To determine the least possible degree of the polynomial graphed, we need to focus on the number of turning points and how they relate to the degree of the polynomial.

Steps to solve:

1. Identify Turning Points: A turning point is a point where the graph changes direction (from increasing to decreasing or vice versa). By counting the number of turning points, we can estimate the degree of the polynomial.

   • From the graph, there are 4 turning points visible.

2. Relating Turning Points to Degree: A polynomial of degree $n$ can have at most $n - 1$ turning points. Thus, if there are 4 turning points, the least possible degree of the polynomial must be $n \geq 5$.

Conclusion:

The least possible degree of the polynomial is 5.

Would you like more details or have any questions on this explanation?

Related Questions:

1. What is the relationship between the number of roots and the degree of a polynomial?
2. How does the end behavior of the graph help identify the degree of a polynomial?
3. Could a higher degree polynomial also match this graph? Why or why not?
4. What effect do multiple roots at the same point have on the turning points of a polynomial graph?
5. How do we determine whether a polynomial is of odd or even degree based on its graph?

Tip:

The degree of a polynomial controls both the number of turning points and the end behavior of the graph, which is helpful for estimating degree from visual clues.