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

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

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