1. The problem is to determine the domain and range of a graph consisting of two pieces: a vertical curve segment from approximately $(-1, -5)$ to $(-1, 2)$ and a short line segment from $(3, 2)$ to $(4, 1)$. 2. The domain of a graph is the set of all possible $x$-values for which the graph has points. 3. The range of a graph is the set of all possible $y$-values that the graph attains. 4. For the vertical curve segment, since it is vertical at $x = -1$, the domain includes only $x = -1$. 5. The $y$-values for this segment go from approximately $-5$ up to $2$, so the range includes all $y$ such that $-5 \leq y \leq 2$ for this piece. 6. For the short line segment from $(3, 2)$ to $(4, 1)$, the domain includes all $x$ between $3$ and $4$, so $3 \leq x \leq 4$. 7. The $y$-values for this segment go from $2$ down to $1$, so the range includes all $y$ such that $1 \leq y \leq 2$ for this piece. 8. Combining both pieces, the domain is the union of the domains of each piece: $\{ -1 \} \cup [3,4]$. 9. The range is the union of the ranges of each piece: $[-5,2] \cup [1,2] = [-5,2]$ since $[1,2]$ is contained in $[-5,2]$. 10. Final answers: - Domain: $\{ -1 \} \cup [3,4]$ - Range: $[-5,2]$