To determine the degree of the polynomial and the sign of the leading coefficient based on the graph provided, let’s analyze its end behavior.

Analysis:

1. The graph shows that as $x$ approaches $-\infty$, $f(x)$ goes up towards $+\infty$.
2. As $x$ approaches $+\infty$, $f(x)$ goes down towards $-\infty$.

Interpretation:

• This behavior corresponds to a polynomial with an odd degree and a negative leading coefficient.
  • Odd-degree polynomials exhibit opposite behaviors at each end (one side going up, the other going down).
  • A negative leading coefficient in an odd-degree polynomial means that as $x \to -\infty$, $f(x) \to +\infty$ and as $x \to +\infty$, $f(x) \to -\infty$.

Conclusion:

The correct selection based on the options provided is:

• Leading Coefficient Negative, Degree - Odd

Would you like more details or have any questions?

Here are some related questions you might find interesting:

1. How do we determine the degree of a polynomial just by looking at its graph?
2. Why does the sign of the leading coefficient affect the end behavior of a polynomial?
3. What are examples of polynomials with positive and negative leading coefficients?
4. How do even-degree polynomial functions differ in end behavior from odd-degree polynomials?
5. How does multiplicity at the roots affect the shape of the polynomial graph?

Tip: The end behavior of polynomial functions gives insight into the degree and leading coefficient sign without needing the explicit function formula.