The given graph is a transformation of the absolute value function $f(x) = |x|$. Let's analyze the graph step by step to find the equation for $g(x)$.

1. Reflection: The graph opens downward for $x < 0$, indicating a reflection over the x-axis on the left side of the y-axis. This means the graph for negative values of $x$ is multiplied by $-1$.

2. Slope: For $x \geq 0$, the graph increases with a slope of 1, which is consistent with the parent function $f(x) = |x|$. However, for $x < 0$, the slope of the graph is steeper. It has a slope of $-2$, indicating a vertical stretch by a factor of 2 for negative $x$-values.

3. Vertex: The vertex of the graph is at $(0, -1)$. This indicates a downward vertical shift of 1 unit.

Putting it all together:

The graph is a piecewise function with the following transformations:

• For $x \geq 0$, the function follows the standard absolute value function, but with a downward shift by 1 unit: $x - 1$.
• For $x < 0$, the graph has a vertical stretch by 2, and it is reflected (negative slope) with the same downward shift.

Thus, the equation for $g(x)$ is: