The graph provided represents a piecewise function with two distinct linear segments. Let's break it down:

1. First segment (for $x \geq 0$):

   • The line passes through points $(0, -1)$ and $(4, 7)$.
   • Using the slope formula, $\text{slope} = \frac{7 - (-1)}{4 - 0} = \frac{8}{4} = 2$.
   • The equation of the line is $y = 2x - 1$ (since the y-intercept is $-1$).

2. Second segment (for $x < 0$):

   • The line passes through points $(-3, 2)$ and $(0, -1)$.
   • Using the slope formula, $\text{slope} = \frac{-1 - 2}{0 - (-3)} = \frac{-3}{3} = -1$.
   • The equation of this line is $y = -x - 1$ (since the y-intercept is also $-1$).

Thus, the piecewise function is: