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!

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!