shows you how to identify the x and y coordinate of any holes in the graph. This video contains plenty of examples and practice problems including those in which factoring quadratic expressions and equations are involved. This video also discusses the transformations that occur when graphing rational functions. Horizontal and Vertical shifts are covered as well as reflection over the y axis and the origin. In addition, this video shows you how to the coordinates of the x intercept and y intercept. Finally, this tutorial shows you how to write the domain and range of a rational function using interval notation. It mentions when parentheses and brackets should be use. Whenever you need to write the domain of a rational function, you need to take into account the vertical asymptote and the x coordinate of any holes in the graph. For the range, you need to remove the horizontal asymptote and the y coordinate of any holes in the curve. This video might be useful for students taking calculus.
Fundamental Theorem of Algebra:
• Fundamental Theorem of...
Rational Expressions - Basic Intro:
• Rational Expressions -...
Simplifying Rational Expressions:
• Simplifying Rational E...
Multiplying Rational Expressions:
• Multiplying Rational E...
Dividing Rational Expressions:
• Dividing Rational Expr...
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Adding & Subtracting Rational Expressions:
• Adding and Subtracting...
Rational Expressions - Unlike Denominators:
• Adding and Subtracting...
Simplifying Complex Rational Expressions:
• Simplifying Complex Ra...
How To Solve Rational Equations:
• Solving Rational Equat...
Rational Equations - Extraneous Solutions:
• Extraneous Solutions o...
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Horizontal and Slant Asymptotes:
• Horizontal Asymptotes ...
Finding Rational Functions Given 2 Points:
• How To Find a Rational...
Rational Functions - X and Y Intercepts:
• How To Find The X and ...
Graphing Advanced Rational Functions:
• Graphing Advanced Rati...
Rational Inequalities:
• Rational Inequalities
________________________________________
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@komartiketmusa8447
4 ай бұрын
splendid!!
0:10 y=1/x -- 2:10 y=1/x^2 4:30 y=1/x-1 11:36 y=(1/x+2)-3 16:30 Graphs of y=1/x 17:54 y=(-1/x+2)+3 22:13 y=(1/(x-2)^2)+1 24:44 y=(-1/(x+1)^2)+2 28:00 HA OF same degree functions 30:44 HA of bottom heavy 31:47 y=((2(x-2))/(x-3) 35:35 y=(3x^2+9x-12)/(x^2+x-2) 44:40 Slant asymptote y=(2x^2+6x-8)/(x-2)
@blockydogy1188
3 жыл бұрын
my hero
@whyareyougae6839
3 жыл бұрын
You dropped this king 👑
@pikatothechu4737
3 жыл бұрын
You're the MVP
3 жыл бұрын
love how gaming also has to do homework
@maitemookamedi1700
2 жыл бұрын
Thank you
anyone else crying in math class? :)
@Fishfriend001
3 жыл бұрын
Yes🥲
@sondersiya
3 жыл бұрын
@@Fishfriend001 yes 😢
@yunosogasii6200
3 жыл бұрын
Yes🥲
@official_kea_rsa
3 жыл бұрын
Every day
@bruh-cb9dc
3 жыл бұрын
yes ma’am
I wouldn't be passing precal if it wasn't for you, really appreciate the videos
@rudyj8948
4 жыл бұрын
Literally same
@memes4themasses365
3 жыл бұрын
I’m with ya rn
@quinive9812
3 жыл бұрын
no matter what i do i still fail pre cal. would it help me pass if i watched all pf his vid?
@No-dy3zk
3 жыл бұрын
I got to do this for Algebra 2.
@Jackripz
3 жыл бұрын
@@No-dy3zk same
man really taught me a whole unit in an hour that my teacher couldn't explain in 2 weeks
@xrzenel_8072
Жыл бұрын
I feel that
@shanepotter6348
Жыл бұрын
You got 2 weeks to learn this? I got 2 days 😭
@princewillanyagagligbo6890
11 ай бұрын
glazing
@MZZ745
9 ай бұрын
@@shanepotter6348I got 1 day💀
@kiriuzi7959
8 ай бұрын
lmao try a day or approx one hour @@shanepotter6348
I started at 2 am and now it's 6 am ... This whole time I was studying graphs and all from your videos 😭♥ Am really thankful for each and every video u made , you just don't know how much this meant to me !! You are a life saver May God bless you and your family My number one hero!!
