Question

$f(x)=\

$$\begin{cases}5 & \\text{for} \\quad -5 < x < 1 \\\\ -x + 8 & \\text{for} \\quad 1 < x < 6\\end{cases}$$

$
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: Plot first piece: horizontal line

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

Step2: Find endpoints for second piece

For $1 < x < 6$, $f(x)=-x+8$.

• At $x=1$: $f(1)=-1+8=7$ (open endpoint at $(1,7)$)
• At $x=6$: $f(6)=-6+8=2$ (open endpoint at $(6,2)$)

Step3: Plot second piece: line segment

Draw a line segment connecting the open endpoints $(1,7)$ and $(6,2)$.

Answer:

The graph consists of:

1. A horizontal open line segment at $y=5$ from $x=-5$ to $x=1$
2. A downward-sloping open line segment from $(1,7)$ to $(6,2)$ (where the line follows $y=-x+8$)

(All endpoints are open circles since the inequalities are strict $<$ not $\leq$)