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From the graph provided, you are asked to find the absolute minimum of the function \( f(x) \) on the interval \( [-12, 5] \). Based on the graph:

- The function reaches its lowest point at \( x = 2 \), where \( f(2) = -4 \).

Thus, the absolute minimum of the function is \( f(2) = -4 \), confirming that **Option A** is correct.

Would you like a more detailed explanation, or do you have any further questions?

Here are 5 related questions to explore further:
1. How do you determine whether a function has an absolute minimum or maximum on a closed interval?
2. What is the difference between a local minimum and an absolute minimum?
3. How would the function's minimum change if the interval were extended beyond \( [-12, 5] \)?
4. Can a function have more than one absolute minimum?
5. How do critical points help in finding absolute extrema of a function?

**Tip:** Always check the endpoints of the interval and critical points within the interval when looking for absolute extrema.

Find the absolute minimum of f on [-12, 5].

Learn how to find the absolute minimum of a function on the interval [-12, 5] using graph interpretation. This example covers key concepts in calculus, including the Extreme Value Theorem. Suitable for high school students.

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