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The problem involves identifying in which fields the graphs of the functions \( y = a \cdot x \) are located when the value of \( a \) changes. The diagram shows four quadrants, numbered 1 to 4, each subdivided into regions that presumably represent the different behaviors of the function based on the slope \( a \).

Here are the interpretations of each condition for \( a \):

1. **\( a > 1 \)**: The slope is positive and steep, so the graph will be in fields where the line rises steeply from left to right. This would correspond to **Field 1** in the upper right and **Field 3** in the lower left.

2. **\( 0 < a < 1 \)**: The slope is positive but less steep (closer to horizontal). This graph will also be in the quadrants where the function rises from left to right, so it corresponds to **Field 2** in the upper right and **Field 4** in the lower left.

3. **\(-1 < a < 0\)**: The slope is negative but less steep (closer to horizontal). This would correspond to graphs that fall from left to right, so it would be in **Field 2** in the upper left and **Field 4** in the lower right.

Thus, the answers should be:

- For \( a > 1 \): **Bereich 1** (Field 1)
- For \( 0 < a < 1 \): **Bereich 2** (Field 2)
- For \(-1 < a < 0\): **Bereich 3** (Field 3)

Would you like further details on how these were determined or have any questions?

### Related Questions:
1. What happens to the graph of \( y = a \cdot x \) when \( a = -1 \)?
2. How does the graph of \( y = a \cdot x \) look when \( a = 0 \)?
3. In which fields would you find graphs for \( a < -1 \)?
4. How does changing the value of \( a \) affect the steepness of the graph?
5. Can you explain the effect of a negative \( a \) value on the direction of the graph?

**Tip:** Always check the value of the slope \( a \) to understand how it affects the graph's direction and steepness in a coordinate plane.

In welchen Feldern verlaufen die Graphen der Funktionen y = a • x, wenn der Wert von a sich ändert? Ordne zu.

Determine in which fields the graphs of y = a • x are located as the slope a changes. This problem covers concepts of linear functions and the behavior of lines for different values of the slope. Suitable for students in Grades 9-11.

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