Suppose that $f$ is a monomial function such that as $x \rightarrow \infty, f(x) \rightarrow-\infty$. Which of the following could be a function formula for $f$ ? Select all that apply.
\[
f(x)=5.5 x^{5}
\]
$f(x)=-3 x^{2}$
$f(x)=-x^{9}$
$f(x)=-\left(\frac{1}{7}\right) x^{4}$
$f(x)=x^{10}$

Step 1 ：A monomial function is a function of the form \(f(x) = ax^n\), where \(a\) is a constant and \(n\) is a nonnegative integer. The function \(f(x)\) tends to \(-\infty\) as \(x \rightarrow \infty\) if and only if \(a < 0\) and \(n\) is an odd integer. This is because if \(n\) is an even integer, then \(f(x)\) will tend to \(+\infty\) as \(x \rightarrow \infty\) regardless of the sign of \(a\). Therefore, we need to find the functions among the given options that satisfy these conditions.

Step 2 ：The functions that satisfy the conditions are \(f(x)=-3 x^{2}\), \(f(x)=-x^{9}\), and \(f(x)=-\left(\frac{1}{7}\right) x^{4}\). These are the functions for which the function value decreases as \(x\) increases, and the function value is negative for all \(x > 0\). Therefore, these are the functions for which \(f(x) \rightarrow -\infty\) as \(x \rightarrow \infty\).

Step 3 ：Final Answer: The function formulas for \(f\) could be \(f(x)=-3 x^{2}\), \(f(x)=-x^{9}\), and \(f(x)=-\left(\frac{1}{7}\right) x^{4}\).