Identifying vertical, horizontal asymptotes and holes

👉 Learn how to find the vertical/horizontal asymptotes of a function. An asymptote is a line that the graph of a function approaches but never touches. The vertical asymptote is a vertical line that the graph of a function approaches but never touches. To find the vertical asymptote(s) of a rational function, we set the denominator equal to 0 and solve for x.

The horizontal asymptote is a horizontal line which the graph of the function approaches but never crosses (though they sometimes cross them). A rational function has a horizontal asymptote of y = 0 when the degree of the numerator is less than the degree of the denominator. A rational function has a horizontal asymptote of y = c, (where c is the quotient of the leading coefficient of the numerator and that of the denominator) when the degree of the numerator is equal to the degree of the denominator. A rational function has no horizontal asymptote if the degree of the numerator is greater than the degree of the denominator.

Organized Videos:
✅ Find the Asymptotes of Rational Functions
✅ Find the Vertical and Horizontal Asymptotes of a Rational Function y=0
✅ Asymptotes of Rational Functions | Learn About
✅ Find the Asymptotes of a Rational Function with Trig
✅ Find the Asymptotes and Holes of a Rational Function
✅ Find the Slant Asymptotes of the Rational Function

Connect with me:

#asymptotes #functions #brianmclogan

[frank]

this guy is getting me through online classes

[DailyBoundRacing]

atp youtube teaches me more than my teachers. Thank You, I have a test tomorrow!!

[Shrugboatt]

Thank you so much for doing this. I'm taking college algebra online and the entry testing was waived due to COVID. I feel like I'm in over my head but these videos are extremely helpful.

[lanadelreysvape]

I always understand whenever I watch your videos, but I never understand my teacher when he teaches lol

[larryprochko]

LMAO This guy is teaching me more in 2 minutes than my professor has in 3 hrs.

[riftiee]

this guys is literally saving me during covid

[michaelwesten]

I'm not sure if it works every time, but it does here - if you use the substitution method, and plug the number back into the function, if you get 0/0 - that indicates a hole.
So you find what makes the denominator 0, which here is 3 - and then plugging 3 into the (2x-6)/(x^2-1) - gives you 0/0, so a hole.

I didn't learn this "removable" way, where you need something to cancel. But ya, maybe someone can correct me if I'm wrong, but I believe you can also do the substitution method (plug in whatever x values give you a denominator = 0) - and 0/0 will indicate a hole.
If plugging the number back into the equation gives you a (Nonzero/0) - then it's a vertical asymptote, not a hole.

[MysticNugget]

My professor is awful sauce. These are helping me understand something much. My teacher does not teach well. Thank you for these videos

[jessicahill]

Thanks so much! I actually understand asymptotes now. Hopefully I pass my test :).

[kingmo]

the students being dead silent after he prompts them is the realest thing

[prequelanimations]

Do you have a video for the exact coordinate for where the hole is?

[yasmineyasmine]

You are saving my life, much thanks!!!

[afakasi]

Idk why these videos aren’t posted in my online 1050 class because this made more sense than the past 2-3 weeks have been 😂

[joyfulburger]

what abt when the degree in the numbers got is greater than the denominator

[ducko]

teaching me more than my ap calc and pre calc teacher

[karanguleria]

I wasn't in the last class period sorry sir :(

[johnbiboytiongco]

Excuse me sir may i ask, , why on the horizontal asymptote is equal to zero?

[ralcjt]

What if the degree of the numerator is more than that of the denominator

[roho]

Math Never dies, so I'll be back




Not because I want to but because I have to.

[evanespino]

what do you do if the numerator isn't factorable?