@Stunz
3 жыл бұрын
How did you do??
@ashwinanand1465
2 жыл бұрын
@@Stunz L
@dissociating1703
2 жыл бұрын
@@ashwinanand1465 💀💀
@declanrodgers8004
2 жыл бұрын
orc
@maryyou556
2 жыл бұрын
Do u have a Playlist for all the videos u watched ?
currently 3am, school in 3 hours, math test 1st period, im fucked.
@squareeyes5942
3 ай бұрын
why do you get up so early to study?? how did the test go
@skandasringari2370
2 ай бұрын
@@squareeyes5942 went swimmingly I got a 94, for me math is easy to understand but I wasn't there for the whole unit so I had to study, also forgot to mention I'm a huge procrastinator
@aaliyahg4
2 ай бұрын
Me right now 🥲
@JacobMachenje
2 ай бұрын
Don't worry bro u ain't alone, you're gonna push through ok, hv some faith
@BamlakMengistu-qf3zx
Ай бұрын
Same here 😭
00:00 Degree of denominator is higher than the numerator. 28:05 Degree of denominator is the same as the numerator. 30:50 Degree of numerator is greater than the denominator.
@jeeves4490
2 жыл бұрын
This is what I've been looking for thanks bro
@vladimirsheydorov3776
Жыл бұрын
thank you!
@juaquiqui-kun4333
Жыл бұрын
@@jeeves4490 and I've been looking for you
@WeirdJeans
2 ай бұрын
@@jeeves4490 andddd I've been lookin for you all over the internet
Im SOOOO glad you added that -3 at 11:43. I've been looking for an example that affects HA, now I know how to interpret it. Thanks a lot!
This guy is a hero. I'm blessed to live in 2019 :)
@safteyhazard
4 жыл бұрын
what about 2020?
@iamgroot7684
3 жыл бұрын
This aged pretty well.
@iamgroot7684
3 жыл бұрын
But also not too well
@samisiddiqi5411
3 жыл бұрын
This aged like fine cheese. But blue cheese that is.
@frankiecott
3 жыл бұрын
@@samisiddiqi5411 that it did
KZread is gold when such videos exists. Thanks a million man
6:04 "now, if you have a piCkY teacher and you wanna draw a graph accurately..." YES I HAVE smh
Absolutely amazing, I was a little frustrated at the beginning but I stuck through to the end and I understand it entirely now. Thank you for your content!
@declanrodgers8004
2 жыл бұрын
046
This video is blessing me right now 😩 my teacher taught us this with so little explanation and this video explains everything in such detail 🙏🏼🙏🏼
at 11:15 the domain should be (-in,1) U (1,in) correct me if I'm wrong.
@nboris31
6 жыл бұрын
yeah, HE actually meant (-inf,1) U (1,inf), it's just some human errors that may just slip in anyone's work
@itayikatiro3564
5 жыл бұрын
Yeah, I noticed that too
@Edgylime6797lowl
4 жыл бұрын
(-in, 1)U(1, in) is correct
@pranavm.9513
4 жыл бұрын
he does it for free calm down
@fryPS
4 жыл бұрын
Your typical Indian Fisherman Literally no one is angry. Everyone is being cool about it.
I've learned a lot from this video! Thouroughly explained how to graph rational functions with ease. The best math teacher in you tube! Thank you Sir! =D
I’ve been taking Algebra II all year. I just realized that I love physics and that I’ll need math in the future. So I’m deciding to learn all pre calc in the next 3 months and then take the final. You’re so much help
@aryanrayana8065
Жыл бұрын
how did that go?
@lolmetyuri
8 ай бұрын
@@aryanrayana8065he didn't make it😢😢
You are a great help, straight forward videos, best on the internet. You are my main reference right now.
I would like to thank you for this amazing 58 minutes of incredible explanation that my teacher couldnt do within months
Your videos to watch are always helpful. I always search you up for Math topic explanations. For a problem, time on the video (10:47 to 11:05), you mentioned the domain as (- ∞,-1) ∪(-1, ∞). However, I feel it should be 1 in the domain not -1
@MainulWasTaken
11 ай бұрын
Me too It should X not equal 1
@drowzZzy_
10 ай бұрын
same thoughts
@superiorjr154
9 ай бұрын
You’re right.
