1. **Problem Statement:** Determine the domain and range of the absolute value function graphed with vertex at $(-2,0)$, decreasing from $(-5,3)$ to $(-2,0)$, and increasing from $(-2,0)$ to $(5,5)$. 2. **Recall the absolute value function form:** The general form is $y = a|x - h| + k$ where $(h,k)$ is the vertex. 3. **Domain:** The domain of an absolute value function is all real numbers because it extends infinitely left and right. $$\text{Domain} = (-\infty, \infty)$$ 4. **Range:** Since the vertex is at $(-2,0)$ and the graph opens upwards (V-shape), the minimum value of $y$ is $0$ at $x=-2$. The graph increases upwards, so the range is all $y$ values greater than or equal to $0$. $$\text{Range} = [0, \infty)$$ 5. **Intervals of increase and decrease:** - The graph decreases from $x = -5$ to $x = -2$. - The graph increases from $x = -2$ to $x = 5$. Expressed in interval notation: $$\text{Decreasing on } (-\infty, -2)$$ $$\text{Increasing on } (-2, \infty)$$ 6. **Summary:** - Domain: $(-\infty, \infty)$ - Range: $[0, \infty)$ - Decreasing on $(-\infty, -2)$ - Increasing on $(-2, \infty)$