1. **State the problem:** Determine the domain and range of the absolute value function graphed, and find the intervals where the graph is increasing and decreasing. 2. **Recall the characteristics of an absolute value function:** An absolute value function typically has a "V" shape with a vertex at the minimum point. 3. **Domain:** The domain is all the possible x-values for which the function is defined. From the graph, the function exists from $x = -5$ to $x = 5$. So, the domain in interval notation is: $$[-5, 5]$$ 4. **Range:** The range is all possible y-values. The lowest point (vertex) is at $y = 0$ and the highest y-value shown is $5$. So, the range in interval notation is: $$[0, 5]$$ 5. **Intervals of increase and decrease:** - The graph is decreasing where the function goes down as $x$ increases. This happens from $x = -5$ to $x = -2$. - The graph is increasing where the function goes up as $x$ increases. This happens from $x = -2$ to $x = 5$. So: - Decreasing interval: $$[-5, -2]$$ - Increasing interval: $$[-2, 5]$$ **Final answers:** - Domain: $$[-5, 5]$$ - Range: $$[0, 5]$$ - Decreasing on: $$[-5, -2]$$ - Increasing on: $$[-2, 5]$$