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Identify the parent function and Identify the transformation represented by the graph.

The graph you provided is a **V-shaped** graph, which is characteristic of the **absolute value function**. The parent function for this type of graph is:

\[
f(x) = |x|
\]

### Identifying the Transformation:
To identify the transformation, we compare the given graph to the parent function \( f(x) = |x| \), which normally has a vertex at \( (0, 0) \).

1. **Horizontal shift**: The vertex of the given graph is located at \( (-6, 0) \), so the graph has been shifted **6 units to the left**.
   
2. **Vertical stretch**: The graph appears to maintain the same slope as the parent function. This indicates no vertical stretch or compression.

Thus, the function that represents the transformation is:

\[
f(x) = |x + 6|
\]

### Summary:
- **Parent function**: \( f(x) = |x| \)
- **Transformation**: Shifted 6 units to the left, no vertical or horizontal stretch/compression.

Would you like more details or have any further questions?

Here are 5 related questions to expand your understanding:
1. How would the graph change if the absolute value function was \( f(x) = |x - 2| \)?
2. What transformation occurs if you multiply the absolute value function by a constant, such as \( 2|x| \)?
3. How do horizontal shifts affect the domain of an absolute value function?
4. What is the effect of reflecting the absolute value function across the x-axis (e.g., \( f(x) = -|x| \))?
5. How do you determine the range of a transformed absolute value function?

**Tip**: For absolute value functions, the vertex represents the minimum (or maximum, if reflected) point, and transformations like shifts and stretches directly affect its position and shape.

Identify the parent function and identify the transformation represented by the graph.

Analyze the graph of an absolute value function, identify the parent function f(x) = |x|, and understand the transformation represented by a horizontal shift of 6 units left. Perfect for students in Grades 8-10.

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