To determine the least degree of a polynomial from its graph, we examine the number of turning points and end behavior:

1. Turning Points: A turning point occurs where the graph changes direction. The number of turning points gives a clue to the degree of the polynomial. A polynomial of degree $n$ can have up to $n-1$ turning points.

   From the graph:

   • There are three turning points (two local maxima and one local minimum).
   • This suggests that the degree of the polynomial must be at least 4 (since a degree-4 polynomial can have up to 3 turning points).

2. End Behavior: The graph seems to have opposite end behaviors on the left and right (falling to the left and rising to the right), indicating that the degree of the polynomial is odd.

Given these clues, the least degree for this polynomial is 5 (it has 3 turning points and an odd degree for the observed end behavior).

Would you like a more detailed breakdown of the steps?

Here are some related questions to explore:

1. What is the general form of a polynomial of degree 5?
2. How can you use the leading coefficient test to determine end behavior?
3. How does the number of roots relate to the degree of the polynomial?
4. What happens when a polynomial has fewer turning points than the degree suggests?
5. Can a graph have more turning points than its degree predicts?

Tip: For polynomials, always check both the number of turning points and the end behavior to determine the degree.