horizontal asymptotes

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Let us learn about "horizontal asymptotes"

Asymptote is a tangent which touches any curve at infinity , so that we cannot meet the curve and the line in real. We study 3 types of Asymptotes viz. Vertical, Horizontal and Slant/oblique Asymptote. Also in standard terms, Horizontal asymptotes are horizontal lines that the graph of the function approaches to 0 on x axis as x tends to +∞ or −∞. Similarly Vertical asymptotes are vertical lines and the graph of the function approaches to 0 on y axis as y tends to +∞ or −∞. Vertical asymptotes are straight lines near which the function grows without bound.When curve doesn't have Vertical or Horizontal then it contains Slant Asymptote.

Y=0 is and example of Horizontal asymptotes and similarly X=0 is an example of vertical asymptotes

Horizontal asymptotes are horizontal lines the graph approaches.

Horizontal Asymptotes CAN be crossed.

To find horizontal asymptotes:

* If the degree (the largest exponent) of the denominator is bigger than the degree of the numerator, the horizontal asymptote is the x-axis (y = 0).

* If the degree of the numerator is bigger than the denominator, there is no horizontal asymptote.

* If the degrees of the numerator and denominator are the same, the horizontal asymptote equals the leading coefficient (the coefficient of the largest exponent) of the numerator divided by the leading coefficient of the denominator

One way to remember this is the following pnemonic device: BOBO BOTN EATS DC

* BOBO - Bigger on bottom, y=0

* BOTN - Bigger on top, none

* EATS DC - Exponents are the same, divide coefficients

The above information is related to 9th grade math.

I hope the above explanation was useful.Keep reading and leave your comments.