Rational Functions:

a rational function can be written as


both N(x) and D(x) are polynomials with D(x) not a zero polynomial


The Zeroes of N(x) are the x-intercepts
The zeroes of D(x) are the vertical asymptotes of the function
The degree of the polynomial in the numerator or N(x) over the degree of the polynomial in the denominator or D(x) is where the horizontal asymptote is.

when the denominator has a higher degree the horizontal asymptote is at y=0

when the denominator and numerator have the same degree the leading coefficient of N(x) over the leading coefficient of D(x) is the horizontal asymptote.

When the denominator has less of a degree of the numerator there is a slant asymptote.

ex.

The zeroes of N(x) or 2 and -3 so those are the x intercepts.

The zeroes of D(x) are -4 and 1. These become the places at which there is a vertical asymptote.

The degrees of the numerator and denominator are equal with both polynomials having a leading coefficient of 1 so the horizontal asymptote is 1.

This is what the graph would look like. 

If we were to have the equation 

There would be a hole in the graph at -7 because zero cannot be divided by zero

Good luck reviewing if you need more help visit these links.

Finding vertical asymptotes of rational functions:

http://www.youtube.com/watch?v=_qEOZNPce60

Precalculus Rational functions (holes and asymptotes)
http://www.youtube.com/watch?v=HINeQfh5ZXU