1. Solving for the Discontinuities of Rational Equations 16 March 2011

2. Horizontal Asymptotes  Degree of Numerator < Degree of Denominator HA: y = 0  Degree of Numerator = Degree of Denominator HA: ratio of leading coefficients  Degree of Numerator > Degree of Denominator HA: doesn’t exist

3. Solving for Vertical Asymptotes and Holes 1. Always factor the numerator and the denominator 1 st ! 2. Identify linear factors in the denominator 3. Figure out where the linear factors in the denominator occur the most

4. Solving for Vertical Asymptotes and Holes, cont. Occur Most in Denominator Occur = # of Times in Numerator and Denominator Occur Most in Numerator  VA  Set factors equal to 0 and solve for x.  Hole  Set factors equal to 0 and solve for x.  Hole  Set factors equal to 0 and solve for x.

5. Example #1

6. Example #2

7. Example #3

8. Example #4