## 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.

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I don't get it

But for the first one, how do you know that the horizontal asymptote is zero?

this guy deserves a medal

Iβm taking a friggin quiz rn and nothing is helping me omgπ

11:19 (-oo,1)u(1,oo) not (-1)

All i see are freaking lines everywhere, hahaha

10Q

Even 4 years after this was posted, this man is helping so many people, he deserves every good thing in life.

He taught 2 weeks of class time in less than an hour

Very helpful videos. Example f(x) = 1/x+1 Domain range shows -1. I am not sure why -1? Thanks.

Your my teacher cause my other one sucks

I would like to thank you for this amazing 58 minutes of incredible explanation that my teacher couldnt do within months

I am taking PreCal in college. I have a 60 right now. There is 12 assignments left and 3 tests left. Overall, 28 assignments and 4 tests. Tests count as 60% and assignments are 40%. Do I have enough time to get that back up to at least 69.50? Please, if someone could guarantee me a passing grade. I will send you $35 a week.

Hello, I was wondering if you could please help me with the following exercise.

To divide the function f(x-1) by (x^2+2x-3), we find that the quotient is Q(x) and the remainder is (x-3). If f(0)=a and f(-4)=b, what is the value of b/a? Thank youu β₯

11:03 the domain ?

procrastination is not my middle name.

10qππ

you are so freaking awsome.. this is so easy to understand.. thank you so much ….. i love it

i'm gonna be honest, i have to do an online test today and i'm just binging all rational functions and equation videos ππ

For the last problem, I believe those local max and mins could be found by taking the first derivative and setting it equal to zero

thank you so much for the tutorial video, your tutorial is one of the best in my opinion, I only watch the one you updated and Khan Academy TvT The others are just not on the point.

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

Watching all 54 minutes of this video was worth it π₯°π

Tnk bra

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U have to change ur channel name bro not only chemistry

Those that gave O.C.T. a thumb down are truly hopeless in calculus, and they blame their hopelessness in advanced math on O.C.T.

i think at 11:16 domain is (-infinty , 1) U (1 , +infinity)

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What if you are given a domain how do you graph

Thank you so much, I really needed this videoπππ

We have an exam tomorrowπ°… wish me luck

Is it always the numerator to be used when finding x and y intercept?

in 24:00 I am sure that you draw a wrong graph.

You are a great help, straight forward videos, best on the internet. You are my main reference right now.

anyone else crying in math class? π

Life saver is explaining

I'm here to learn basics for advance math so I can understand memes, π . Thank you so much

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?

This man is a legend

what do you mean by "when want to find the domain of a function particularly a vertical Function, remove all the X-values and the VA that you have"?

Thanks a lot this help me in guiding my son, Math is kinda hard now adays ππ

fuck math

The video is amazing but I just want to suggest increasing the volume of your voice. Aside that, Nice content!

I started at 2 am and now it's 6 am …

This whole time I was studying graphs and all are from your videos πβ₯

Am really thankful for all what u did , u just don't know how much this means to me π u r really a life saver may God bless u n ur family

My number one hero!!

11:00

14:20