Examples
Rational function of degree 3:The rational function is not defined at .
The rational function is defined for all real numbers, but not for all complex numbers, since if x were a square root of (i.e. the imaginary unit or its negative), then formal evaluation would lead to division by zero:, which is undefined.
The rational function, as x approaches infinity, is asymptotic to .
A constant function such as f(x) = π is a rational function since constants are polynomials. Note that the function itself is rational, even though f(x) is irrational for all x.
The rational function is equal to 1 for all x except 0, where there is a removable singularity.
The sum, product, or quotient (excepting division by the zero polynomial) of two rational functions is itself a rational function: however, the process of reduction to standard form may inadvertently result in the removing of such discontinuities unless care is taken.
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