1. **Problem Statement:** Determine the domain and range of the given piecewise linear function with points and segments connecting (-10, -4) to (-5, -6), (-5, -6) to (0, 5), and (0, 5) to (4, 2). Represent both domain and range in set-builder and set-interval notation. 2. **Understanding Domain and Range:** - The **domain** is the set of all possible input values (x-values) for which the function is defined. - The **range** is the set of all possible output values (y-values) the function can take. 3. **Domain Analysis:** - The function starts at x = -10 (filled point) and ends at x = 4 (open circle). - Since the point at x = 4 is an open circle, x = 4 is not included in the domain. - Therefore, the domain is all x such that $-10 \leq x < 4$. 4. **Range Analysis:** - The y-values at the key points are: -4 at x = -10 (filled), -6 at x = -5 (open), 5 at x = 0 (filled), and 2 at x = 4 (open). - The minimum y-value is -6 (open at x = -5), so y = -6 is not included. - The maximum y-value is 5 (filled at x = 0), so y = 5 is included. - The function covers all y-values between -6 and 5 because the segments connect these points continuously. - Therefore, the range is all y such that $-6 < y \leq 5$. 5. **Set-Builder Notation:** - Domain: $\{x \mid -10 \leq x < 4\}$ - Range: $\{y \mid -6 < y \leq 5\}$ 6. **Set-Interval Notation:** - Domain: $[-10, 4)$ - Range: $(-6, 5]$ **Final answer:** - Domain: - Set-builder: $\{x \mid -10 \leq x < 4\}$ - Interval: $[-10, 4)$ - Range: - Set-builder: $\{y \mid -6 < y \leq 5\}$ - Interval: $(-6, 5]$