Question

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

$$\begin{cases} x + 3 & \\text{for} & -1 < x \\leq 2 \\\\ -x + 9 & \\text{for} & 2 < x < 6 \\end{cases}$$

$
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 $f(x)=x+3$, $-1

• At $x=-1$ (open): $f(-1)=-1+3=2$
• At $x=2$ (closed): $f(2)=2+3=5$

Step2: Find endpoints for second segment

For $f(x)=-x+9$, $2

• At $x=2$ (open): $f(2)=-2+9=7$
• At $x=6$ (open): $f(6)=-6+9=3$

Step3: Plot and connect segments

Draw a line from $(-1, 2)$ (open circle) to $(2, 5)$ (closed circle). Draw a line from $(2, 7)$ (open circle) to $(6, 3)$ (open circle).

Answer:

The piecewise function is graphed with:

1. A line segment for $f(x)=x+3$ with an open endpoint at $(-1, 2)$ and a closed endpoint at $(2, 5)$
2. A line segment for $f(x)=-x+9$ with an open endpoint at $(2, 7)$ and an open endpoint at $(6, 3)$