1. **State the problem:** We need to graph the piecewise function: $$f(x) = \begin{cases} x - 3 & \text{for } x \neq 0 \\ -1 & \text{for } x = 0 \end{cases}$$ 2. **Understand the function:** - For all $x$ except 0, the function is a line $y = x - 3$. - At $x=0$, the function value is $-1$, which is different from the line's value at 0. 3. **Evaluate the line at $x=0$:** $$f(0) = 0 - 3 = -3$$ 4. **Interpret the piecewise definition:** - The line $y = x - 3$ is graphed everywhere except at $x=0$ (open circle at $(0,-3)$). - At $x=0$, the function value is $-1$ (closed circle at $(0,-1)$). 5. **Summary for graphing:** - Draw the line $y = x - 3$ for $x \in (-10,0) \cup (0,10)$ with an open circle at $(0,-3)$. - Plot a closed circle at $(0,-1)$. This shows a jump discontinuity at $x=0$. **Final answer:** The graph is the line $y = x - 3$ with an open circle at $(0,-3)$ and a closed circle at $(0,-1)$.