1. **State the problem:** We need to graph the piecewise function $$f(x) = \begin{cases} 1 - 2x & \text{if } x < 2 \\ x - 3 & \text{if } x \geq 2 \end{cases}$$ and determine which graph (A or B) correctly represents it. 2. **Understand the pieces:** - For $x < 2$, the function is $f(x) = 1 - 2x$, a line with slope $-2$. - For $x \geq 2$, the function is $f(x) = x - 3$, a line with slope $1$. 3. **Evaluate at the boundary $x=2$:** - Left side limit: $f(2^-)=1 - 2(2) = 1 - 4 = -3$ (open circle since $x<2$). - Right side value: $f(2) = 2 - 3 = -1$ (closed circle since $x \geq 2$). 4. **Plot key points and slopes:** - For $x<2$, line passes through $(2, -3)$ with slope $-2$. - For $x \geq 2$, line passes through $(2, -1)$ with slope $1$. 5. **Interpret graph features:** - The graph has a jump discontinuity at $x=2$. - The left piece is a decreasing line ending at an open circle at $(2, -3)$. - The right piece is an increasing line starting at a closed circle at $(2, -1)$. 6. **Conclusion:** - The correct graph shows two rays meeting at $x=2$ with an open circle at $(2, -3)$ and a closed circle at $(2, -1)$. Hence, the graph matching these conditions is **Graph A**. Final answer: **Graph A** correctly represents the function.