Rational Functions: have discontinuitites - Limits on the domain and graphs of rational functions.
by Kristen McCuen
1. Degree of Numerator and Denominator Polynomial
1.1. Horizontal Asymptotes
1.1.1. Case 1
1.1.1.1. Degree in numerator < Degree in Denominator
1.1.1.1.1. HA @ y = 0
1.1.2. Case 2
1.1.2.1. Degree in numerator = Degree in denominator
1.1.2.1.1. HA @ y=ratio of coefficients
1.1.3. Case 3
1.1.3.1. Degree in the numerator > Degree in denominator
1.1.3.1.1. More that one degree - No HA
1.1.3.1.2. Exactly one degree greater
2. Denominator Polynomial
2.1. Holes
2.1.1. A factor that cancels in the numerator and denominator
2.1.1.1. Set factor equal to zero and solve for x
2.1.1.1.1. Plug x into simplified equation to get y
2.2. Vertical Asymptotes
2.2.1. Any factor in the denominator that does not cancel
2.2.1.1. Set factor equal to zero and solve for x