1. **State the problem:** We have a piecewise function defined as $$f(x) = \begin{cases} -2x & \text{if } x < 0 \\ 2x & \text{if } x \geq 0 \end{cases}$$ We need to graph this function and determine its range. 2. **Graph the function:** - For $x < 0$, the function is $f(x) = -2x$. This is a line with slope 2 (since $-2x$ for negative $x$ is positive), passing through the origin. - For $x \geq 0$, the function is $f(x) = 2x$, a line with slope 2 starting at the origin. 3. **Analyze the graph:** - At $x=0$, both pieces meet at $f(0) = 0$. - For $x<0$, $f(x) = -2x$ is positive and increases as $x$ moves left. - For $x \geq 0$, $f(x) = 2x$ is also positive and increases as $x$ moves right. 4. **Determine the range:** - Since both branches produce values $\geq 0$ and the minimum value at $x=0$ is 0, the range is all values from 0 to infinity. 5. **Answer:** - The graph is a V-shaped graph opening upward with vertex at $(0,0)$, matching choice C. - The range is $[0, \infty)$, so the correct choice is A. **Final answers:** - Graph choice: C - Range: $[0, \infty)$