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The question asks to "state the least possible degree" of a polynomial based on the graph provided. 

From analyzing the graph, here are the key features that help determine the degree of the polynomial:

1. **Turning Points:** The number of turning points (places where the graph changes direction) helps to estimate the degree of the polynomial. This graph seems to have **three turning points**, which suggests a degree of at least 4, as the maximum number of turning points for a polynomial is \(n - 1\) where \(n\) is the degree.

2. **End Behavior:** The graph's end behavior (both ends going in opposite directions) suggests that the degree of the polynomial is **odd**, and the leading coefficient is positive. This rules out degree 4, suggesting a minimum degree of 5.

Therefore, the least possible degree of the polynomial is **5**, since it fits both the turning point rule and the end behavior.

Would you like more details or have any questions about this? 

Here are five questions related to this topic:
1. What are turning points in the context of polynomial functions?
2. How does the degree of a polynomial relate to its turning points?
3. What is the significance of end behavior in determining polynomial degree?
4. How do you determine the leading coefficient from a graph?
5. What is the difference between odd and even degree polynomials in terms of graph behavior?

**Tip:** The degree of a polynomial affects not only the number of turning points but also the overall shape and direction of the graph's ends!

For the given graph, state the least possible degree. Justify your answer.

Analyze the graph of a polynomial function to determine the least possible degree based on turning points and end behavior. Learn about key concepts such as polynomial degrees, graph analysis, and how the number of turning points relates to the degree of the function.

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