1. **Problem:** Determine the domain and range of the function shown in the first graph, which is a line segment from $(-3,-3)$ (not included) to $(1,4)$ (included). 2. **Formula and rules:** For a line segment, the domain is the set of all $x$-values between the endpoints, considering whether endpoints are included or not. The range is the set of all $y$-values between the minimum and maximum $y$ on the segment. 3. **Step-by-step solution:** - The graph starts at $x = -3$ with an open circle, so $x = -3$ is not included. - The graph ends at $x = 1$ with a closed circle, so $x = 1$ is included. - Therefore, the domain is $\{x \mid -3 < x \leq 1, x \in \mathbb{R}\}$. - The $y$-values start just above $-3$ (not included) and go up to $4$ (included). - So the range is $\{y \mid -3 < y \leq 4, y \in \mathbb{R}\}$. 4. **Explanation:** The open circle at $(-3,-3)$ means the point is not part of the function, so the domain and range exclude those exact values. The closed circle at $(1,4)$ means the function includes that point. **Final answer:** Domain: $-3 < x \leq 1$ Range: $-3 < y \leq 4$