A rational function is a fraction of polynomials. It cannot be divided by zero, so the denominator cannot equal zero. To graph a rational function: 1) Identify horizontal asymptotes by comparing the degrees of the numerator and denominator polynomials. 2) Identify holes by factoring the numerator and denominator and finding common factors. 3) Identify vertical asymptotes by setting the denominator equal to zero and solving.

1. A rational function is a function that can be written in the form of a polynomial divided by a polynomial, Examples: Because rational functions are expressed in the form of a fraction, the denominator of a rational function cannot be zero, since division by zero is not defined.

2. Graphing Rational Functions Step 1: Identify our horizontal asymptotes. First, Look at the degree of the numerator….here it’s a 1. Then, look at the degree of the denominator….this one is a 2. Use the following rules to find the horizontal asymptote: Numerator degree > denominator degree NO HORIZONTAL ASYMPTOTE Denominator degree > numerator degree y = 0 Numerator degree = denominator degree y = the quotient of leading coefficients. Here there is a horizontal asymptote at y = 0

4. We know that this function is undefined when the denominator is 0. So, let us find for which x-values the denominator is equal to zero. Our graph will contain vertical asymptotes at these x-values. Set anything still in the denominator equal to zero and solve. Step 3: Identify vertical asymptotes. So we have an horizontal asymptote at x = 3/2.