Question

piecewise
$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
\

$$\begin{tikzpicture}scale=0.5 \\draw-> (-8,0) -- (8,0) noderight {$x$}; \\draw-> (0,-8) -- (0,8) nodeabove {$y$}; \\foreach \\x in {-8,-6,-4,-2,2,4,6} \\draw (\\x,0.1) -- (\\x,-0.1) nodebelow {$\\x$}; \\foreach \\y in {-8,-6,-4,-2,2,4,6} \\draw (0.1,\\y) -- (-0.1,\\y) nodeleft {$\\y$}; \\drawblue (-6,-4) -- (-1,1); \\fillblue (-6,-4) circle (2pt); \\fillblue (-1,1) circle (2pt); \\drawblue (-1,7) -- (4,2); \\fillwhite (-1,7) circle (2pt); \\fillblue (4,2) circle (2pt); \\end{tikzpicture}$$

b
\

$$\begin{tikzpicture}scale=0.5 \\draw-> (-8,0) -- (8,0) noderight {$x$}; \\draw-> (0,-8) -- (0,8) nodeabove {$y$}; \\foreach \\x in {-8,-6,-4,-2,2,4,6} \\draw (\\x,0.1) -- (\\x,-0.1) nodebelow {$\\x$}; \\foreach \\y in {-8,-6,-4,-2,2,4,6} \\draw (0.1,\\y) -- (-0.1,\\y) nodeleft {$\\y$}; \\drawblue (-6,-4) -- (0,2); \\fillblue (-6,-4) circle (2pt); \\fillblue (0,2) circle (2pt); \\drawblue (0,7) -- (4,3); \\fillwhite (0,7) circle (2pt); \\fillblue (4,3) circle (2pt); \\end{tikzpicture}$$

Explanation:

Step1: Find endpoints of first piece

For $h(x)=x+2$, $-6\leq x\leq-1$:
When $x=-6$, $h(-6)=-6+2=-4$ (closed dot: $(-6,-4)$)
When $x=-1$, $h(-1)=-1+2=1$ (closed dot: $(-1,1)$)

Step2: Find endpoints of second piece

For $h(x)=6-x$, $-1< x\leq4$:
When $x=-1$, $h(-1)=6-(-1)=7$ (open dot: $(-1,7)$)
When $x=4$, $h(4)=6-4=2$ (closed dot: $(4,2)$)

Step3: Match to graph

Verify which graph has these points:

• First segment: from $(-6,-4)$ (closed) to $(-1,1)$ (closed)
• Second segment: from $(-1,7)$ (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 line; open dot at $(-1,7)$, closed dot at $(4,2)$ for the second line)