How to find HORIZONTAL ASYMPTOTES (KristaKingMath)

To find the horizontal asymptotes of a rational function (a fraction in which both the numerator and denominator are polynomials), you want to compare the degree of the numerator and denominator.

If the degree of the numerator is equal to the degree of the denominator, then the horizontal asymptote is given by the ratio of the coefficients on the highest degree terms.

If the degree of the numerator is less than the degree of the denominator, then the horizontal asymptote is the x-axis, or the line y=0.

If the degree of the numerator is greater than the degree of the denominator, then the function has no horizontal asymptote.

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Hi, I’m Krista! I make math courses to keep you from banging your head against the wall. ;)

Math class was always so frustrating for me. I’d go to a class, spend hours on homework, and three days later have an “Ah-ha!” moment about how the problems worked that could have slashed my homework time in half. I’d think, “WHY didn’t my teacher just tell me this in the first place?!”

[Warlord]

nice job. i wish i had you as my teacher back in high school. *sigh*
high school teachers are bad, college professors are even worse. 90% of my knowledge come from youtube, 10 percent from homworks/recitation, and 0% from lecture these days

[markzuckerbread]

You've probably heard this a thousand times by now but you've saved me from my terrible teachers

[kanikasharma]

you just managed to explain to me in 7 minutes what my math teacher could not explain to me in 30.
Nice job 👏👏

[less]

Finally someone who can answer my question

[elizabethavalos]

Thank you Krista, excellent explanation.

[elijahangelosantos]

Wow this was actually easy and really helpful. Thanks.

[lukedifato]

this is awesome but I love how precalculus taps around calculus. This is a perfect example where you're basically solving a limit conceptually.

[jeffreyleon]

thanks so very Much!!! You are an amazing person at explaining these thins. I had some trouble understanding my teacher's worksheet since I got sick and missed an entire day of school. You are amazing and hope you make me re videos :)

[KlsonBob]

thank you! solid, solid explanation that was, very clear

[sansa]

thank you so much :)))) this is so much faster than doing long division for all functions!!!!

[parkermanns]

Greatest video ever. It actually helped!!

[jasmin-czid]

This help me soo much! My teachers teaching how the case 1-3 and yet i dont understand it:D thanks for thiss!

[DeathSilver]

Great explanation! But why can't, for example, x^2 be an oblique asymptote since the highest degree of n must be 1 higher than the highest degree of d?

[ericlareza]

Yeaaahhhh thank you, your teaching helped me a lot :D

[hamadaldhanhani]

what if there was root and a function underneath it in the denominator .. how to solve it

[ade.]

sigh why do I learn more by watching your videos than in class

[mclovin]

Are there always horizontal asymptotes when it is a fraction?

[alexintheskies]

Hi, this doesn't seem to be the case for the polynomial (2x+8)/(x^2-2x-8)
According to the rules, a proper polynomial fraction always has H.A y=0
but when plotting this out, there is an x-int at x=-4, hence there cannot be a H.A at y=0


Would you be able to explain this? Cheers!

[lukesavino]

I wish you were my teacher, mine is confusing.

[yeny]

I graphed the graph of "g" and the horizontal asymptote is not at y=0. What a I doing wrong here? was this just to show us how to find horizontal asymptotes or are you saying that graph as an asymptote at y=0? because I checked and it doesn't so Im not sure. I think I'm the one missing something here. Thank you so much for your videos!