How To Find The Vertical Asymptote of a Function

This algebra video tutorial explains how to find the vertical asymptote of a function. It explains how to distinguish a vertical asymptote from a hole and how to factor rational functions in order to identify all vertical asymptotes in a function. This video contains plenty of examples and practice problems for you to master this concept.
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...
_____________________________________
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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[@TheOrganicChemistryTutor]

Final Exams and Video Playlists: www.video-tutor.net/ Full-Length Videos & Worksheets: www.patreon.com/MathScienceTutor/collections Next Video: kzbin.info/www/bejne/oafLoahnidCGoKs Functions and Graphs: kzbin.info/www/bejne/kIWop2uFo6yUrtE Transformations of Functions: kzbin.info/www/bejne/qqq0faNsrZJ6pbc Graphing Polynomial Functions: kzbin.info/www/bejne/qICylpmaprKpqqM

[@kkakakkaka6617]

The way I’m doing a test rn and using these videos you my hero bro😭😭

[@jamzam9807]

Literally same

[@lleafaell7836]

lol same

[@kgothatsomokgatlhe9970]

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[@allietaylor244]

i’m doing that rn

[@memeland8430]

Wait we have a test?

[@bullsfan9162]

My dude, your videos are getting me thru calc 😂😂

[@takashishironika6825]

Fast forward 2 years and this is the same thing I would say right now

[@gerardotorresgalvan3802]

@@takashishironika6825same lmao

[@XianXian666]

Me when studying for college entrance exams 😭

[@glidecamz]

Calc? Why am I doing this in alg 2

[@estasbienbabosoo]

@@glidecamz right lmaoaoaoao

[@ckimels1479]

2:50 S O W H A T W E H A V E R E M A I N I N '

[@OfficiallyThorne]

This made me laugh

[@jujubean6436]

I absolutely loved this!

[@georgesadler7830]

MR. Organic Chemistry Tutor, thank you for a solid introduction to Finding Vertical Asymptotes in precalculus. Learning these concepts are very helpful in all levels of advanced mathematics.

[@joshualangford841]

Algebra. I'm here because of pre cal

[@jackwilson7018]

I think this is in a pre-calculus video

[@robertsacks1208]

Facts. Me too

[@blakesteenrod4765]

Same here - my quiz is tomorrow

[@winxxdee9746]

Mine is Gen Math

[@lexnicole6649]

GenMath🥴

[@sebastiandomingos335]

Dude this is so helpful, my teacher just fails at teaching he just goes up to the board and starts talking without explaining each step and when we tell him what are the steps he just does the problem the same way again. 🤦🤦‍♀️🤦‍♂️ This seriously is helpful

[@blessings2277]

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[@krishmalhotra2767]

Not even a min into the video and I've already found what I was looking for. Thank you haha

[@mylesken6122]

Very well presented. Thank you.

[@oooohapenny4707]

Thank you SO much. You are better than any professor I've ever had and make learning so easy and fun!!! Thanks again.

[@jingyiwang5113]

Thank you so much for your detailed explanation! It is really helpful!

[@khanhlam1481]

thank you so much, your video is very clear and easy to understand.

[@lola2873]

You have no idea how much you have helped me

[@_perryperry]

Is it a pre-requisite to factor first all of the polynomials (numerator & denominator) before graphing the rational function or that's just for getting the Vertical Asymptotes?

[@user-rv4ep1bs2p]

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Exam tomorrow and these are saving my life!

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I just passed my test because of this video. Thank you sm 😭!

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From KSA thanks bro u are my hero

[@user-fb1jm8kg3q]

Thank you very much❤

[@Kinocobalt]

I'm dying in the last one

[@jgkage727]

Thank you for showing me how to factor

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[@user-rv4ep1bs2p]

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You're all i need

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Once again, THANK YOU!

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hey could you please make a video on thermal physics.....more specifically on thermal properties of matter....thanks!

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[@shalatea5574]

Thank you so much, your explanations are always on point. I wish I could like this video 1000 times

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Bro this guy is some marvel math hero

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[@mathtutorph5718]

Can I ask why do you need to factor both the numerator and denominator (which is a linear numerator and quadratic denominator) in order to get the vertical asymptote? And why can't we just solve only the denominator? Why do we need to factor the numerator too? Sorry for my ignorance and thank you to someone who can answer my confusion. I've been stuck studying this for days.

