Question

The entire graph of the function g is shown in the figure below. Write the domain and range of g as intervals or unions of intervals.

Answer 1

Answers:

Domain = $[-5, -2] \cup [1,5)$

Range = $(-4,4]$

=============================================

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 $-5 \le x \le -2$ is part of the domain. We write that as $[-5,-2]$is part of the domain's answer. The other part is $[1, 5)$. 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 $[-5, -2] \cup [1,5)$ 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 $-4 < y \le 4$ which we write as $(-4, 4]$

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.