To determine the least possible degree of the polynomial graphed:

1. Count the Turning Points: The turning points are where the graph changes direction. By inspecting the graph, we see 4 turning points.

2. Relation Between Turning Points and Degree: The maximum number of turning points of a polynomial is one less than its degree ($n - 1$, where $n$ is the degree). Therefore, the degree of the polynomial must be at least one more than the number of turning points.

   • In this case, since there are 4 turning points, the least possible degree of the polynomial is $4 + 1 = 5$.

Thus, the least possible degree of the polynomial is 5.

Would you like further explanation or additional details? Here are some related questions to expand your understanding:

1. How do turning points help identify the degree of a polynomial?
2. What does the degree of a polynomial indicate about its end behavior?
3. Could this polynomial be of an even degree? Why or why not?
4. How do the x-intercepts of the graph relate to the polynomial's degree?
5. Can you always predict the degree of a polynomial graph based on its appearance?

Tip: Always remember, the number of turning points provides a lower bound for the degree minus one.