Describe the end behavior of the graph of the function.
\[
\begin{array}{r}
f(x)=-5(4)^{x}-9 \\
\text { As } x \rightarrow-\infty, f(x) \rightarrow \square \text {. As } x \rightarrow \infty, f(x) \rightarrow
\end{array}
\]

Step 1 ：The function given is an exponential function, where the base of the exponential function is 4, which is greater than 1, and the coefficient of the exponential function is -5, which is less than 0.

Step 2 ：As x approaches negative infinity, the value of \(4^x\) approaches 0, and the function \(f(x)\) approaches -9.

Step 3 ：As x approaches positive infinity, the value of \(4^x\) approaches positive infinity, but because of the negative coefficient, the function \(f(x)\) approaches negative infinity.

Step 4 ：Final Answer: \(\boxed{\text{As } x \rightarrow -\infty, f(x) \rightarrow -9. \text{ As } x \rightarrow \infty, f(x) \rightarrow -\infty.}\)