Rational Function Graph Characteristics

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Back

Front

Domain of a Rational Function

Back

Analyze the Denominator Only:

Cannot Divide by Zero

Exclude the Zeros of the Denominator

Front

Discontinuities of Rational Functions

Back

Factor the Numerator and Denominator:

1. 1. Removable Discontinuities: factors that are in both the numerator and denominator.

2. 2. Infinite Discontinuities: factors that are in the denominator only.

Front

Holes and Vertical Asymptotes

Back

Holes: x value is removable discontinuity (factor in the numerator and denominator). To find the y-value, plug the x into the reduced form.

Vertical Asymptotes: x = # from factor that is in the denominator only (or after reduced). MUST WRITE as x =

Front

x-intercepts of rational function

Back

Zeros of the numerator after reduced or with no matches in the denominator.

Front

y-intercepts of rational functions

Back

Plug x = 0 into reduced version

Front

Symmetry of a Rational Function

Back

Front

Inverses of Rational Functions

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