Question

h(x) = \

$$\begin{cases} 6, & -8 \\leq x < -4 \\\\ 3, & -4 \\leq x \\leq 5 \\end{cases}$$

what is the graph of h?
choose 1 answer:
a (with graph: y-axis from -8 to 8, x-axis from -8 to 8; blue dot at (-8,6), blue line to open circle at (-4,6); blue dot at (-4,3), blue line to blue dot at (5,3))
b (with graph: y-axis from -8 to 8, x-axis from -8 to 8; blue dot at (-8,6), blue line to blue dot at (-4,6); open circle at (-4,3), blue line to blue dot at (5,3))

Explanation:

1. Analyze the first piece: $h(x)=6$ for $-8\leq x<-4$. This is a horizontal line at $y=6$, with a closed dot at $x=-8$ (since $x=-8$ is included) and an open dot at $x=-4$ (since $x=-4$ is not included here).
2. Analyze the second piece: $h(x)=3$ for $-4\leq x\leq5$. This is a horizontal line at $y=3$, with closed dots at both $x=-4$ (since $x=-4$ is included here) and $x=5$ (since $x=5$ is included).
3. Match to the options: Option A has the correct line segments and dot types for both pieces.

Answer:

A. <The graph with a horizontal line at y=6 from x=-8 (closed dot) to x=-4 (open dot), and a horizontal line at y=3 from x=-4 (closed dot) to x=5 (closed dot)>