1. **State the problem:** We need to find the values of the function $g$ at $x=0$, $x=1$, and $x=2$ based on the given graph description. 2. **Analyze $g(0)$:** The graph shows a filled point at $(0,3)$ and an open circle at $(0,2)$. A filled point means the function value is defined there, while an open circle means the function is not defined at that point. Therefore, $g(0) = 3$ because the filled point at $(0,3)$ indicates the function's value. 3. **Analyze $g(1)$:** The graph from $x=0$ to $x=3$ is a piecewise linear segment descending from an open circle at $(0,2)$ down to approximately $(3,-1)$. Since $g(1)$ is on this segment, we estimate the value by linear interpolation. The segment starts at $(0,2)$ and ends near $(3,-1)$. The slope $m$ is: $$m = \frac{-1 - 2}{3 - 0} = \frac{-3}{3} = -1$$ Using point-slope form: $$g(1) = 2 + (-1)(1 - 0) = 2 - 1 = 1$$ 4. **Analyze $g(2)$:** The problem states $g(2) = \text{DNE}$ (Does Not Exist), so the function is not defined at $x=2$. **Final answers:** $$g(0) = 3$$ $$g(1) = 1$$ $$g(2) = \text{DNE}$$