Question

question
graph the following function on the axes provided.

$f(x)=\

$$\begin{cases}1 & \\text{for} & -5 < x < -2\\\\-x - 1 & \\text{for} & -2 < x \\leq 3\\end{cases}$$

$

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: Graph first piece: horizontal line

For $-5 < x < -2$, $f(x)=1$. This is a horizontal line segment with open endpoints at $(-5,1)$ and $(-2,1)$.

Step2: Find endpoints for second piece

First, at $x=-2$ (open, since domain is $-2 < x \leq 3$): $f(-2)=-(-2)-1=1$, so open point at $(-2,1)$.
At $x=3$ (closed): $f(3)=-(3)-1=-4$, so closed point at $(3,-4)$.

Step3: Graph second piece: line segment

Draw a line connecting the open point $(-2,1)$ to the closed point $(3,-4)$, extending only over $-2 < x \leq 3$.

Answer:

• A horizontal open line segment at $y=1$ from $x=-5$ (open circle) to $x=-2$ (open circle).
• A line segment from the open circle at $(-2,1)$ to the closed circle at $(3,-4)$.