Question

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

$$\begin{cases} -x - 1 & \\text{for } -4 < x < 1 \\\\ -2x + 1 & \\text{for } 1 < x \\leq 5 \\end{cases}$$

$
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: Analyze first piece

For $-4 < x < 1$, $f(x) = -x -1$. Calculate endpoints: at $x=-4$, $f(-4)=3$ (dashed, since $x=-4$ not included); at $x=1$, $f(1)=0$ (dashed, since $x=1$ not included here). Plot line through these points with dashed ends.

Step2: Analyze second piece

For $1 < x \leq 5$, $f(x) = -2x +1$. Calculate endpoints: at $x=1$, $f(1)=-1$ (open circle, $x=1$ not included); at $x=5$, $f(5)=-9$ (solid, $x=5$ included). Plot line through these points with open start and solid end.

Step3: Combine segments

Draw both line segments on the grid as described. The first segment is from (-4,3) (dashed) to (1,0) (dashed); the second from (1,-1) (open) to (5,-9) (solid). No overlap at $x=1$.

Answer:

(Graph description: Two line segments. First segment: dashed endpoints at (-4,3) and (1,0), solid line between them. Second segment: open circle at (1,-1), solid endpoint at (5,-9), solid line between them.)