Answer:
Domain: all real numbers
Range: -6 ≤ y < -2 ∪ 1 < y
Step-by-step explanation:
You want the graph and domain and range of the piecewise function ...
[tex]f(x)=\begin{cases}-2x-5,\qquad x < -3\\x-3,\qquad -3\le x < 1\\x+2,\qquad x\ge1\end{cases}[/tex]
Graph
The graph is shown in the attachment.
Domain
The function is defined for all values of x, so the domain is ...
"all real numbers"
Range
The graph extends upward from y = -6, but there is a gap in y-values between -2 and 1. The range must exclude that region:
-6 ≤ y < -2 ∪ 1 < y
