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The problem presents the graph of an exponential function \( f(x) \). The graph seems to asymptotically approach \( y = 0 \) from below, and the function increases rapidly for negative \( x \), indicating it's likely of the form:

\[
f(x) = A \cdot e^{Bx} + C
\]

### Analyzing the graph:
1. The horizontal asymptote appears to be at \( y = 0 \), so \( C = 0 \).
2. The curve starts steeply from the negative side and approaches \( 0 \) as \( x \to \infty \), suggesting that the base of the exponent is negative for positive values of \( x \), meaning \( A \) is negative.
3. For values of \( x \) around 0, \( y \) is approximately \( -1 \), indicating the function might pass through \( (0, -1) \).

### Likely equation:
This suggests the function could take the form:

\[
f(x) = -e^{-x}
\]

Would you like further details or clarification on this explanation?

Here are five related questions for further exploration:
1. What is the general form of an exponential function?
2. How does the horizontal asymptote affect the form of the exponential function?
3. What happens to an exponential function as \( x \to \infty \) and \( x \to -\infty \)?
4. How can you determine the constant \( A \) in an exponential function from a graph?
5. How do different base values of \( e \) or other numbers change the shape of the graph?

**Tip:** When determining the equation of a graph, always look for key features like intercepts, asymptotes, and growth behavior to guide your choice of the function's form.

Gegeben sei ein Ausschnitt des Graphen einer exponentiellen Funktion f. Geben Sie zum abgebildeten Funktionsgraphen eine passende Funktionsgleichung an.

Determine the equation of the exponential function from the given graph. This problem involves key mathematical concepts such as exponential functions, horizontal asymptotes, and graph interpretation. Suitable for students in Grades 9-12.

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