1. **State the problem:** We are given a V-shaped graph centered at the origin (0,0) and extending upwards symmetrically along the y-axis. We need to write the function $g(x)$ in the form $a|x - h| + k$, where $a$, $h$, and $k$ are integers or simplified fractions. 2. **Recall the form of an absolute value function:** The general form is $$g(x) = a|x - h| + k$$ where: - $a$ controls the slope and direction (positive $a$ opens upwards, negative $a$ opens downwards), - $h$ is the horizontal shift, - $k$ is the vertical shift. 3. **Analyze the graph:** The graph is centered at the origin, so the vertex is at $(h, k) = (0, 0)$. 4. **Determine the slope $a$:** The graph extends upwards symmetrically. From the points given, for example, at $x=2$, $g(x)=4$; at $x=4$, $g(x)=8$. Calculate the slope: $$a = \frac{g(2) - g(0)}{2 - 0} = \frac{4 - 0}{2} = 2$$ 5. **Write the function:** Since $h=0$ and $k=0$, the function is $$g(x) = 2|x|$$ **Final answer:** $$g(x) = 2|x|$$