1. The problem asks to state the domain of the given piecewise function based on the graph description. 2. The domain of a function is the set of all possible input values (x-values) for which the function is defined. 3. From the graph description: - The function starts at $x = -4$ with a solid dot, meaning the function is defined at $x = -4$. - It continues in a straight line to $x = 0$ with a solid dot, so the function is defined for all $x$ between $-4$ and $0$ inclusive. - Then it decreases to an open circle at $x = 2$, meaning the function is not defined at $x = 2$ from this part. - After $x = 2$, the function continues upward to a solid dot at $x = 4$, so it is defined for $x$ between $2$ and $4$ inclusive. 4. Therefore, the domain includes all $x$ from $-4$ to $2$ but not including $2$, and from $2$ to $4$ including $4$. 5. In interval notation, this is written as: $$[-4, 2) \cup [2, 4]$$ This means the function is defined for all $x$ in the intervals $[-4, 2)$ and $[2, 4]$. Final answer: The domain is $$[-4, 2) \cup [2, 4]$$.