Question

h(x) = \

$$\begin{cases} x + 2, & -6 \\leq x \\leq -1 \\\\ 6 - x, & -1 < x \\leq 4 \\end{cases}$$

what is the graph of h?
choose 1 answer:
a \includegraphicsscale=0.5{grapha.png}
b \includegraphicsscale=0.5{graphb.png}

Explanation:

Step1: Find endpoints of first piece

For $h(x)=x+2$, $x=-6$: $h(-6)=-6+2=-4$ (closed dot, since $x=-6$ is included).
$x=-1$: $h(-1)=-1+2=1$ (closed dot, since $x=-1$ is included).

Step2: Find endpoints of second piece

For $h(x)=6-x$, $x=-1$: $h(-1)=6-(-1)=7$ (open dot, since $x=-1$ is not included).
$x=4$: $h(4)=6-4=2$ (closed dot, since $x=4$ is included).

Step3: Match to options

Check the two linear segments: first segment connects $(-6,-4)$ (closed) to $(-1,1)$ (closed); second segment connects $(-1,7)$ (open) to $(4,2)$ (closed). This matches option A.

Answer:

A. <The graph with a closed dot at (-6,-4), closed dot at (-1,1) for the first segment; open dot at (-1,7), closed dot at (4,2) for the second segment>