https://file.aiquickdraw.com/mathbot/file/1730348970484lmpeuqkb.jpg

To determine the least possible degree of the polynomial function from the graph, we can analyze the number of turning points.

### Step-by-Step Solution:
1. **Count the Turning Points**: A turning point is where the graph changes direction, either from increasing to decreasing or vice versa.
   - From the image, we see **five turning points**.

2. **Determine Degree Using Turning Points**: For a polynomial of degree \( n \), the maximum number of turning points it can have is \( n - 1 \). Therefore:
   \[
   n - 1 = 5 \Rightarrow n = 6
   \]

3. **Conclusion**: The minimum degree of the polynomial is **6**.

Would you like further details on how polynomial degree relates to turning points or have any questions?

Here are some related questions:
1. How does the degree of a polynomial affect its end behavior?
2. Can a polynomial of degree 6 have fewer than 5 turning points?
3. What are the characteristics of polynomials with an odd degree?
4. How do we determine the leading coefficient’s sign based on a graph?
5. What would change if the polynomial had an additional turning point?

**Tip**: Remember, the degree of a polynomial function is at least one more than its maximum number of turning points.

Determine the least possible degree of the polynomial function shown.

Learn how to determine the least possible degree of a polynomial function by analyzing the number of turning points on its graph. This example with five turning points reveals essential concepts of polynomial functions and graph analysis, making it suitable for students in Grades 10-12.

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