A rational functions is a function of the form f(x)=p(x)/q(x), where p(x) and q(x) are polynomials and q(x)≠0 ,q(x)≠0 .
The domain of a rational function consists of all the real numbers x=0 except those for which the denominator is x= 0 .
reciprocal for a number x, denoted by 1/x or x −1, is a number which when multiplied by x yields the multiplicative identity, 1.. The multiplicative inverse of a fraction a/b is b/a.
Therefore rational and reciprocal function are same type of function. Because of both function discontinuous, Hence both asymptotes will exist in both functions.
Rational and reciprocal function