Question

$f(x)=\begin{cases} -3x - 6 & \text{for } x
eq -1 \\ 1 & \text{for } x=-1 end{cases}$
line closed circle open circle
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 line's key points

First, identify points for $y=-3x-6$ (valid for $x
eq-1$):

• When $x=0$, $y=-3(0)-6=-6$ → $(0, -6)$
• When $x=-2$, $y=-3(-2)-6=0$ → $(-2, 0)$
• When $x=-1$, $y=-3(-1)-6=-3$ → $(-1, -3)$ (this is excluded, so open circle)

Step2: Plot the line

Draw a straight line through $(0, -6)$ and $(-2, 0)$.

Step3: Mark excluded point

Place an open circle at $(-1, -3)$ (since $x=-1$ is not part of this segment).

Step4: Mark defined point

Place a closed circle at $(-1, 1)$ (since $f(-1)=1$).

Answer:

1. Draw a line connecting the points $(0, -6)$ and $(-2, 0)$.
2. Add an open circle at $(-1, -3)$.
3. Add a closed circle at $(-1, 1)$.