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The problem provides values of a continuous real function \( f: \mathbb{R} \to \mathbb{R} \) at several points:

1. \( f(-e) = -2.71 \)
2. \( f(-0.1e) = 3.14 \)
3. \( f(-0.01) = 0.05 \)
4. \( f(0.01) = 27.18 \)
5. \( f(1) = -0.027 \)
6. \( f(e) = 5 \)
7. \( f(3) = 5 \)
8. \( f(2e) = -2 \)

The question asks for the minimum number of zeros of \( f \) (values of \( x \) for which \( f(x) = 0 \)).

### Solution Outline
To determine the minimum number of zeros, we can apply the **Intermediate Value Theorem** (IVT), which states that if \( f \) is continuous on an interval \([a, b]\) and takes values of opposite signs at \( a \) and \( b \), then there exists at least one root \( c \in (a, b) \) such that \( f(c) = 0 \).

### Applying the Intermediate Value Theorem
Looking at the function values provided:

1. Between \( f(-e) = -2.71 \) and \( f(-0.1e) = 3.14 \), the function changes sign, so there is at least one root in this interval.
2. Between \( f(1) = -0.027 \) and \( f(e) = 5 \), the function again changes sign, indicating at least one more root in this interval.
3. Between \( f(e) = 5 \) and \( f(2e) = -2 \), the function changes sign once more, indicating at least one more root in this interval.

### Conclusion
By applying the Intermediate Value Theorem in these intervals, we find at least three intervals where \( f \) must cross the x-axis. Therefore, **the function \( f \) has at least 3 zeros**.

### Answer
The correct choice is:
- **3**

Would you like further details on this approach or clarification on any part?

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Here are some related questions that expand on this topic:

1. What is the Intermediate Value Theorem, and how is it applied in different scenarios?
2. How can we determine if a function has exactly three zeros, rather than just at least three?
3. What are other methods to find the zeros of a function besides the Intermediate Value Theorem?
4. How does continuity of a function play a role in determining its roots?
5. Can the Intermediate Value Theorem be applied to non-continuous functions? Why or why not?

**Tip:** When analyzing function behavior across intervals, always check if the function changes sign. This change often hints at the existence of a root within the interval.

Von der stetigen reellen Funktion f : R → R sei bekannt, dass f(-e) = -2.71, f(-0.1e) = 3.14, f(-0.01) = 0.05, f(0.01) = 27.18, f(1) = -0.027, f(e) = 5, f(3) = 5 und f(2e) = -2. Wie viele Nullstellen besitzt f mindestens?

Analyze a continuous function with given values at specific points to determine the minimum number of zeros using the Intermediate Value Theorem. The problem explores key concepts in calculus and continuity.

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