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To map Figure \( R \) onto Figure \( S \), we need to determine a sequence of geometric transformations such as translations, rotations, reflections, or dilations.

Looking at the two figures:

1. **Reflection**: The first thing we can observe is that Figure \( R \) is a reflection of Figure \( S \) across the x-axis. The shapes have the same dimensions and orientation, but one is positioned above the x-axis and the other below.

2. **Translation**: After reflecting Figure \( R \), it will be positioned above the x-axis but needs to be shifted horizontally to align with Figure \( S \). By observing the coordinates of the corresponding points, Figure \( R \) needs to be translated horizontally to the right to map onto Figure \( S \).

### Step-by-Step Transformations:
1. **Reflect Figure \( R \) across the x-axis**: This moves Figure \( R \) to the region below the x-axis.
   
2. **Translate Figure \( R \) horizontally**: The coordinates of \( R \) will need to shift rightwards by a certain number of units. By inspection, we can see this horizontal translation is approximately 9 units to the right.

Thus, the transformations to map Figure \( R \) onto Figure \( S \) are:
- Reflect across the x-axis.
- Translate 9 units to the right.

Let me know if you want further details or explanations! Here are some related questions you could explore:

1. How can you write the transformation as a function?
2. How do reflections affect the coordinates of a point?
3. What other types of transformations could map Figure \( R \) to Figure \( S \)?
4. How do translations affect the orientation of figures?
5. Can you describe a sequence of transformations for other figures on the coordinate plane?

**Tip:** When performing reflections, focus on how the signs of the coordinates change depending on the axis you're reflecting across.

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

Learn how to map Figure R onto Figure S through a series of geometric transformations, including reflections across the x-axis and translations. This problem covers key concepts in coordinate geometry and is suitable for students in Grades 8-10.

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