1. **State the problem:** We are given the graph of a function $f$ and need to estimate: (a) the domain and range of $f$ using interval notation. (b) the intervals where $f$ is increasing and where $f$ is decreasing. 2. **Analyze the domain:** The domain is the set of all $x$-values for which the function is defined. From the graph, the function starts at $x=0$ (closed dot) and ends at $x=4$ (closed dot). Thus, the domain is $$[0,4].$$ 3. **Analyze the range:** The range is the set of all $y$-values the function attains. From the graph, the lowest $y$-value is $1$ (at $x=0$ and $x=4$), and the highest $y$-value is $3$ (at $x=2$). Thus, the range is $$[1,3].$$ 4. **Determine intervals of increase and decrease:** - From $x=0$ to $x=2$, the function goes upward from $y=1$ to $y=3$, so $f$ is increasing on $$[0,2).$$ - From $x=2$ to $x=4$, the function goes downward from $y=3$ to $y=1$, so $f$ is decreasing on $$(2,4].$$ 5. **Summary:** - Domain: $$[0,4]$$ - Range: $$[1,3]$$ - Increasing on $$[0,2)$$ - Decreasing on $$(2,4]$$