Rational function
A rational function is any function which can be written as the ratio of two polynomial functions.
Any function of one variable, x, is called a rational function if, and only if, it can be written in the form:
[tex]\begin{gathered} f(x)=\frac{P(x)}{Q(x)} \\ \end{gathered}[/tex]
Yes, a rational function always have an aymptote.
It always have an asymptote because the denominator can never be zero.
Yes, It is possible to have holes in the graph of a rational function.
The main reason why there is a hole because if there is the same factor in the numerator and denominator, there is a hole.
