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To determine the series of transformations that map Figure \( I \) onto Figure \( J \), we need to carefully analyze the positions and orientations of the two figures.

### Step-by-Step Process:

1. **Reflection across the x-axis:**
   - Figure \( J \) appears to be an upside-down version of Figure \( I \), so a reflection over the x-axis would map the shape from above the x-axis (where Figure \( I \) is) to below it (where Figure \( J \) is).
   
2. **Translation:**
   - After reflecting Figure \( I \) over the x-axis, we can see that Figure \( J \) is shifted downward and to the right. This suggests a translation is needed.
   - Translation can be calculated by looking at the movement of a specific point from Figure \( I \) to Figure \( J \).
     - For example, if we consider a point on Figure \( I \), such as \( (-1, 6) \), after reflecting over the x-axis, it will be at \( (-1, -6) \). We then need to translate it to its corresponding point on Figure \( J \), which could be something like \( (-1, -3) \), so this requires a vertical translation upward by 3 units.

Thus, the series of transformations that would map Figure \( I \) onto Figure \( J \) would be:

1. Reflect Figure \( I \) over the x-axis.
2. Translate the resulting figure downward (or upward) by the necessary amount to align with Figure \( J \).

Would you like more details on any of these transformations, or how to calculate them specifically?

### Related Questions:
1. What is the general rule for reflection over the x-axis in coordinate geometry?
2. How can we calculate the exact translation needed after a reflection?
3. Can there be a rotation involved in this transformation process?
4. How can transformations be combined into a single matrix operation?
5. What is the effect of reflecting over both the x-axis and y-axis in sequence?

### Tip:
When analyzing transformations, always break them down into the simplest operations (reflection, rotation, translation) to avoid confusion.

Determine a series of transformations that would map Figure I onto Figure J.

Discover how to map Figure I to Figure J using a series of transformations. This involves reflecting over the x-axis and translating on the coordinate plane. This solution is suitable for students in Grades 8-10 and covers key transformation concepts in geometry.

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