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has {{math|''d''}} distinct solutions in {{math|''z''}} except for certain values of {{math|''w''}}, called ''critical values'', where two or more solutions coincide or where some solution is rejected [[point at infinity|at infinity]] (that is, when the degree of the equation decreases after having [[clearing denominators|cleared the denominator]]).
In the case of [[complex number|complex]] coefficients, a rational function with degree one is a ''[[Möbius transformation]]''.▼
The [[degree of an algebraic variety|degree]] of the [[graph of a function|graph]] of a rational function is not the degree as defined above: it is the maximum of the degree of the numerator and one plus the degree of the denominator.
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The ___domain of {{mvar|f}} is the set of complex numbers such that <math>Q(z)\ne 0</math>.
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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Rational functions are representative examples of [[meromorphic function]]s.<ref>{{cite book | last=Ablowitz | first=Mark J. | author1-link = Mark Ablowitz | last2=Fokas | first2=Athanassios S. | author2-link=Athanassios Fokas | title=Complex Variables | publisher=Cambridge University Press | date=2003 | isbn=978-0-521-53429-1|p=150}}</ref>
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