State the end behavior of the function
\[
\begin{array}{l}
f(x)=-3 x^{4}+x^{3}+2 x^{2}-9 x-8 \\
\text { As } x \rightarrow-\infty, f(x) \rightarrow \square \\
\text { As } x \rightarrow \infty, f(x) \rightarrow \square
\end{array}
\]

Step 1 ：The end behavior of a function is determined by the leading term, which is the term with the highest degree. In this case, the leading term is -3x^4.

Step 2 ：As x approaches negative or positive infinity, the value of the function will be dominated by this term.

Step 3 ：Since the degree of the leading term is even and the coefficient is negative, as x approaches negative infinity, the function will approach positive infinity, and as x approaches positive infinity, the function will approach negative infinity.

Step 4 ：\(\boxed{\text{As } x \rightarrow -\infty, f(x) \rightarrow \infty}\)

Step 5 ：\(\boxed{\text{As } x \rightarrow \infty, f(x) \rightarrow -\infty}\)