The graph in your image shows two distinct parts, which suggest a piecewise function. Let's break it down to express this function:

1. Left segment: This appears to be a horizontal line from $x = -9$ to $x = 2$. The line has a constant value at $y = 0$, except at $x = 2$, where there's an open circle, meaning the function does not include the point $(2, 0)$.

2. Right segment: Starting at $x = 2$, the graph shows a line with a positive slope, moving upwards. The segment begins at $(2, -3)$ and passes through points like $(4, 0)$ and $(6, 3)$, indicating a linear relationship.

Equation for the Piecewise Function:

1. For $x \in [-9, 2)$, the function is constant at $y = 0$. Hence: $f(x) = 0 \quad \text{for} \quad -9 \leq x < 2$

2. For $x \geq 2$, the function follows a linear equation. To find the slope, use the points $(2, -3)$ and $(6, 3)$. The slope $m$ is calculated as: $m = \frac{3 - (-3)}{6 - 2} = \frac{6}{4} = \frac{3}{2}$ Now, use the point-slope form of a line: $y - (-3) = \frac{3}{2}(x - 2)$ Simplifying this gives: $f(x) = \frac{3}{2}(x - 2) - 3 \quad \text{for} \quad x \geq 2$

Complete Piecewise Function: