The graph displayed shows a transformation of the absolute value function $f(x) = |x|$. Based on the graph, we can observe that the vertex of the graph is at the point $(0, 2)$ instead of the origin $(0, 0)$, which indicates a vertical shift of the absolute value function by 2 units upwards. Additionally, the slope of the lines on both sides appears to be unchanged from the standard $f(x) = |x|$.

Therefore, the transformation rule for $g(x)$ would be: $g(x) = |x| + 2$ This represents a vertical translation of the parent function $f(x) = |x|$ by 2 units upwards.

Would you like more details or explanations?

Here are some related questions for further practice:

1. What would the function look like if there was a horizontal shift to the right by 3 units?
2. How does a reflection over the x-axis affect the function rule for $f(x) = |x|$?
3. If the graph was stretched vertically by a factor of 2, what would the function rule be?
4. How would the function rule change if the graph was shifted 4 units down?
5. What is the effect of shifting the graph both vertically and horizontally?

Tip: Vertical shifts affect only the constant term in the absolute value function, while horizontal shifts modify the variable inside the absolute value symbol.