Question

f(x) = \

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

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 segment

For $f(x)=-2x-4$, when $x=-4$:
$y=-2(-4)-4=8-4=4$ (closed dot, since $x=-4$ is included)
When $x=-1$:
$y=-2(-1)-4=2-4=-2$ (open dot, since $x=-1$ is not included)

Step2: Plot first line segment

Draw a line connecting $(-4, 4)$ (closed dot) to $(-1, -2)$ (open dot).

Step3: Find endpoints for second segment

For $f(x)=2$, when $x=-1$:
$y=2$ (open dot, since $x=-1$ is not included)
When $x=4$:
$y=2$ (open dot, since $x=4$ is not included)

Step4: Plot second line segment

Draw a horizontal line connecting $(-1, 2)$ (open dot) to $(4, 2)$ (open dot).

Answer:

The graph consists of:

1. A line segment from $(-4, 4)$ (closed dot) to $(-1, -2)$ (open dot) for $-4 \leq x < -1$
2. A horizontal line segment from $(-1, 2)$ (open dot) to $(4, 2)$ (open dot) for $-1 < x < 4$