The graph provided appears to depict a piecewise function $g(x)$, composed of three distinct linear segments. Let's analyze each section of the graph:

1. First segment (leftmost):

   • This is a horizontal line on the interval $-9 \leq x \leq -4$ with an open circle at $x = -9$ and a closed circle at $x = -4$.
   • The function has a constant value of $y = -9$ over this interval.
   • Equation: $g(x) = -9$ for $-9 < x \leq -4$.

2. Second segment (middle):

   • This segment is an increasing line from $(1, 4)$ to $(3, 8)$, with closed circles at both endpoints.
   • The slope of this line can be calculated as $m = \frac{8 - 4}{3 - 1} = 2$, and the equation of the line in point-slope form is: $g(x) = 2(x - 1) + 4 = 2x + 2$
   • Equation: $g(x) = 2x + 2$ for $1 \leq x \leq 3$.

3. Third segment (rightmost):

   • This is another increasing line from $(6, 2)$ to $(8, 6)$, with an open circle at $x = 6$ and a closed circle at $x = 8$.
   • The slope of this line is $m = \frac{6 - 2}{8 - 6} = 2$, and the equation of the line is: $g(x) = 2(x - 6) + 2 = 2x - 10$
   • Equation: $g(x) = 2x - 10$ for $6 < x \leq 8$.

The Piecewise Function: