To determine the least possible degree of the polynomial represented by the graph, follow these steps:

1. Count the number of turning points: Turning points are where the graph changes direction. From the image, there are 4 turning points.

2. Use the relationship between degree and turning points: The maximum number of turning points for a polynomial is always one less than its degree. Hence, if there are 4 turning points, the degree of the polynomial must be at least $4 + 1 = 5$.

3. Check behavior at the ends: The graph appears to have opposite end behaviors (rising on one side and falling on the other). This indicates the degree of the polynomial is odd, which matches a degree of 5.

Final Answer:

The least possible degree of the polynomial graphed is 5.

Would you like further clarification or examples? Here are 5 related questions for deeper understanding:

1. What is the relationship between the degree of a polynomial and the number of x-intercepts it can have?
2. How can the leading coefficient affect the end behavior of a polynomial graph?
3. What distinguishes even-degree polynomials from odd-degree polynomials graphically?
4. How can you determine whether a turning point is a local maximum or minimum?
5. Can a polynomial of degree 5 have fewer than 4 turning points?

Tip: Always count the turning points and analyze end behavior to identify the degree of a polynomial!