1. **Problem Statement:** We are given a piecewise function: $$g(x) = \begin{cases} x + 2, & x \leq -3 \\ \frac{1}{2}x - 4, & x > -3 \end{cases}$$ We need to verify if the graph description with a filled circle at $(-3, -1)$ for the first piece and an open circle at the same point for the second piece is correct. 2. **Evaluate the function at the boundary $x = -3$ for each piece:** - For $x \leq -3$, $$g(-3) = -3 + 2 = -1$$ - For $x > -3$, $$g(-3) = \frac{1}{2}(-3) - 4 = -\frac{3}{2} - 4 = -\frac{3}{2} - \frac{8}{2} = -\frac{11}{2} = -5.5$$ 3. **Interpretation:** - Since the first piece is defined for $x \leq -3$, the point $(-3, -1)$ is included and should be a filled circle. - The second piece is defined for $x > -3$, so the point $(-3, -5.5)$ is not included, and the graph should have an open circle at $x = -3$ for the second piece. 4. **Check the graph description:** - The graph shows a filled circle at $(-3, -1)$ on the first piece, which is correct. - The graph shows an open circle at $(-3, -5.5)$ for the second piece, but the description says the open circle is at $(-3, -1)$, which is incorrect. **Final conclusion:** The filled circle at $(-3, -1)$ is correct. The open circle should be at $(-3, -5.5)$, not at $(-3, -1)$. Therefore, the graph description is partially correct but the open circle position is incorrect.