Function Intervals A50Dd4

1. **Problem Statement:** We analyze the graph of a piecewise function described as follows: - Increasing from $x = -10$ to $x = -7$ - Decreasing from $x = -7$ to $x = -5$ - Constant from $x = -5$ to $x = -2$ - Increasing from $x = -2$ to $x = -1$ - Constant from $x = -1$ to $x = 10$ We need to find intervals where the function is increasing, decreasing, constant, and determine its domain and range using interval notation. 2. **Intervals where the function is increasing:** The function rises on two intervals: $$\text{Increasing intervals} = (-10, -7) \cup (-2, -1)$$ 3. **Intervals where the function is decreasing:** The function falls on one interval: $$\text{Decreasing interval} = (-7, -5)$$ 4. **Intervals where the function is constant:** The function is constant on two intervals: $$\text{Constant intervals} = [-5, -2] \cup [-1, 10]$$ 5. **Domain of the function:** The domain covers all $x$ values from the smallest to the largest given: $$\text{Domain} = [-10, 10]$$ 6. **Range of the function:** From the graph description: - The function rises from some value at $x=-10$ to a higher value at $x=-7$ - Then decreases to a lower value at $x=-5$ - Remains constant from $x=-5$ to $x=-2$ - Rises again from $x=-2$ to $x=-1$ - Remains constant from $x=-1$ to $x=10$ Assuming the lowest value is at $x=-10$ and the highest at $x=-1$ or $x=10$, the range is continuous between these values. Hence, the range is: $$\text{Range} = [f(-10), f(-1)]$$ Since exact function values are not given, we denote the range as the interval covering all output values from the minimum at $x=-10$ to the maximum at $x=-1$ (or $x=10$). **Summary:** - Increasing: $(-10, -7) \cup (-2, -1)$ - Decreasing: $(-7, -5)$ - Constant: $[-5, -2] \cup [-1, 10]$ - Domain: $[-10, 10]$ - Range: $[f(-10), f(-1)]$ (exact values depend on graph scale)