1. **State the problem:** We need to find the domain and range of the function $f$ based on the graph description. 2. **Recall definitions:** - The **domain** of a function is the set of all possible $x$-values for which the function is defined. - The **range** of a function is the set of all possible $y$-values the function can take. 3. **Analyze the graph segments:** - The first segment starts at $x = -3$ with a closed dot at $y = -3$ and ends at $x = -1$ with an open circle at $y = -1$. This means the function is defined for $x$ in the interval $[-3, -1)$. - The second segment starts at $x = 3$ with a closed dot at $y = -4$ and ends at $x = 5$ with an open circle at $y = 2$. This means the function is defined for $x$ in the interval $[3, 5)$. 4. **Write the domain:** $$\text{Domain} = [-3, -1) \cup [3, 5)$$ 5. **Analyze the range:** - For the first segment, $y$ goes from $-3$ (closed) up to but not including $-1$ (open), so the range part is $[-3, -1)$. - For the second segment, $y$ goes from $-4$ (closed) up to but not including $2$ (open), so the range part is $[-4, 2)$. 6. **Write the range:** $$\text{Range} = [-4, -1) \cup [-4, 2) = [-4, 2)$$ Note that the union of $[-4, -1)$ and $[-4, 2)$ is simply $[-4, 2)$ because $[-4, 2)$ includes $[-4, -1)$. **Final answer:** - Domain: $[-3, -1) \cup [3, 5)$ - Range: $[-4, 2)$