Question

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

$$\begin{cases}-x-8 & \\text{for } x < -5\\\\-4 & \\text{for } x > 4\\end{cases}$$

$
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 endpoint for $x<-5$

Substitute $x=-5$ into $f(x)=-x-8$:
$f(-5) = -(-5)-8 = 5-8 = -3$
This is an open endpoint at $(-5, -3)$ since $x<-5$.

Step2: Find second point for $x<-5$

Choose $x=-8$:
$f(-8) = -(-8)-8 = 8-8 = 0$
This gives the point $(-8, 0)$.

Step3: Graph first segment

Draw a line through $(-8, 0)$ and the open endpoint $(-5, -3)$, extending leftward.

Step4: Graph second segment for $x>4$

$f(x)=-4$ is a horizontal line. It has an open endpoint at $(4, -4)$ (since $x>4$), and extends rightward (e.g., to $(8, -4)$).

Answer:

1. For $x < -5$: Draw a line with an open endpoint at $(-5, -3)$ passing through $(-8, 0)$, extending left indefinitely.
2. For $x > 4$: Draw a horizontal line with an open endpoint at $(4, -4)$ passing through $(8, -4)$, extending right indefinitely.