1. **State the problem:** We need to find the range of a piecewise function described by three horizontal segments: - A segment at $y=3$ extending right from an open circle at $x=1$ (so $y=3$ for $x>1$ but not including $x=1$). - A segment at $y=0$ from $x=-3$ to $x=1$ with closed endpoints (so $y=0$ for $-3 \leq x \leq 1$). - A segment at $y=-3$ extending left from an open circle at $x=-2$ (so $y=-3$ for $x<-2$ but not including $x=-2$). 2. **Analyze each segment's $y$-values:** - The first segment covers $y=3$ but does not include the point at $x=1$ (open circle), so $y=3$ is included for $x>1$. - The second segment covers $y=0$ with closed endpoints at $x=-3$ and $x=1$, so $y=0$ is included. - The third segment covers $y=-3$ for $x<-2$ but excludes $x=-2$ (open circle), so $y=-3$ is included for $x<-2$. 3. **Determine if the $y$-values are included in the range:** - Since the segments at $y=0$ and $y=3$ include their $y$-values (closed or extending beyond open circle), $0$ and $3$ are in the range. - The segment at $y=-3$ extends left from an open circle at $x=-2$, so $y=-3$ is included for $x<-2$. 4. **Combine the $y$-values:** The range consists of the values $-3$, $0$, and $3$. 5. **Express the range:** The range is the union of these discrete values: $$\{-3, 0, 3\}$$ **Final answer:** The range of the piecewise function is $\{-3, 0, 3\}$.