The graph you provided is a translation of the absolute value function $f(x) = |x|$. To determine the function rule for $g(x)$, we need to analyze the translation by looking at the vertex and shape of the graph.

1. The graph of $f(x) = |x|$ has a vertex at $(0, 0)$, but $g(x)$ appears to have been shifted.
2. By inspecting the graph, it seems that the vertex of $g(x)$ is at $(0, 4)$, meaning there has been a vertical translation of 4 units upwards.
3. The slope of the graph remains the same as the basic $|x|$ function, so there is no horizontal stretching or reflection.

Given these observations, the translation of the function can be expressed as: $g(x) = |x| + 4$

Thus, the function rule for $g(x)$ is $g(x) = |x| + 4$.

Let me know if you'd like more details or have any questions!

Here are some follow-up questions for further exploration:

1. How do vertical translations affect the graph of absolute value functions?
2. What happens if the translation is to the left or right instead of up or down?
3. How can you describe the effect of a horizontal stretch or shrink on absolute value graphs?
4. What is the impact of reflecting an absolute value function across the x-axis?
5. How can you graph more complex transformations of absolute value functions?

Tip: Always check the vertex of the transformed graph to determine the direction and amount of translation!