Consider the function $$f(x) = \frac{27 x^3+ 18 x^2 - 171 x+ 54 }{-3 x^3 - 3 x^2+ 42 x+ 72 }$$
The root(s) of $f(x)$ are:
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The graph of $f(x)$ has hole(s) when $x$ has the following value(s):
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The graph of $f(x)$ has vertical asymptotes when $x$ is:
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The graph of $f(x)$ has a horizontal asymptote at $y=$