[@icesnowflake5510]

I had trouble with that too. Its because lets say we solve for x, and we have 2 solutions as our vertical asymptote. If you were to graph it, it would show only one of the VA. For example, 3x-6/x^2-7x+10. The denominator factored is (x-5)(x-2) which is 5 and 2. I graphed it, and it only showed 5 as the vertical asymptote. Thats why we simplify it to get the correct VA. x-2 cancels with x-2 in the numerator. -----> 3(x-2)/(x-5)(x-2). x-2 cancels, and we are left with x-5.

[@DARITZ13]

I have a Quiz and a Test comming up on this and I still can’t understand anything at all. I have seen alot of videos and I feel like its not clicking this on me… idk what I’m gonna do 😭 Ps: your explanations are really good and on point but its not your fault, its me… I feel so dumb for not being able to understand or at least have an idea on this. 🥺

[@csssss1009]

Just to add a comment for this 2-year-old question…I think that’s because sometimes there exists at least one term that can be cancelled (same term appears both in denominator and numerator) and they’re not actually where vertical asymptote at.

[@aaron9262]

factoring it is always safer!

[@sonalimohapatra5821]

Thanks

[@user-bu8mg7uq3s]

thank you

[@artheniangaerlan3049]

dude how are you so goood at maath!

[@munisailkhomova9266]

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[@aimanimtiaz1066]

amazing

[@keclectic8461]

Using this to cram for my final

[@NickTortorici]

The government should pay you

[@The3DprintingMaster]

ABSOLUTE LEGEND

[@ellahinata9834]

Someone please help, my test is tomorrow. So for 1:28, my teacher would say that the VA is only the unique piece in the denominator. Since there are two 4s, how would you know which in unique??

[@SyTheGuy]

I dont understand why professors overcomplicate when it is this easy

[@noahtah1511]

that last one was crazy for me

[@strwbrrysanhwa3060]

I just got an ad in the middle of this vid going "STILL SEARCHING KZbin FOR MATH HELP? ARE THE VIDEOS FROM 2006 REAAALY HELPING??-" they ask this as I am understanding this concept in 5 mins when I couldn't get it in the 2 weeks we've been doing it in class

[@isaiahkare]

How can you know how and when to determine the curve or let me say the line, how will you know which direction it must face and curve

[@papa-bv8ow]

well I guess Ill just fail my test cuz idg the last one and its going to be on my test

[@johnvargas761]

What about when there is natural log or cos and sin ?

[@lanadelray9169]

Can we say absolute value of x over x have V.A?

[@staceymills7481]

Why.......do math teachers complicate everything. Thank you for your service sir.

[@arthurthevelin2073]

This video only talks about asymptotes of rational functions. Could you make one that's more general, also treating cases like f(x)=logx, where the vertical asymptote is x=0.

[@aroosakakar4824]

Sir plzz upload physical chemistry videos

[@zeustesoro8909]

What if there's no constant and there's an x^3?

[@alexei1672]

how did you graph it in 0:44 ?

[@dunno9143]

Wht if the denominator and numerator cannot be cancelled?

[@orimakungo8245]

do the graphs of y=lnx and y=cosx have vertical asymptote??

[@nedayigit8708]

vertical asymptote of y=lnx is x=0, but y=cosx does not have a vertical asymptote.

[@laylagzali]

When we say "x = 2 is a hole" do we mean that the function is discontinuous at 2?

[@natalieodonnell7136]

Math angel 😇

[@nathanwijaya753]

Anyone know why the numerator at 10:30 (5(x+1)) is ignored?

[@FoodDN.23]

For finding vertical asymptote only denominator should equal zero.

[@yoonSeungho.18]

can you try to somve this f(x)=x-7 [over] x+5 ??? using vertical asymptote

[@grizzIe]

X = - 5

[@yoonSeungho.18]

@@grizzIe so you just need to focus on below and transpose the num. and change the sign?

[@faizanawaz3844]

But why not x-1 in the last example

[@amdelrushjunebesquillo4325]

What if the denominator is x³

[@jacobdiehl9777]

Car horn at 5:10

[@johnsoto7112]

what if the function isnt a fraction?

[@daff5507]

Confused on why we had to solve the numerator for the last problem, when we only used the denominator to get the VA:

[@bg8739]

Can there be more than one vertical asymptote?

