1. The problem is to find the function $g(x)$ in the form $a|x - h| + k$ that matches the described graph. 2. The graph is a V-shaped absolute value function with vertex at the origin $(0,0)$, so $h=0$ and $k=0$. 3. The function is therefore $g(x) = a|x|$. 4. To find $a$, use the point $(10,4)$ on the graph. 5. Substitute $x=10$ and $g(10)=4$ into the function: $$4 = a|10| = 10a$$ 6. Solve for $a$: $$a = \frac{4}{10} = \frac{2}{5}$$ 7. Thus, the function is: $$g(x) = \frac{2}{5}|x|$$ This matches the graph with vertex at $(0,0)$ and points $(10,4)$ and $(-10,4)$. Final answer: $$g(x) = \frac{2}{5}|x|$$