1. **State the problem:** 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. **Analyze the graph:** The graph is an absolute value function with a vertex at $(0,0)$. 3. **Identify the vertex:** Since the vertex is at $(0,0)$, we have $h=0$ and $k=0$. 4. **Determine the slope:** The graph forms an inverted V shape. The left segment goes from $(-10,-10)$ to $(0,0)$, which has slope $$m = \frac{0 - (-10)}{0 - (-10)} = \frac{10}{10} = 1.$$ The right segment goes from $(0,0)$ to $(10,-10)$, which has slope $$m = \frac{-10 - 0}{10 - 0} = \frac{-10}{10} = -1.$$ 5. **Since the graph is an inverted V, the absolute value function is reflected vertically:** This means $a$ is negative. 6. **Write the function:** The standard absolute value function is $|x|$, which has slopes $1$ and $-1$. To invert it, multiply by $-1$: $$g(x) = -|x|$$ 7. **Check the vertex form:** Here, $a = -1$, $h = 0$, and $k = 0$. **Final answer:** $$g(x) = -|x|$$