The graph shown represents a transformation of the basic absolute value function $f(x) = |x|$. To determine the equation for $g(x)$, we need to identify the transformations applied to $f(x)$.

Observations:

1. Reflection: The graph opens downward, suggesting that the function has been reflected over the x-axis. This means a negative sign is introduced.
2. Vertical Stretch: The "V" shape of the graph is more pronounced, indicating a vertical stretch. The slope appears to be steeper than the standard $f(x) = |x|$.
3. Translation: The graph is centered at the origin, so no horizontal or vertical shifts are evident.

Step-by-Step Analysis:

1. The reflection introduces a negative sign, so we start with $-|x|$.
2. The slope on each side of the vertex is 2, indicating a vertical stretch by a factor of 2.

Thus, the transformation is described by the function: $g(x) = -2|x|$

This is the formula for the transformed graph.

Would you like further clarification or more details? Here are 5 related questions:

1. What are other types of transformations (besides reflection and stretch) that can be applied to functions?
2. How would you modify the function if the graph had a horizontal shift?
3. What happens if there is both a vertical stretch and a horizontal compression?
4. How does a horizontal reflection affect the graph of a function like $f(x) = |x|$?
5. What are the key differences between vertical and horizontal transformations?

Tip: Always check the vertex of an absolute value function graph, as it gives clues about translations and reflections.