Question

graph the following function on the axes provided.
$f(x)=\

$$\begin{cases}x + 4&\\text{for } -3\\leq x\\leq 0\\\\-2x + 7&\\text{for } 0< x\\leq 6\\end{cases}$$

$
click and drag to make a line. click the line to delete it.
click on an endpoint of a line to change it.

Explanation:

Step1: Find endpoints for first piece

For $f(x)=x+4$, $x=-3$: $y=-3+4=1$; $x=0$: $y=0+4=4$. Closed endpoints at (-3,1) and (0,4).

Step2: Find endpoints for second piece

For $f(x)=-2x+7$, $x=0$: $y=7$ (open endpoint); $x=6$: $y=-2(6)+7=-5$ (closed endpoint).

Step3: Plot and connect segments

Draw line from (-3,1) to (0,4). Draw line from (0,7) to (6,-5). Mark open circle at (0,7), closed circles at others.

Answer:

(Graph description: Two line segments. First segment from (-3,1) to (0,4) (closed endpoints). Second segment from (0,7) (open endpoint) to (6,-5) (closed endpoint).)