What is a horizontal asymptote

👉 Learn all about asymptotes of a rational function. A rational function is a function, having a variable in the denominator. An asymptote is a line that the graph of a function approaches but never touches. There are the vertical, the horizontal and the slant/oblique asymptotes.

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.

A slant (oblique) asymptote usually occurs when the degree of the polynomial in the numerator is higher than the degree of the polynomial in the denominator. To find the slant asymptote of a rational function, we divide the numerator by the denominator using either long division or synthetic division. The quotient obtained when the numerator is divided by the denominator is the slant asymptote of the function.

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

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[Sultan_A]

Good Job, Brian McLogan, Keep It Up. KIU

[brianmclogan]

I am keep watching my videos, I will be making videos all year long

[keithhudson]

Sir, you are a godsend. Thank you, thank you, thank you!!! I thought I understood it, but now I think I really understand it.

[shf]

The vadio is very old when I was in the first year of primary school and now I am in the first year of university. Thank you. I understood the lesson.

[brianmclogan]

haha probably don't mind my speaking, I misspell and misspeak all the time

[onesandzerospdf]

Thanks for your help. Just one question though, why do we need to learn this?

[shabnamara]

Thank you so much Sir...your videos helped me soo much in maths..love from india..

[Mx-dpgo]

Is there a base formula for Horizontal Asyptopes as there is for Vertical ones, because the vertical one is something like 1/x. Is the horizontal on something like ax/x? Since there should be an x on the numerator?
Thanks so much for the help!

[xxxpissoff]

Man you're amazing! Thank you very much!

[ozbondweefin]

You mentioned that there are cases when the curve WILL cross the HA. Would you elaborate on that case?

[josemercado]

how do you know if its a y asmptote or a x asymptote?

[shocker]

love it. but i think u called it an asymptope instead of an asymptote lol

[crystalnero]

Thanks for ur upload... It helped me alot..

[arshidwani]

Why shouldn't both the infinities reach zero,

[beverlybeepath]

Not gonna lie this topic may freak me out sir ....

[SolidSiren]

Why do you keep saying "asymptope"? Is that another accepted spelling?

[arshidwani]

Why shouldn't both the infinities reach zero,