1. **Problem Statement:** Given the graph of a function $f$ with points at $(-3,1)$, $(0,-1)$, $(1,2)$, and $(3,1)$, estimate the domain, range, and intervals where $f$ is increasing or decreasing. 2. **Domain:** The domain is the set of all $x$-values for which the function is defined. From the graph, $f$ is defined from $x=-3$ to $x=3$. So, the domain is $$[-3,3].$$ 3. **Range:** The range is the set of all $y$-values the function takes. The lowest $y$-value is $-1$ at $x=0$, and the highest is $2$ at $x=1$. So, the range is $$[-1,2].$$ 4. **Intervals of Increase and Decrease:** - From $x=-3$ to $x=0$, the function decreases from $1$ to $-1$. - From $x=0$ to $x=1$, the function increases from $-1$ to $2$. - From $x=1$ to $x=3$, the function decreases from $2$ to $1$. Therefore: - Increasing on the interval $$(0,1)$$ - Decreasing on the intervals $$(-3,0) \cup (1,3).$$ **Final answers:** - Domain: $$[-3,3]$$ - Range: $$[-1,2]$$ - Increasing: $$(0,1)$$ - Decreasing: $$(-3,0) \cup (1,3)$$