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The graph provided shows a V-shaped function, which is a translation of the parent function \( f(x) = |x| \). To find the equation of the translated function \( g(x) \), we must analyze its shift and form.

### Step-by-step approach:

1. **Determine the vertex (h, k)**:  
   The vertex of the parent function \( f(x) = |x| \) is located at (0, 0). In this case, the vertex of the function \( g(x) \) has shifted. From the graph, the vertex is at \( (-2, 6) \). Therefore, \( h = -2 \) and \( k = 6 \).

2. **Determine the vertical stretch/compression (a)**:  
   The slope of the arms of the V in the parent function \( f(x) = |x| \) is 1. In this graph, the slope is still 1, meaning there is no vertical stretch or compression. Thus, \( a = 1 \).

3. **Form the equation**:  
   The general form for a translated absolute value function is:
   \[
   g(x) = a|x - h| + k
   \]
   Substituting the values \( a = 1 \), \( h = -2 \), and \( k = 6 \), we get:
   \[
   g(x) = |x + 2| + 6
   \]

### Final Answer:
\[
g(x) = |x + 2| + 6
\]

Let me know if you'd like further clarification or details!

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Here are 5 related questions to expand on this:

1. How would the graph change if \( a = -1 \)?
2. What is the effect of changing the value of \( h \) in the equation \( g(x) = a|x - h| + k \)?
3. How would the equation change if the graph were translated 3 units down instead of up?
4. How does the slope of the lines relate to the value of \( a \)?
5. What would happen to the graph if \( k \) was negative?

**Tip**: Always check both the vertex and the slopes when writing the equation of an absolute value function!

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

Learn how to write the function rule for g(x), a translation of the absolute value function f(x) = |x|, by analyzing shifts and transformations. This problem demonstrates the application of algebraic concepts related to function translations. Suitable for students in Grades 8-10.

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