The given function is:

$f(x) = -3x^5 + 2x^4 + 5x^2 - x + 9$

This is a polynomial function of degree 5. Here are some key features you might be interested in:

1. Degree: The highest power of $x$ is 5, which means the polynomial is of degree 5. This typically results in a graph with up to 5 turning points.

2. Leading Term: The leading term is $-3x^5$. This term dominates the behavior of the function for large values of $x$, and because the coefficient is negative, the ends of the graph will approach negative infinity as $x \to \infty$ and positive infinity as $x \to -\infty$.

3. Constant Term: The constant term is 9, which gives the value of the function when $x = 0$. So, $f(0) = 9$.

Would you like to explore more details, such as finding the derivative, the roots, or behavior at certain points?

5 Related Questions:

1. How do you find the critical points of the function $f(x)$?
2. What are the roots (zeros) of the polynomial $f(x)$?
3. How does the graph of the function behave as $x$ approaches positive and negative infinity?
4. What is the first derivative of $f(x)$, and how can it help find local extrema?
5. Can you find the inflection points of the function using the second derivative?

Tip: The leading term in a polynomial function plays a major role in determining the graph's end behavior.