1. **Problem Statement:** Determine the domain and range of the given piecewise line graph with endpoints at approximately $(-5,-5)$ and $(1,2)$, and vertices near $(-4,-2)$ and $(0,-3)$. 2. **Domain:** The domain is the set of all $x$-values covered by the graph. - From the graph, the leftmost point is at $x=-5$ and the rightmost point is at $x=1$. - Since the endpoints are solid, these values are included. - Therefore, the domain in interval notation is $$[-5,1]$$. - As a compound inequality, the domain is $$-5 \leq x \leq 1$$. 3. **Range:** The range is the set of all $y$-values covered by the graph. - The lowest $y$-value on the graph is approximately $-5$ at $x=-5$. - The highest $y$-value is approximately $2$ at $x=1$. - Since these points are included (solid endpoints), the range in interval notation is $$[-5,2]$$. - As a compound inequality, the range is $$-5 \leq y \leq 2$$. 4. **Summary:** - Domain: $$[-5,1]$$ and $$-5 \leq x \leq 1$$ - Range: $$[-5,2]$$ and $$-5 \leq y \leq 2$$