Rational Functions:

A rational function can be written as:

f(x) = N(x)

         D(x)

where N(x) and D(x) are polynomials and D(x) is not a zero polynomial. Every polynomial is a rational function.

To graph a rational function you have to find

- x-intercept

- y-intercept

- vertical asymptote

- horizontal asymptote

- the vertical asymptotes are the zeros of the denominator

- the graph has a horizontal asymptote if the degrees of the polynomials are the same. The horizontal asymptote is the ratio of the coefficients. 

To graph the function 

f(x) =          x                

        - x - 2

   

- the x-intercept is (0,0)

- the y-intercept is (0,0)

- the vertical asymptotes are x = -1 and x = 2 

- no horizontal asymptote