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To determine the absolute maximum and minimum values from the graph of the function \( f \) over the interval \([-5, 5]\), we need to look for the highest and lowest points within that domain. Here's the step-by-step approach:

### Absolute Maximum:
- The graph shows the highest point at \( x = 2 \), where the \( y \)-coordinate is 3.5 (which is \( \frac{7}{2} \)).
- Therefore, the absolute maximum occurs at \( (2, \frac{7}{2}) \).

### Absolute Minimum:
- The lowest point of the graph is at \( x = -5 \), where \( y = -3.5 \) (which is \( -\frac{7}{2} \)).
- Thus, the absolute minimum is at \( (-5, -\frac{7}{2}) \).

### Conclusion:
- Maximum \( (x, y) = (2, \frac{7}{2}) \)
- Minimum \( (x, y) = (-5, -\frac{7}{2}) \)

Would you like more details on this process or have any questions?

Here are some related questions you might consider:
1. How do you determine the critical points of a function?
2. What is the difference between a local and absolute extremum?
3. Why are endpoints important in identifying absolute extrema?
4. Can a function have multiple absolute maxima or minima?
5. How do the first and second derivative tests help in finding extrema?

**Tip:** When finding absolute extrema, always check both the critical points and the endpoints of the interval.

You are given the graph of a function f defined on the interval [-5, 5]. Find the coordinates of the absolute maximum and the absolute minimum of f, if they exist.

Learn how to find the absolute maximum and minimum points of a function from its graph over a closed interval, with a detailed explanation and solution for the given graph on [-5, 5]. Suitable for high school students in Grades 10-12 studying calculus or precalculus.

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