@nerimaken482
7 ай бұрын
ok good i was confused 😭
@JoeSwick41
6 ай бұрын
thank you, i was thinking the same..
i'm gonna be honest, i have to do an online test today and i'm just binging all rational functions and equation videos 😀💔
I'm so grateful for this video. My math class is going a little too fast to keep up so you help me learn everything and have time to process it.
Thanks for you're contribution! i have been using this channel for three years.and it helped me a lot. i belive that you wiil teach my field of study in the future. i have full confident that i will be surved by your channel again. 🙏🙏🙏🙏
Wow , your way of teaching is extremely wonderful ,I really really appreciate your work 👏👏👏👏
Hi! Mr.chemistry tutor, I think the domain of the function in 11:26 is 1 not -1. The Vertical asymptote is x=1.
@EldanaG
2 жыл бұрын
Exactly what i thought... i was like Huh??
@cotyb5028
2 жыл бұрын
That's why I started reading the comments ha. Thanks!
@timeelapse619
2 жыл бұрын
Phew I thought I missed something
@soramin7926
2 жыл бұрын
Thx it confused me a little bit lol
@paulmaggiar8274
Жыл бұрын
@@maryyou556 1/x-1. x=1. 1 renders the denominator 0. 1 is the VA. What is throwing you off is that he got the domain wrong.
Thank you very much for taking your time to make these video's!! They are extremely helpful!
I have to say, I've watched about 50 of your videos, and a million times, thank you for what you do. I'm in precal and my class is tough for me. You really help me understand everything. Better than my professor explains it. seriously, you're the GOAT!!!!
@sanopann1896
Жыл бұрын
i just want to ask what grade you learning this stuffs mister
@WeirdJeans
2 ай бұрын
@@sanopann1896 12th ?
Hey. This guy is basically a genius in everything. He probably need to get an reward for that.
You're a genius. Thank you. Couldn't survive without you.
We need more people like you Thank you for your teaching.
this man an khan academy are my go-tos endless examples and explains everything thorough. Thank god for this individual
I had really given up asymptotes but this video is a life saver thanks alot pal
thank u so much my math teacher could never
I think I've watched this video at least once a year during high school. It's a tradition now.
Thank you so much man, you explain things really clearly and a lot better than most school teachers
How do I find a function when I have points? There is no x or y intercept, and only a horizontal asymptote.
Hi at 11:20, isn’t the domain (-infinity, 1)U(1, infinity)?
I love you. I say it every time I watch one of your videos. You give me hope for our species, thank you for sharing your talents with the world 🙌🙌🙌
omg you are a life saver because i had no idea how to do the graphing part but you explained it so well
Whoever made the video.. I will find you and I will marry you .. much needed video for my summer precalculus class
@youtubeweb3009
3 жыл бұрын
what if he doesn't want to marry you? haha just askin' though
@WeirdJeans
2 ай бұрын
@@youtubeweb3009use force
Relearning everything thanks for these videos!
I am very thankful for such a meaningful asymptote video. It's explained in detail carefully considering most possible cases of rational functions.
Thank You Sir, You are patient , articulate , and very thorough in your explanations . God Bless You ,and your parents
@sanopann1896
Жыл бұрын
i just want to ask what grade you learning this stuffs mister
Nice presentation very easy to understand... Math teachers should be precise in their explanations like you do...
@declanrodgers8004
2 жыл бұрын
9
Very great work JG, Always thank you.
Thank you so much!! You are the best.
This video was better than the last two weeks of reading about graphing rational functions. Thank you!
@sanopann1896
Жыл бұрын
i just want to ask what grade you learning this stuffs mister
@GabrielSanchez-rh6lv
Жыл бұрын
@@sanopann1896 i was taking a college algebra class. And believe me when I tell you this, math is not something I am good at. I struggle to have motivation to learn it and remember the formulas and understand why things are the way they are. But just apply yourself enough even if you may never do it again because learning is learning and you learn about yourself and ways that things make sense to you.
You are the best thing that has ever happened to us
Thank you so much. I totally understand all the things!
