The graph provided appears to show a polynomial function $h(x)$. Let's analyze it step by step based on the requirements:

1. Degree of the Function:
   The degree of a polynomial is related to the number of turning points (local maxima and minima) and the end behavior of the graph. The graph appears to have 3 turning points: one maximum, one minimum, and another maximum. A polynomial function with $n$ turning points generally has degree $n+1$.

   • Since there are 3 turning points, the degree of this function is most likely 4.

2. Sign of the Leading Coefficient:
   The leading coefficient of a polynomial controls the direction of the end behavior.

   • As $x \to -\infty$, $h(x) \to -\infty$ (the graph goes down on the left).
   • As $x \to +\infty$, $h(x) \to +\infty$ (the graph goes up on the right).
     This indicates the leading coefficient is positive, as a positive leading coefficient in an even-degree polynomial results in both ends going in the same direction (down on the left and up on the right).

3. Number of Turning Points:
   The number of turning points corresponds to the local maxima and minima.

   • The graph shows exactly 3 turning points (as described earlier).

Summary:

• Possible Degree: 4
• Sign of Leading Coefficient: Positive
• Number of Turning Points: 3

Would you like more details or have any questions?

Here are 5 related questions to consider:

1. How can we determine the possible degree of a polynomial if the graph has no turning points?
2. How does the sign of the leading coefficient change the end behavior for an odd-degree polynomial?
3. What is the relationship between the degree of a polynomial and the maximum number of turning points it can have?
4. Can a polynomial have fewer turning points than its degree minus 1? Why or why not?
5. What does it mean if the leading coefficient of a polynomial is negative?

Tip: For polynomials, the maximum number of turning points is always one less than the degree.