https://file.aiquickdraw.com/mathbot/file/1726416311369k6gem19b.jpg

The graph you provided shows \( g(x) \), which is a transformation of the function \( f(x) = |x| \), an absolute value function. The task is to write the function rule for \( g(x) \) in the form \( a|x - h| + k \), where \( a \), \( h \), and \( k \) are integers or simplified fractions.

### Key Observations:
1. **Vertex**: The vertex of the graph (the point where the V-shape changes direction) is located at \( (0, 0) \). This indicates no horizontal or vertical shift, so \( h = 0 \) and \( k = 0 \).
   
2. **Slope**: The graph has two linear sections (one on each side of the vertex). Both sides have slopes of \( 1 \) and \( -1 \), which suggests that the "stretch" factor \( a = 1 \). This means the graph is not vertically stretched or compressed.

### Conclusion:
Since there is no horizontal shift, vertical shift, or stretching, the function is simply:
\[
g(x) = |x|
\]

Would you like any additional explanations or details? Here are five related questions to expand your understanding:

1. How would the function change if the vertex shifted to a different point, say \( (h, k) \)?
2. What would happen to the graph if the slope (stretch factor) \( a \) were a number other than 1?
3. Can you describe how horizontal translations affect absolute value functions?
4. How would the graph change if the function were \( g(x) = -|x| \)?
5. What is the domain and range of the given function \( g(x) = |x| \)?

**Tip**: The absolute value function \( f(x) = |x| \) forms a V-shape, with transformations affecting its orientation, slope, and position on the graph.

The graph shows g(x), which is a transformation of f(x) = |x|. Write the function rule for g(x).

Learn how to determine the transformation of the absolute value function f(x) = |x| to g(x) from the graph. This includes identifying shifts, stretches, and slopes, explained for Grades 9-11 students.

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