Answer
$f\left( x \right) = \frac{3}{{x - 3}}$
Work Step by Step
$$\eqalign{
& {\text{Vertical asymptote: }}x = 3 \cr
& {\text{To obtain a vertical asymptote at }}x = 3,{\text{ set in the}} \cr
& {\text{denominator of the rational function an expression }} \cr
& {\text{whose real root is }}x = 3,{\text{ using }}x - 3 \cr
& f\left( x \right) = \frac{3}{{x - 3}} \cr
& {\text{Horizontal asymptote: }}y = 0 \cr
& {\text{To obtain a horizontal asymptote at }}y = 0,{\text{ the degree}} \cr
& {\text{of the numerator must be less than the degree of the denominator}}{\text{, }} \cr
& {\text{the denominator is }}x - 3{\text{ }}\left( {{\text{linear function}}} \right),{\text{then set the }} \cr
& {\text{numerator equal to }}3{\text{ }}\left( {{\text{Constant}}} \right). \cr
& f\left( x \right) = \frac{3}{{x - 3}} \cr} $$
