The image shows a graph that is piecewise linear, with two distinct line segments. Let’s analyze the graph step by step to express the function as a piecewise function:

Analyzing the graph:

1. First segment:

   • This line starts at $(-2, -1)$ and goes horizontally to $(0, -1)$.
   • It is a horizontal line with $y = -1$ for $x \in [-2, 0]$.

2. Second segment:

   • The second line segment starts at $(0, 0)$ and passes through $(2, 2)$.
   • It has a positive slope and is a linear function.
   • Using the slope formula $\frac{y_2 - y_1}{x_2 - x_1} = \frac{2 - 0}{2 - 0} = 1$, we conclude the slope is $1$.
   • The equation of the line is $y = x$ for $x \in (0, 2]$.

Piecewise Function Representation:

Thus, the piecewise function for this graph is: