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The problem is asking for the **fewest possible number of zeros** of a continuous function \( f \) on the interval \([-2, 3]\) based on the table provided. Let's examine the table of values:

| \( x \)  | -2  | -1  | 0   | 1   | 2   | 3   |
|---------|------|------|-----|-----|-----|-----|
| \( f(x) \) | -2   | 5    | 2   | -4  | -1  | 3   |

To solve the problem, we will apply the **Intermediate Value Theorem**, which tells us that if a function is continuous on an interval, and the function changes signs between two points, then there is at least one zero in between those points.

### Analyzing the table values:
1. From \( x = -2 \) to \( x = -1 \), \( f(x) \) changes from \(-2\) to \(5\). Since the sign changes (from negative to positive), there is at least one zero between \( x = -2 \) and \( x = -1 \).
2. From \( x = -1 \) to \( x = 0 \), \( f(x) \) changes from \(5\) to \(2\). There is no sign change here, so no zero between \( x = -1 \) and \( x = 0 \).
3. From \( x = 0 \) to \( x = 1 \), \( f(x) \) changes from \(2\) to \(-4\). Since the sign changes (from positive to negative), there is at least one zero between \( x = 0 \) and \( x = 1 \).
4. From \( x = 1 \) to \( x = 2 \), \( f(x) \) changes from \(-4\) to \(-1\). There is no sign change, so no zero between \( x = 1 \) and \( x = 2 \).
5. From \( x = 2 \) to \( x = 3 \), \( f(x) \) changes from \(-1\) to \(3\). Since the sign changes (from negative to positive), there is at least one zero between \( x = 2 \) and \( x = 3 \).

### Conclusion:
There are at least **three intervals** where a sign change occurs, meaning there are at least **three zeros** in the interval \([-2, 3]\). 

Therefore, the fewest possible number of zeros is **three**, and the correct answer is **D: Three**.

Would you like more details or further clarification? Here are five related questions you might find interesting:

1. What is the Intermediate Value Theorem and how is it applied?
2. How can we estimate the location of zeros more precisely based on function values?
3. Can a continuous function have more zeros than suggested by sign changes?
4. How do discontinuities affect the number of zeros in a function?
5. What methods can be used to find the exact zeros of a function?

**Tip**: Always check for sign changes in a continuous function to estimate the number of zeros between given points!

Selected values of a continuous function f are given in the table above. What is the fewest possible number of zeros of f in the interval [-2, 3]?

Learn how to determine the fewest possible number of zeros of a continuous function based on given values in the interval [-2, 3]. This problem involves the Intermediate Value Theorem and analyzing function behavior over intervals.

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