Question

question 8
sketch a graph of $f(x)=\

$$\begin{cases}2&\\text{if }x\\leq - 1\\\\-x + 1&\\text{if }-1lt x\\leq 2\\\\1&\\text{if }xgt 2\\end{cases}$$

$
note: you must graph the linear pieces first, then the open and closed circles at the endpoints.

Explanation:

Step1: Plot first piece ($x\leq-1$)

Horizontal line $y=2$ left of $x=-1$, closed circle at $(-1,2)$.

Step2: Plot second piece ($-1

Line $y=-x+1$: when $x=-1$, $y=2$ (open circle); $x=2$, $y=-1$ (closed circle). Connect points.

Step3: Plot third piece ($x>2$)

Horizontal line $y=1$ right of $x=2$, open circle at $(2,1)$.

Answer:

The graph consists of:

1. A horizontal line $y=2$ for $x\leq-1$ (closed circle at $(-1,2)$).
2. A line $y=-x+1$ from open circle $(-1,2)$ to closed circle $(2,-1)$.
3. A horizontal line $y=1$ for $x>2$ (open circle at $(2,1)$).

(Note: This is a textual description of the graph as requested by the problem's sketch instruction.)