https://file.aiquickdraw.com/mathbot/file/1726080449183mu4qe2kz.jpg

The graph provided depicts a piecewise linear function where the postman walks a fixed distance from the post office, and the transformation is based on the absolute value function \( y = |x| \).

### Step-by-step analysis:
1. **Parent function**: The parent function \( y = |x| \) is V-shaped and symmetrical about the y-axis.
2. **Transformations**:
   - The graph has been **reflected about the x-axis** because the graph starts decreasing after \( x = 0 \).
   - There seems to be a **vertical stretch** by a factor of 2, as the slope is steeper than the standard \( y = |x| \) graph.
   - The vertex of the graph has shifted to the right (indicating a **horizontal shift of 4 units to the right**) and upwards (**vertical shift of 8 units up**).

Thus, the correct series of transformations would include a reflection about the x-axis, vertical stretch by a factor of 2, horizontal shift 4 units to the right, and vertical shift 8 units up.

### Answer:
The correct option is **A**.

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Would you like further details or have any questions?

Here are 5 related questions to expand your understanding:
1. How do you determine the vertical stretch or compression of a graph?
2. What impact does reflecting a graph across the x-axis have on the function?
3. How does a horizontal shift affect the equation of a function?
4. How can you differentiate between a horizontal and vertical shift in a graph?
5. What is the effect of a vertical shift on the vertex of an absolute value function?

**Tip**: When analyzing transformations, always consider the vertex's position, the slope, and the direction in which the graph opens.

The graph represents a transformation of the parent function y = |x|. Which series of transformations accurately describe the graph shown?

Understand the transformation of the parent function y = |x| with reflections, vertical stretches, and horizontal and vertical shifts. Learn how these transformations are applied to describe real-world scenarios such as distance vs. time graphs. Suitable for Grades 9-12.

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