Question

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

$$\begin{cases} x-3 & \\text{for} & -3< x<1 \\\\ x+1 & \\text{for} & 1< x\\leq5 \\end{cases}$$

$
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 left segment endpoints

For $f(x)=x-3$, $-3

• At $x=-3$: $f(-3)=-3-3=-6$ (open point: $(-3, -6)$)
• At $x=1$: $f(1)=1-3=-2$ (open point: $(1, -2)$)

Step2: Plot left open segment

Draw a line connecting $(-3, -6)$ (open) to $(1, -2)$ (open).

Step3: Find right segment endpoints

For $f(x)=x+1$, $1

• At $x=1$: $f(1)=1+1=2$ (open point: $(1, 2)$)
• At $x=5$: $f(5)=5+1=6$ (closed point: $(5, 6)$)

Step4: Plot right segment

Draw a line connecting $(1, 2)$ (closed) to $(5, 6)$ (closed).

Answer:

A piecewise graph with:

1. An open segment from $(-3, -6)$ to $(1, -2)$
2. An open point at $(1, -2)$ and a closed point at $(1, 2)$
3. A segment from $(1, 2)$ (closed) to $(5, 6)$ (closed)