[@aryanahuja9709]

yes! the last video I watched had an example of a rational function with a denominator of a difference of squares (DOS), x^2 - 4. He explained how there would be 2 asymptotes in this case, x=4 and x=(-4)

[@mathtutorph5718]

@@aryanahuja9709 how can we graph two asymptotes?

[@aryanahuja9709]

@@mathtutorph5718 in the context of vertical asymptotes, here's how it's done: (x-7)/((x^2)-x-6) To find the vertical asymptotes, we set the denominator to 0 right? So in this case if we factor the denominator, we'll get an answer of (x-3)(x+2)=0 So on a graph, you'll mark the lines x=3 and x=(-2).... giving you your two vertical asymptotes To graph it, just use like 5 points in each of the areas to get the idea of the shape of the graph... area 1 would be from (-infinity, -2).... area 2 would be (-2, 3) and area 3 would be (3, positive infinity) But if you take the concept of asymptotes into trigonometry.... then oh boy... tanX will give you pretty much infinite numbers of vertical asymptotes... try it on desmos.com (just type y=tanX)

[@mathtutorph5718]

@@aryanahuja9709 in that example of yours, our horizontal asymptote would be 0, right? Can we graph these two vertical asymptotes together with the horizontal asymptote? Thank you answering btw

[@aryanahuja9709]

@@mathtutorph5718 yes in the example above, the horizontal asymptote is indeed 0 since the degree of the numerator is smaller than the degree of the denominator. And yes you can graph it too. Now, I am notsire how the graph looks like of course but it could look like and exponential function in area 1 (between negative infinity and -2) where it never touches either of the asymptotes. In area 2, between -2 and 3, I may look like either a parabola opening up or down, or it may very well have shape of a cube function where it never touches the two vertical asymptotes. Now, i am not sure about everything that goes behind the scenes, but if the shape is of a cube function, then it is allowed to cross the horizontal asymptote whereas if it's a parabola it isn't. And in the area 3, from 3 to positive infinity, the shape could be something like another exponential function just reflected over the x axis. You could find the exact shape on desmos.com Lol sorry for the long and boring answer but do you get it or you can ask me if you have any other questions :)

[@gersongodinez8203]

What does the f in f(x) mean?

[@user-hi7ic3zy6k]

y

[@cess8861]

5:04 what if it's not possible?

[@phantomw0lf1e26]

what is my x has nothing with it like y= (-2/x) -3

[@rantingmyazzoff1886]

What about 1/3x-7 ???

[@zoe_lor]

vertical asymptote ate x = 7/3

[@eddiemorales5861]

I’m here but I’m in AP Calculus😅

[@user-se6qc8ci1q]

f(x)=1/x find vertical asymptote

[@pom80]

if anyone is watching where did he get the possitive 2x gais and negative 3x

[@medicisounds1384]

Why wouldn’t x-2 be an asymptote

[@GharBaharvlogs]

Nice 🌹🌲💐🌲🌹💐🌲🌹💐🌲🌹💐🌲🌹

[@sub2me543]

0 - 3 = 0?

[@bjyx_x3w18]

What is the vertical asymptope of x^2(x-1)? And why?

[@izyanali1635]

Rumours still say, he is figuring it out

[@kofiluddin6991]

@@izyanali1635lmfaoo

[@meyafajardo2918]

May I borrow your brain cells please? Jke

[@VeritasEtAequitas]

It's a long A sound though. A-symptote meaning "not", rather than ass'm tote.

[@IvorySplinter]

Ur low key him

[@user-bf1pb3kg7b]

okay

[@raysao3266]

fml

[@pmdchi]

no bass voice is uncomfortable

[@ItsCoderDan]

god factoring is so dumb why cant i just solve it as is they mean the same thing T-T

[@nickgates9093]

This mans said that there was no sq root of 4 3:56

[@zduke5979]

Wtf is this

[@blvzvr]

Mentions difference of squares but doesn’t explain it 🤦🏽‍♂️

[@kim1.1.1.1]

Yeah cuz it's basic algebra. You're supposed to know it, given that you're studying this topic already

[@ojd414]

Skill issue

[@blvzvr]

@@ojd414 yes captain obvious 😂 that’s why I’m watching a tutorial. Nice try tho

[@ojd414]

@@blvzvr you need a tutorial within a tutorial?Double skill issue

[@kalle7533]

Allah just give him hidaya ya Allah let is he going to jannah ❤️🥹enshalla