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.