Graphing Rational Functions with Vertical and Horizontal Asymptotes

[@billnye8318]

This guy has helped me so many times in math class.

[@ThinkwellVids]

Alex, the domain and range are different from the asymptotes. The domain consists of all values that x can be. The range consists of all values f(x) can be. The asymptotes are values that the function approaches but never reaches.

[@justaman-f8b]

May God always guide you to the right path, great professional professor! You helped me a lot..

[@peachyspalace]

5:32 Haha they forgot to put it in.

[@yousefsassya]

lol yeah haha. I was like, herro where the calculator....???

[@jaqenhgarlalala7108]

HAAHHA YEAH! Just look at that.

[@kemberlycollins1199]

Hope you are safe and healthy with your family I just wanted to say thank you for helping understand better math. You are an angel God has sent me. Thanks a lot 🙏🙏🙏

[@scarlettq81820]

my life became so much easier after watching this

[@kpg3221]

zee kay Facts

[@justinoverstreet13]

"its just like raisins, you can never have just one" lol wut

[@jackwilson4324]

What about the Slant/Oblique Asymptote of the first one, X+2-3/X, but ignore the remainder, and it's f(X) = x+2, a linear function, aren't you supposed to graph them?

[@rainbow-si6ur]

thought so as well

[@someonerandom1010]

You sir, truly are fantastic. My Precalculus teacher didn't explain anything to the class. I have a test tomorrow and she never even mentioned the word Asympototes. Thank you so much, hope i do well tomorrow.

[@victoriamiles]

I really like your videos. I saw you present at NCTM once and you are very funny! Your personality comes through in your videos. Also like the visuals you use.

[@MMjd137]

i agree with you

[@hazem7860]

why is there a Zero while there is a horizontal Asymptote at y=0 at min 5:14 ? please answer :D

[@edwardwang7929]

The first one，f(x) = x+2-3/x ，is very similar to the first one in the video of oblique asymptotes，f(x) = x+2+3/(x-1) ，both graphs of them have y=x+2 as their oblique asymptotes.

[@davidwhitecross1021]

What about the oblique/slanted asymptote for the first one?

[@brockfournier6055]

thats what I’m questioning

[@gibsonj338]

The oblique/slanted asymptote for the first one would be x+2.

[@erickastansbury9985]

Thanks :) This was an easy-to-follow video

[@superpowerforhire]

I highly recommend this guy as a teacher... Math+laughters

[@reiks-r4405]

f(x) = 3x^2 - 12 = 3(x^2 - 4) = 3 (x+ 2) (x-2) *For those of us that still looking for the GCF and DOTS

[@Akashascosset]

@thinkwellvids how can we get access to your private calculus videos? I love this guys videos

[@Chadathin]

How does it have a horizontal asymptote at y= 0 AND cross the x-axis?

[@Jesus.saved.me2000]

What if you have x^2 +3x/x^2 + x - 6? I know you factor at the denominator but there are two x's in the numerator

[@jessagonzales8126]

Thanks, it's a great help!

[@christabelakwa5587]

i dnt understand hw u started graphing .how did u obtain the numbers in order to plot them on the graph @thinkwellVids

[@Jesus.saved.me2000]

Christabel Akwa you just choose your own values to plug in around zero usually so it isn't too difficult

[@christabelakwa5587]

thanks dear

[@lazyduck5436]

Where did you get the values in the table of points?

[@indiehindi]

I know this is a three year old comment but for anyone else wondering this, you can just pick random numbers for x. Plug that number into the equation for x, and the answer gives you your y value.

[@dezyyzed7346]

Um and where were you pointing at

[@panduananto1033]

What is easy point?

[@Globox822]

Thank you

[@kaustubh1360]

It was very helpful

[@myeshawarthen5436]

X^2-5x/x^3-4x

[@Mcraider09]

dat hair doe

[@AscendedWarriors]

this video was made in the 50's

[@ismael7886]

with a 4k camera

[@kaustubh1360]

Thank you sir

[@scalabrineplayoff3pt46curr7]

its steven colbert

[@dalalhamadalajmi]

I love you

[@approving581]

sure ntwana