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The [[degree of an algebraic variety|degree]] of the 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.
In some contexts, such as in [[asymptotic analysis]], the ''degree'' of a rational function is the difference between the degrees of the numerator and the denominator.<ref>{{cite book |last1=Bourles |first1=Henri |title=Linear Systems |date=2010 |publisher=Wiley |isbn=978-1-84821-162-9 |page=515 |url=https://onlinelibrary.wiley.com/doi/book/10.1002/9781118619988 |access-date=5 November 2022}}</ref>{{at|___location=Section 13.6.1 ''Rational functions''}}<ref>{{cite book |last1=Bourbaki |first1=N. |title=Algebra II |date=1990 |publisher=Springer |isbn=3-540-19375-8 |page=A.IV.20}}</ref>{{at|___location=Chapter IV ''Polynomials and rational fractions'', Section 3 ''Rational fractions'', Subsection 2 ''Degrees''}}
In [[network synthesis]] and [[Network analysis (electrical circuits)|network analysis]], a rational function of degree two (that is, the ratio of two polynomials of degree at most two) is often called a '''{{vanchor|biquadratic function}}'''.<ref>Glisson, Tildon H., ''Introduction to Circuit Analysis and Design'', Springer, 2011 {{ISBN|9048194431}}.</ref>
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