The graph shows a piecewise-defined function. We need to determine the correct function for $f(x)$ based on the two segments shown:

1. First segment: The line starts at point $(-1, -2)$ and goes up to $(2, 3)$. To determine its equation, calculate the slope: $\text{slope} = \frac{3 - (-2)}{2 - (-1)} = \frac{5}{3}.$ Using point-slope form $y - y_1 = m(x - x_1)$ with the point $(-1, -2)$ and slope $\frac{5}{3}$, we get: $y + 2 = \frac{5}{3}(x + 1).$ Simplifying: $y = \frac{5}{3}x + \frac{5}{3} - 2 = \frac{5}{3}x - \frac{1}{3}.$

   Therefore, for $-1 \leq x \leq 2$, the equation is $f(x) = \frac{5}{3}x - \frac{1}{3}$.

2. Second segment: The line starts at $(2, 3)$ and extends horizontally to the right. Since it's a horizontal line, its equation is simply $y = 3$ for $x \geq 2$.

Thus, the piecewise function is: