Question

g(x) = \

$$\begin{cases} 3x + 4, & -4 \\leq x < 0 \\\\ -4, & 0 \\leq x \\leq 6 \\end{cases}$$

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

Explanation:

Step1: Find left segment endpoints

For $g(x)=3x+4$, $x=-4$: $g(-4)=3(-4)+4=-8$ (closed dot, since $x=-4$ is included). $x=0$: $g(0)=3(0)+4=4$ (open dot, since $x=0$ is not included).

Step2: Find right segment endpoints

For $g(x)=-4$, $x=0$: $g(0)=-4$ (closed dot, since $x=0$ is included). $x=6$: $g(6)=-4$ (closed dot, since $x=6$ is included).

Step3: Match to options

Option B has the left segment with closed dot at $(-4,-8)$, open dot at $(0,4)$, and right segment with closed dots at $(0,-4)$ and $(6,-4)$, which matches our calculations.

Answer:

B. <The graph with left line segment having closed dot at (-4,-8) and open dot at (0,4), and horizontal line segment from (0,-4) (closed dot) to (6,-4) (closed dot)>