Question

g(x) = \

$$\begin{cases} -8, & -9 \\leq x < 3 \\\\ 4, & 3 \\leq x \\leq 9 \\end{cases}$$

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

Explanation:

Step1: Analyze first piece of function

For $-9 \leq x < 3$, $g(x)=-8$. This is a horizontal line at $y=-8$, with a closed dot at $x=-9$ (since $x=-9$ is included) and an open dot at $x=3$ (since $x=3$ is not included).

Step2: Analyze second piece of function

For $3 \leq x \leq 9$, $g(x)=4$. This is a horizontal line at $y=4$, with closed dots at both $x=3$ and $x=9$ (since both endpoints are included).

Step3: Match to the options

Option A has a horizontal line at $y=-8$ with closed dot at $x=-9$, open dot at $x=3$, and a horizontal line at $y=4$ with closed dots at $x=3$ and $x=9$, which matches our analysis.

Answer:

A. The graph with a horizontal line at $y=-8$ (closed dot at $x=-9$, open dot at $x=3$) and a horizontal line at $y=4$ (closed dots at $x=3$ and $x=9$)