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The image contains a task in German that reads:

"Skizzieren Sie zum Graphen \( G_f \) der Funktion \( f \) in Ihrem Heft den Graphen \( G_F \) einer Stammfunktion \( F \) von \( f \) und beschreiben Sie Ihr Vorgehen."

Translation:  
"Sketch the graph \( G_F \) of an antiderivative \( F \) for the function \( f \) next to the graph \( G_f \) of the function \( f \) in your notebook and describe your procedure."

This task involves plotting the graph of an antiderivative (indefinite integral) \( F \) corresponding to a given function \( f \), based on the four provided graphs.

Here’s an interpretation of the graphs:

1. **Graph (a):** This is a straight line with a negative slope, representing a linear function. The antiderivative will be a quadratic function (parabola). The slope is constant, so the graph of \( F \) should show a consistent curvature.
   
2. **Graph (b):** This is a parabola, indicating a quadratic function. The antiderivative will be a cubic function. The graph of \( F \) will rise faster as \( x \) increases, showing the cubic curve's rapid growth.

3. **Graph (c):** This appears to be a sinusoidal curve (oscillating function). The antiderivative of such a function will be a phase-shifted sinusoidal curve, as integrating sine or cosine functions gives similar oscillating patterns.

4. **Graph (d):** The graph shows a steep curve that looks like part of an exponential or a power function. The antiderivative of this function will likely show even steeper growth, resembling a higher-order polynomial or exponential curve.

Would you like me to generate detailed antiderivatives for each of these functions, or do you have any specific questions regarding these graphs?

Here are five related questions to consider:
1. How do you determine the general shape of the antiderivative based on the graph of the original function?
2. What is the effect of a constant slope on the graph of the antiderivative?
3. How does a change in concavity in the graph of \( f \) translate to the graph of \( F \)?
4. What happens when you integrate sinusoidal functions like sine or cosine?
5. How does increasing the degree of the original function affect the complexity of the antiderivative?

**Tip:** The antiderivative's slope at any point corresponds to the value of the original function at that point.

Skizzieren Sie zum Graphen G_f der Funktion f in Ihrem Heft den Graphen G_F einer Stammfunktion F von f und beschreiben Sie Ihr Vorgehen.

Learn how to sketch the graph of an antiderivative (indefinite integral) for a given function based on its graph. This task involves interpreting linear, quadratic, sinusoidal, and exponential functions and their corresponding integral curves. Ideal for students in Grades 11-12.

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