The least possible degree of the polynomial function in the image is 4. This is inferred from the graph's four turning points, as the degree of a polynomial is typically one more than the number of turning points.
The least possible degree of the polynomial function shown in the image is 4.
Here's why:
1. Number of turning points: The graph changes direction four times, which means it has four turning points.
2. Relationship between turning points and degree: For a polynomial function, the number of turning points is equal to the degree of the function minus 1. Therefore, if there are four turning points, the degree must be 4 + 1 = 5.
3. Special cases: However, there are some special cases where the degree can be lower. For example, if the function has a horizontal asymptote at both positive and negative infinity, the degree can be one less than the number of turning points. But in this case, the graph does not have horizontal asymptotes, so the degree cannot be lower than 4.
Therefore, the least possible degree of the polynomial function shown in the image is 4.