Graphing Advanced Rational Functions With Asymptotes and Holes Using Transformations

This algebra video tutorial explains how to graph rational functions with asymptotes and holes. It includes horizontal asymptotes, vertical asymptotes, and slant asymptotes. This video discusses the process of graphing rational functions using transformations. It also mentions how to determine the domain and range of the rational function. This video contains plenty of examples and practice problems on graphing rational functions.

Fundamental Theorem of Algebra:

Rational Expressions - Basic Intro:

Simplifying Rational Expressions:

Multiplying Rational Expressions:

Dividing Rational Expressions:

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Adding & Subtracting Rational Expressions:

Rational Expressions - Unlike Denominators:

Simplifying Complex Rational Expressions:

How To Solve Rational Equations:

Rational Equations - Extraneous Solutions:

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Horizontal and Slant Asymptotes:

Finding Rational Functions Given 2 Points:

Rational Functions - X and Y Intercepts:

Graphing Advanced Rational Functions:

Rational Inequalities:

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Final Exams and Video Playlists:

Full-Length Videos and Worksheets:

[megan]

when u learn more here than in math...

[jeffreyyuan]

this guy is literally my teacher for half my classes

[mariamdiallo]

With out you I will be repeating very math class thank you my May Allah bless you.

[annatropez]

You have saved me in so many subjects, physics and chemistry especially. For some reason I just now stumbled on your precalculus videos after many years of crying over math class and my teachers incapability of teaching. I don't know how you do it but I haven't understood graphing for many years but after this video Im finally getting a grasp of it. Thank you thank you thank you.

[Nemoguzapomnit]

So great stuff! Thx a lot. Btw why at 18:40 you typed range as (-∞, 2) ∪ (2, ∞)? Y-intercept has it's maximum at 1.75 there's no other points betweet 1.75 and 2

[FatmaAlMandhari]

i have a question !! plz anyone !! reply

[Lana-ordz]

Great explanation! I look forward to more college algebra videos and business calculus

[lucasharper]

thanks so much man this was a lifesaver for my high school test. keep it up!

[LucaRT]

Learned more in an hour before my test from these vids than all of my lectures combined

[naftalemdaniel]

One year ago, they told me to take this course again or to do the test in order to go to university but I was suspicious for the test, as soon as I watched this video, I said ok for the test and I passed it thanks to you.

[FunTycoon]

It was 1 and 9 actually, if what I did was correct ;)

[mohammedkhaled]

Instead of writing ( - inf, 1.5 ) U ( 9, inf ) you had to write ( - inf, 1 ] U [ 9, inf )

[rohankatreddy]

Shouldn't the range for the function 1/(x^2-4) + 2 be Range: (-infinite, 2-(1/4)) U (2, infinite). Correct me if I am wrong :)

[mortenfransrud]

Do you have a video on finding the function of the values on the graph?

Have problems with a rational function equation where I need to find the values of A, B, C by studying that graph.

(Ax+b)/(CX+1)

I'm just stuck...

[momentswithnahcassie]

thanks alot i understood in less than an hr and i have a test tomorrow

[georgesadler]

MR. Organic Chemistry Tutor, thank you for Graphing Advanced Rational Functions with Asymptotes and Holes using Transformations.

[mdisrafilansari]

At x=2 the function is undefined... Why not draw asymptote at that point? Please explain

[devajnakaran]

This video was great thank you but in the last example is there a method to find the local maximum/minimum without relying on a GDC/on calculus?

[philiplee]

Why not make Xs into fraction and graph the equation by limits?

[hanif]

i want to ask...if 1 in the question at minute 18:30 changed to other number.do the answer still same