Question

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

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

$
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 $f(x)=x+5$

For $x=-2$ (not included): $f(-2) = -2 + 5 = 3$ (open point at $(-2, 3)$)
For $x=1$ (included): $f(1) = 1 + 5 = 6$ (closed point at $(1, 6)$)

Step2: Plot first line segment

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

Step3: Find endpoints for $f(x)=-x+3$

For $x=1$ (not included): $f(1) = -1 + 3 = 2$ (open point at $(1, 2)$)
For $x=5$ (not included): $f(5) = -5 + 3 = -2$ (open point at $(5, -2)$)

Step4: Plot second line segment

Draw a line from open $(1, 2)$ to open $(5, -2)$.

Answer:

The piecewise function is graphed as:

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