f\left(x\right)=-3x^{5}+2x^{4}+5x^{2}-x+9

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.

Explore the key features of the polynomial function f(x) = -3x^5 + 2x^4 + 5x^2 - x + 9, including its degree, end behavior, and constant term. This problem covers important concepts like polynomial degree, turning points, and behavior as x approaches infinity. Suitable for students in Grades 10-12.

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