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To determine the transformations that map Figure \( S \) onto Figure \( T \), we will analyze the necessary steps.

### Step 1: Identify the transformations

1. **Reflection**: Observe that Figure \( T \) appears to be a reflection of Figure \( S \) over the \( x \)-axis. After reflecting, the figure would maintain its size and shape but flip to the other side of the \( x \)-axis.
  
2. **Translation**: After reflecting over the \( x \)-axis, Figure \( S \) needs to be translated. From the reflected position of Figure \( S \), move it right and down to match Figure \( T \).

### Verifying the steps:
- **Reflection over the \( x \)-axis**: Points of Figure \( S \), such as \( (-8, 6) \), would reflect to \( (-8, -6) \). The entire figure will flip to the lower half of the graph.
- **Translation**: After reflecting, you need to move Figure \( S \)'s reflected version horizontally to align with the position of Figure \( T \). The translation required would be approximately 13 units right and 1 unit down.

### Conclusion
The transformation that maps Figure \( S \) to Figure \( T \) is:
1. **A reflection over the \( x \)-axis**, followed by
2. **A translation 13 units to the right and 1 unit down**.

Would you like a more detailed explanation of each step?

### Relative Questions
1. What other transformations could be applied if the figures were rotated?
2. How would the transformation change if Figure \( T \) were located in another quadrant?
3. Can you verify the reflection and translation using coordinate points?
4. How would you describe a transformation involving rotation instead of reflection?
5. Is it possible to achieve the same result using a different sequence of transformations?

### Tip
When identifying transformations, always start by examining reflections, rotations, and translations separately to understand the sequence required for accurate mapping.

Determine a series of transformations that would map Figure S onto Figure T.

Explore the steps required to map Figure S onto Figure T using a reflection over the x-axis followed by a translation. This problem demonstrates how geometric transformations, such as reflection and translation, are applied to shapes in the coordinate plane. Suitable for students in Grades 8-10.

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