Asymptotes

When dealing with graphing rational functions you have my asymptotes.  The asymptotes may be vertical, horizontal or slant.

If the highest exponent of all terms in the numerator is less than the highest exponent of all terms in the denominator, the horizontal asymptote is y = 0

for example f(x) = x/(x^3 + 3)

If the  highest exponent of all terms in the numerator is one greater than the highest exponent of all terms in the denominator, there is a vertical asymptote and slant asymptote, which is found by doing long division

for example f(x) = (x^2 + 2x + 3)/(x + 1)

Doing long division you get x +1 with a remainder of 2.. the slant asymptote is y = x + 1, ignore the remainder.

If the highest exponent of all terms in the numerator equals the highest exponent of all terms in the denominator, the horizontal asymptote is the coefficients of the highest terms divided.

for example, f(x) = 2x/(x + 2), the horizontal asymptote is y= 2x/x, y = 2

Veritcal asymptotes, if they exist are found by setting the denominator to zero and solving for x.