1. The problem asks to determine the continuity of the function $g(x)$ at specific points based on the graph description. 2. At $x = -2$, the graph has a closed dot at $(-2,0)$ and the segment starts there, so $g$ is continuous from the right at $x = -2$ (correct). 3. At $x = -1$, there is an open circle at $(-1,1)$ on the segment from $-2$ to $-1$, and also an open circle at $(-1,1)$ starting the horizontal line to $0$. Since the function value is not defined at $-1$ (open circle), $g$ is not continuous at $x = -1$ (correct). 4. At $x = 0$, there is a closed dot at $(0,1)$ on the horizontal line and an open circle at $(0,0)$ on the upward sloping line. The function value at $0$ is $1$, but the limit from the left is $1$ and from the right is $0$, so $g$ is not continuous at $0$ (correct). 5. At $x = 1$, there is an open circle at $(1,2)$ on the upward sloping line and a closed dot at $(1,0)$ on the curve. The function value is $0$, but the limit from the left is $2$, so $g$ is not continuous at $1$ (correct). 6. At $x = 2$, there is an open circle at $(2,0)$ on the curve, so the function is not defined at $2$, meaning $g$ is discontinuous at $2$ (correct). 7. At $x = 3$, the graph is not defined beyond $2$, so $g$ is not continuous from the right at $3$ (correct). Final corrected answers: 1. Continuous from the right at $x = -2$: ✓ 2. Continuous at $x = -1$: ✗ 3. Continuous at $x = 0$: ✗ 4. Continuous at $x = 1$: ✗ 5. Discontinuous at $x = 2$: ✓ 6. Continuous from the right at $x = 3$: ✗