Rational Functions

A rational function is a polynomial divided by a polynomial, basically a fraction with polynomials in the numerator and denominator.  Examples are x^2+3x-2/3x^2+8x-7 and 2/x-7 or even 3x^2-5. However rational functions are not allowed to have square roots or fractions in them like 3-sqrt 4/6+x. Rational functions can generally be expressed as f(x)= p(x)/q(x) as long as q(x) does not equal zero.  To find the roots of a rational function you have to find where the graph crosses the x axis or the x intercepts of the equation. To find the vertical asymptotes you just set the denominator equal to zero and solve for x. For horizontal asymptotes if the degree of the numerator equals the denominator then you divide the leading degree of the numerator and denominator, if the degree of the numerator is less than the denominator than y=0 and if the degree of the numerator is greater than the degree of the denominator then the horizontal asymptotes do not exist. Here is an example of a rational function graphed.