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is the ratio of two polynomials with complex coefficients, where {{math|''Q''}} is not the zero polynomial and {{math|''P''}} and {{math|''Q''}} have no common factor (this avoids {{math|''f''}} taking the indeterminate value 0/0).
The ___domain of {{mvar|f}} is the set of complex numbers such that <math>Q(z)\ne 0,</math> and its range is the set of the complex numbers {{mvar|w}} such that <math>P(z)
Every rational function can be naturally extended to a function whose ___domain and range are the whole [[Riemann sphere]] ([[complex projective line]]).
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