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The graph shown is a transformation of the absolute value function \( f(x) = |x| \). The original function \( f(x) = |x| \) is V-shaped and has its vertex at the origin (0, 0).

From the graph:
- The vertex of the transformed graph is at the point \( (0, 2) \), meaning the entire graph has been shifted upward by 2 units. 
- Additionally, the slopes of the lines on either side of the vertex appear to be different from the standard absolute value function. The slope of the left side is steeper (negative slope), and the slope on the right side is also steeper (positive slope), indicating a vertical stretching or compression.

Thus, the equation for this transformed graph can be written as:
\[
g(x) = 2 - |x|
\]
This represents a reflection of the absolute value function with a vertical shift of 2 units upward.

Would you like a deeper explanation of transformations or have any questions on this? Here are five related questions that can help expand your understanding:

1. What are the different types of transformations that can be applied to a function?
2. How would the graph change if the vertex were shifted to a different point?
3. How does stretching or compressing affect the slope of a linear part of a piecewise function like \( f(x) = |x| \)?
4. Can you describe how the equation of the absolute value function changes if the graph is reflected over the y-axis instead?
5. How would the graph change if the function inside the absolute value were shifted horizontally?

**Tip**: Always check for vertical and horizontal shifts, reflections, and stretching/compressing when analyzing transformations.

The graph above is a transformation of the function f(x) = |x|. Write an equation for the function graphed above.

Learn how to write the equation of a transformed absolute value function based on its graph. This problem covers key transformations such as vertical shifts and reflections, suitable for students in Grades 8-10.

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