Answer
The domain: $(-\infty,3)\cup(3,\infty)$
The vertical asymptote: $x=3$
The horizontal asymptote: $y=2$
See graph
Work Step by Step
The function is undefined when the denominator is $0$:
$$x-3=0$$ $$x=3$$
Thus, the domain is $(-\infty,3)\cup(3,\infty)$.
The vertical asymptote is then $x=3$.
Since the degree of the numerator is equal to the degree of the denominator, the horizontal asymptote is the quotient of the leading coefficient of the numerator and the leading coefficient of the denominator:
$$y=\frac{2}{1}$$ $$y=2$$
Thus, the horizontal asymptote is $y=2$.
The sketch of the graph of the function is as shown.
