1. The problem is to graph the piecewise function: $$f(x) = \begin{cases} 2 - 2x & \text{if } x < 2 \\ x - 1 & \text{if } x \geq 2 \end{cases}$$ 2. For piecewise functions, we graph each piece on its domain and check continuity at the boundary point $x=2$. 3. For $x < 2$, the function is $f(x) = 2 - 2x$. - Calculate $f(2)$ from the left: $2 - 2(2) = 2 - 4 = -2$. - Since $x=2$ is not included in this piece, the point $(2, -2)$ is an open circle. 4. For $x \geq 2$, the function is $f(x) = x - 1$. - Calculate $f(2)$ from the right: $2 - 1 = 1$. - Since $x=2$ is included here, the point $(2, 1)$ is a filled circle. 5. Plot the first line segment for $x < 2$ with slope $-2$ and intercept $2$ ending at an open circle at $(2, -2)$. 6. Plot the second line segment for $x \geq 2$ with slope $1$ and intercept $-1$ starting at a filled circle at $(2, 1)$. 7. The graph has a jump discontinuity at $x=2$ because the left and right limits differ. 8. Comparing the descriptions: - Option A describes a rising line for $x < 2$ ending with an open circle near $(2, -2)$ and a falling line for $x \geq 2$ starting at $(2, -1)$, which does not match our function. - Option B describes a falling line segment visible on the right side only, which also does not match. 9. The correct graph should have a falling line segment for $x < 2$ ending at $(2, -2)$ open circle and a rising line segment for $x \geq 2$ starting at $(2, 1)$ filled circle. Therefore, neither A nor B matches the function correctly. Final answer: Neither graph A nor B correctly represents the function $f(x)$ as given.