Answers:
Domain = [tex][-5, -2] \cup [1,5)[/tex]
Range = [tex](-4,4][/tex]
=============================================
Explanation:
The domain is the set of allowed x value inputs. We note that the left-most point is when x = -5, and this point has a closed or filled in endpoint, so we're including this x value in the domain.
The left piece has its other endpoint at x = -2, so the interval [tex]-5 \le x \le -2[/tex] is part of the domain. We write that as [tex][-5,-2][/tex]is part of the domain's answer. The other part is [tex][1, 5)[/tex]. We include x = 1 but exclude x = 5 as there's a hole here.
Use the union symbol to glue the two intervals together and we end up with [tex][-5, -2] \cup [1,5)[/tex] as the full domain.
----------------------------
The range is the set of possible y values. The lowest point is when y = -4, but we exclude this endpoint since there's an open hole here. The highest point is when y = 4. The range is [tex]-4 < y \le 4[/tex] which we write as [tex](-4, 4][/tex]
Since there are no gaps in the range, we don't use any union symbols here. Any y value between -4 and 4 is possible, other than y = -4 itself.
