Rational Functions: have discontinuitites - Limits on the domain and graphs of rational functions.

1. Denominator Polynomial

1.1. Holes

1.1.1. A factor that cancels in the numerator and denominator

1.1.1.1. Set factor equal to zero and solve for x

1.1.1.1.1. Plug x into simplified equation to get y

1.2. Vertical Asymptotes

1.2.1. Any factor in the denominator that does not cancel

1.2.1.1. Set factor equal to zero and solve for x

2. Degree of Numerator and Denominator Polynomial

2.1. Horizontal Asymptotes

2.1.1. Case 1

2.1.1.1. Degree in numerator < Degree in Denominator

2.1.1.1.1. HA @ y = 0

2.1.2. Case 2

2.1.2.1. Degree in numerator = Degree in denominator

2.1.2.1.1. HA @ y=ratio of coefficients

2.1.3. Case 3

2.1.3.1. Degree in the numerator > Degree in denominator

2.1.3.1.1. More that one degree - No HA

2.1.3.1.2. Exactly one degree greater