Thank you so much, I really needed this video👏👏👏
Thank you so much...you save me from this math for my grade 11 this 2020
Omfg I’m literally crying 😭 I’ve been struggling to understand and now I do!!!!!! THANK YOUU
you are the only one i listen to. You are a hero and understandable one. I thank you alot
I really appreciate you. I'm learning a lot
this guy deserves a medal
On the last rational : How do you know that (3, 23.8) is the vertex for that parabola?
Thank you for taking your time to explain this wonderful video
thank you very much for making this video
Super helpful, awesome! A big thank you to you!
@user-ny3dl1ju4e
4 жыл бұрын
And also you can use demos to find points as well.
Thank you!!!! really helped.
Thanks a lot this help me in guiding my son, Math is kinda hard now adays 😭😀
whats domain and range of the graph f(x) =2/x, i dont know what changes from this trandformation
This man has saved many lives
This man literally saved me I have no clue about anything in pre calc 😭
Can you please elaborate. Why is it the value of range/horizontal asymptote must be ax/bx, if y=ax+c/bx+e. For ex. The vertical asymptote must equate to 0 since having a 0 denominator is undefined.
Is it always the numerator to be used when finding x and y intercept?
13:20 "Oh Wow That's Terrible 🤣😂🥺"
@sweetener2535
4 жыл бұрын
Romeo Poomore Jshdjej that was adorable 😂
When this 60min video teaches you more and better than 4 2h precalculus classes
I genuinely love you
Awesome video, I didn't understand the last thing in but still awesome video
THANK YOU i have a math test today and this really helped me!!
I've been trying to figure out how to find the holes of a rational function for weeks and just figured it out 37:57
Thanks you soo much for your help :) Your video really helped me
This man is a legend
You are saving the world!!!
Thank you so much for saving my grade!!
thanks mate, I`m about to lose my scholarship, yet i hope that some staff that you taught me will help me to keep it! :)
This helped so much thank you
Thank you sm , my self study pre cal is consistent
Again, thank you very much. I really appreciate the videos you’re making. It really helped a lot😄.
I have a huge test tomorrow, thank you so much for your help.
@sanopann1896
Жыл бұрын
i just want to ask what grade you learning this stuffs miss
Thanks for your effort
This guy saved my math grade!!!
Really clarifies all our doubts
helped me pass my unit exam with this thanks bro👍
I appreciate u a lot I have understood all thing rational graph within this 58 minutes than my teacher trying to get me into rational graph well for an hours
@sanopann1896
Жыл бұрын
hi miss monaliza i just want to ask what grade you learning this stuffs
You’re a life saver omg thank u 😭😭 this is the first math video where I fully understood something.
Thank you for helping me
This video is amazing thank you
at 53:16 , shouldn't there be a bracket on 4.2 because it's touching? so it's be (-infi, 4,2]
@pa_u_los
4 жыл бұрын
Yeah, and also it should be a bracket in the 23.8 i guess, as it where it's the last point until the limit with the asymptote. It would be R (-\infty, 4.2] U [23.8, \infty] The thing is that this guy obviously is not going to read the comments, and good comments like this one get dissapear behind all the shit comments like Oh my god tysm! or whatever other shit. So yeah. I hope I'm right; if not tell me so. Edit: I'm right, you can try yourself with WA (WolframAlpha) that's what I did.
i literally fell asleep during class and saw random shit… ty😭😭 uve been saving my ass since algebra 1
Does anyone know if he has calculus 1 2 and 3 videos as well? I’m going to need those over the coming year!
the x-int at 39:36 is i believer +4, not -4 therefore when doing the line, it'll eventually touch the +4 as it goes down by the right side after th curve touches the P.O.D or the hole
thank you, I don't learn from my assigned teacher, I learn from you lol
love your work
Thank you so muchhh!!!
44:10 how about the y-intercept of the range should it be included
In finding the x -intercept for the problem at 40:00 do you not distribute 3 to (x + 4) then equate it to 0?
@Johnsonhzs
Жыл бұрын
Yup he didn't
god bless you . i have learned so much from you
Urgent! How do I know if a graf has extremepoints? For example: x/(x-2)? If in supposed to draw this graph, how should I know not to waste time on derivating x/(x-2) and setting it equal to 0?