Question

$$g(x) = \
LATEXBLOCK0
$$

what is the graph of $g$? choose 1 answer: a graph a b graph b

Explanation:

Step1: Find endpoints for first segment

For $g(x)=-3x-8$, $-4\leq x\leq0$:
When $x=-4$: $g(-4)=-3(-4)-8=12-8=4$ (closed dot, since $x=-4$ is included)
When $x=0$: $g(0)=-3(0)-8=-8$ (closed dot, since $x=0$ is included)

Step2: Find endpoints for second segment

For $g(x)=-3x+9$, $0< x\leq3$:
When $x=0$: $g(0)=-3(0)+9=9$ (open dot, since $x=0$ is not included)
When $x=3$: $g(3)=-3(3)+9=-9+9=0$ (closed dot, since $x=3$ is included)

Step3: Match to graph

Compare the calculated endpoints to the options: the first segment connects $(-4,4)$ (closed) to $(0,-8)$ (closed); the second connects $(0,9)$ (open) to $(3,0)$ (closed), which matches option B.

Answer:

B. The graph with a closed dot at $(-4,4)$ connected to a closed dot at $(0,-8)$, and an open dot at $(0,9)$ connected to a closed dot at $(3,0)$