Answer
The domain: $(-\infty,5)\cup(5,\infty)$
The vertical asymptote: $x=5$
The slant asymptote: $y=4x+20$
See graph
Work Step by Step
The function is undefined when the denominator is $0$:
$$x-5=0$$ $$x=5$$
Thus, the domain is $(-\infty,5)\cup(5,\infty)$.
The vertical asymptote is then $x=5$.
Since the degree of the numerator is one more than the degree of the denominator, the slant asymptote is the quotient of the numerator and the denominator and ignore the remainder:
$$y=\frac{4x^2}{x-5}=4x+20+\frac{100}{x-5}$$
Ignoring the remainder, the slant asymptote is:
$$y=4x+20$$
The sketch of the graph of the function is as shown.
