To determine the least possible degree of the polynomial function represented by the given graph, we need to consider the key characteristics of the graph, particularly the number of turning points and the end behavior.

1. Number of Turning Points: The turning points are where the graph changes direction from increasing to decreasing or vice versa. From the graph:

   • There are 3 turning points visible (1 going up, 1 going down, and then 1 more going up).

2. Relation Between Degree and Turning Points: A polynomial of degree $n$ can have at most $n-1$ turning points. Therefore, if there are 3 turning points, the minimum degree $n$ must satisfy: $n-1 \geq 3 \implies n \geq 4$

3. End Behavior: The ends of the graph suggest a higher degree polynomial:

   • As $x \to -\infty$, $f(x) \to -\infty$
   • As $x \to +\infty$, $f(x) \to +\infty$

   This behavior is consistent with a polynomial of even degree where the leading coefficient is positive.

Combining these observations, the minimum degree that satisfies these conditions is 4. Therefore, the least possible degree of the polynomial function represented by the graph is:

d) 4

Do you want more details or have any questions about this solution? Here are some relative questions to expand your understanding:

1. What are the characteristics of a polynomial graph with an odd degree?
2. How do we determine the leading coefficient's sign from the graph?
3. How do the roots of the polynomial relate to its graph?
4. What happens to the polynomial's degree if more turning points are added?
5. How does the degree of a polynomial affect its shape and number of x-intercepts?
6. Can a polynomial of degree 4 have fewer than 3 turning points?
7. How can we use derivatives to find turning points in a polynomial function?
8. How do changes in the coefficients of a polynomial affect its graph?

Tip: When analyzing polynomial graphs, always consider the number of turning points and end behavior to estimate the polynomial's degree.