1. The problem asks us to graph the piecewise function: $$f(x) = \begin{cases} 3 - 2x & \text{if } x < 2 \\ 2x - 5 & \text{if } x \geq 2 \end{cases}$$ 2. For $x < 2$, the function is $f(x) = 3 - 2x$. This is a line with slope $-2$ and y-intercept $3$. 3. Calculate the value at the breakpoint $x=2$ for the first piece (to confirm the graph point): $$f(2) = 3 - 2(2) = 3 - 4 = -1$$ Since the first piece is defined for $x < 2$, the point $(2, -1)$ is not included in this piece. 4. For $x \geq 2$, the function is $f(x) = 2x - 5$, a line with slope $2$ and y-intercept $-5$. 5. Calculate $f(2)$ for the second piece: $$f(2) = 2(2) - 5 = 4 - 5 = -1$$ The point $(2, -1)$ is included here as a filled dot. 6. Plot the first line from left up to but not including $x=2$, ending at $(2, -1)$ with an open circle. 7. Plot the second line starting at $(2, -1)$ with a filled dot, and extend it rightward. 8. The graph described matches these calculations with the breakpoint at $(2, -1)$ and the slopes as provided. Final answer: The graph consists of two line segments joining continuously at $(2, -1)$ with the piecewise definition as stated.