Question

draw the piecewise function:
$f(x)=\

$$\begin{cases}5 & \\text{if } -5\\leq x\\leq 1 \\\\ -x - 3 & \\text{if } x > 1 \\end{cases}$$

$

draw lines (using double segment tool for lines continuing towards infinity), then place any open or closed dots as needed.

Explanation:

Step1: Plot first segment (constant)

For $-5 \leq x \leq 1$, $f(x)=5$. This is a horizontal line segment with closed dots at $x=-5$ (point $(-5,5)$) and $x=1$ (point $(1,5)$).

Step2: Plot second segment (linear)

For $x>1$, $f(x)=-x-3$. First, find the starting point: at $x=1$, $f(1)=-1-3=-4$, use an open dot at $(1,-4)$. Then find another point, e.g., $x=2$: $f(2)=-2-3=-5$ (point $(2,-5)$), and extend the line to the right (towards infinity) since $x$ increases without bound.

Answer:

1. Draw a horizontal line segment connecting $(-5, 5)$ (closed dot) to $(1, 5)$ (closed dot).
2. Draw a line starting at $(1, -4)$ (open dot), passing through $(2, -5)$, and extending infinitely to the right (increasing $x$ direction).