Question

Question was provided via image upload.

Explanation:

Step1: Find endpoints of first piece

For $g(x)=x+8$, $x=-8$: $g(-8)=-8+8=0$ (closed dot, since $x=-8$ is included). $x=-2$: $g(-2)=-2+8=6$ (open dot, since $x=-2$ is not included in this interval).

Step2: Find endpoints of second piece

For $g(x)=8-\frac{1}{2}x$, $x=-2$: $g(-2)=8-\frac{1}{2}(-2)=9$ (closed dot, since $x=-2$ is included). $x=6$: $g(6)=8-\frac{1}{2}(6)=8-3=5$ (closed dot, since $x=6$ is included).

Step3: Match to graph

Check that the first segment goes from $(-8,0)$ (closed) to $(-2,6)$ (open), and the second goes from $(-2,9)$ (closed) to $(6,5)$ (closed), which matches Graph A.

Answer:

A. The graph with a closed dot at (-8,0), open dot at (-2,6) for the first segment, and closed dots at (-2,9) and (6,5) for the second segment.