1. The problem asks to find the function rule for $g(x)$, which is a transformation of $f(x) = |x|$. 2. The general form for transformations of the absolute value function is: $$g(x) = a|x - h| + k$$ where $a$ controls vertical stretch/compression and reflection, $h$ is the horizontal shift, and $k$ is the vertical shift. 3. From the graph description, the vertex of $g(x)$ is at $(0,0)$, so $h=0$ and $k=0$. 4. The graph is a V-shape opening downward, meaning the function is reflected over the x-axis. This implies $a$ is negative. 5. The graph passes through points $(-10, -10)$ and $(10, -10)$. 6. Substitute $x=10$ and $g(10)=-10$ into the function: $$-10 = a|10 - 0| + 0 = a \times 10$$ 7. Solve for $a$: $$a = \frac{-10}{10} = -1$$ 8. Therefore, the function rule is: $$g(x) = -1|x| = -|x|$$ Final answer: $g(x) = -|x|$