Answer
By equating the denominator of the rational function to zero, the vertical asymptote of $f\left( x \right)$ can be determined.
Work Step by Step
A function $f\left( x \right)$ is a rational function if it is written in the form
$f\left( x \right)=\frac{P\left( x \right)}{Q\left( x \right)}$ …… (1)
Where $P\left( x \right),Q\left( x \right)$ are the polynomial functions of x in simplest form, and $Q\left( x \right)$ cannot be a zero function.
In order to find the vertical asymptotes of the rational function, equate the polynomial $Q\left( x \right)$ to zero.
Then, the zeros of the polynomial $Q\left( x \right)$ give the vertical asymptote of the rational function.
For example, let $f\left( x \right)=\frac{{{x}^{3}}+2x-3}{\left( x-2 \right)\left( x+3 \right)}$
Then equate the denominator of the above rational function with $0$. The roots of the polynomial $Q\left( x \right)$ give the vertical asymptote.
Thus, the vertical asymptotes of $f\left( x \right)$ will be $2$ and $-3$.
