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.