for any equation, what is an easy way of finding an asymptote? by the way im only up to a high school level in math ... :)

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- Nov 21st 2007, 11:56 PMwhitestratfindng asymptotes
for any equation, what is an easy way of finding an asymptote? by the way im only up to a high school level in math ... :)

- Nov 22nd 2007, 02:24 AMMacleef
To find vertical asymptotes, you must find the zeros of the denominator

Ex. $\displaystyle \frac{3}{x-2}$

$\displaystyle x = 2

$

To find horizontal asymptotes, compare the degree of the numerator and the degree of the denominator of the rational function:

1. If the degree is the numerator < degree of the denominator, then the horizontal asymptote is 0

Ex. $\displaystyle \frac{3}{x-2}$

horizontal asymptote = 0

2. If the degree is the numerator = degree of the denominator, then the horizontal asymptote is:

$\displaystyle \frac{leading.coefficient.of.numerator}{leading.co efficient.of. denominator}$

ex. $\displaystyle \frac{2x-2}{3x+4}$

horizontal asymptote = $\displaystyle \frac{2}{3}$

3. If the degree is the numerator > degree of the denominator, then there is no horizontal asymptote

ex. $\displaystyle \frac{2x^2-2}{3x+4}$

There is no horizontal asymptote