To express the graph as a piecewise function, let's analyze each segment of the graph:

1. First Segment:

   • This segment starts at the point (-6, -8) and ends at (2, 4).
   • We can find the equation of the line by determining the slope ($m$) and using the point-slope form.

   Slope Calculation: $m = \frac{4 - (-8)}{2 - (-6)} = \frac{4 + 8}{2 + 6} = \frac{12}{8} = \frac{3}{2}$

   Using the point-slope form with the point (-6, -8): $y - (-8) = \frac{3}{2}(x - (-6))$ Simplifying, we get: $y = \frac{3}{2}x + 1$

   This segment is valid for $-6 \leq x < 2$ (it’s open at $x = 2$ because there’s an open circle at that point).

   So, the function for this segment is: $y = \frac{3}{2}x + 1 \quad \text{for} \quad -6 \leq x < 2$

2. Second Segment:

   • This segment starts at $x = 2$ and ends at $x = 6$, with the points (2, 5) and (6, 7).
   • Since this segment is linear, we can calculate the slope and find its equation similarly.

   Slope Calculation: $m = \frac{7 - 5}{6 - 2} = \frac{2}{4} = \frac{1}{2}$

   Using the point-slope form with the point (2, 5): $y - 5 = \frac{1}{2}(x - 2)$ Simplifying, we get: $y = \frac{1}{2}x + 4$

   This segment is valid for $2 < x \leq 6$ (open at $x = 2$ and closed at $x = 6$).

   So, the function for this segment is: $y = \frac{1}{2}x + 4 \quad \text{for} \quad 2 < x \leq 6$

Final Piecewise Function:

Combining these two segments, the piecewise function is: