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The problem involves analyzing a polynomial function \( f(x) \) based on its graph and filling out the information regarding the degree, leading coefficient, number of distinct real zeros, and relative extremes.

### Let's break this down step-by-step based on the graph shown:

1. **Degree of \( f(x) \)**: 
   - The graph of the polynomial function crosses the x-axis 3 times and has a total of 4 turning points (which suggests it's a 5th-degree polynomial).
   - A polynomial's degree is equal to the number of its turning points plus 1 for odd-degree polynomials. Therefore, the degree of \( f(x) \) is **5**.

2. **Leading Coefficient**:
   - The end behavior of the graph can help identify the sign of the leading coefficient. Since the graph starts in the negative y-direction and ends in the positive y-direction (falling on the left and rising on the right), this indicates that the leading coefficient is **positive**.

3. **Distinct Real Zeros**:
   - The graph crosses the x-axis in three distinct places, indicating that there are **3 distinct real zeros**.

4. **Relative Extremes**:
   - There are turning points where the graph changes direction (from increasing to decreasing or vice versa). In this case, there are **4 relative extremes** (local maxima or minima).

### Filling in the blanks:
- The degree of \( f(x) \) is **5**.
- The leading coefficient is **positive**.
- There are **3** distinct real zeros.
- There are **4** relative extremes.

Would you like further details on this, or do you have any specific questions?

### Related Questions:
1. How can you determine the degree of a polynomial from its graph?
2. What does the leading coefficient of a polynomial tell you about the graph's end behavior?
3. How do you count the number of real zeros from a graph?
4. What is the difference between a local maximum and a local minimum on a polynomial graph?
5. Can the degree of a polynomial be even if its graph crosses the x-axis?

### Tip:
The number of real zeros of a polynomial is equal to the number of times it intersects the x-axis, and the degree of the polynomial provides an upper bound for the total number of zeros (real and complex combined).

The polynomial function f(x) is graphed below. Fill in the form below regarding the features of this graph. The degree of f(x) is __, and the leading coefficient is __. There are __ distinct real zeros and __ relative extremes.

Analyze the graph of a polynomial function to determine its degree, leading coefficient, distinct real zeros, and relative extrema. This problem focuses on polynomial function properties, turning points, and graph behavior.

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