1. The problem asks to find the function rule for $g(x)$, which is a translation of the absolute value function $f(x) = |x|$. 2. The general form for a translated absolute value function is: $$g(x) = a|x - h| + k$$ where $a$ is the vertical stretch/compression and reflection factor, $h$ is the horizontal shift, and $k$ is the vertical shift. 3. From the graph description, the vertex of $g(x)$ is at $(0,6)$. 4. Since the vertex of $f(x) = |x|$ is at $(0,0)$, the horizontal shift $h = 0$ because the vertex is not moved left or right. 5. The vertical shift $k$ is the $y$-coordinate of the vertex, so $k = 6$. 6. The slopes of the arms are $1$ on the right and $-1$ on the left, which matches the slope of $f(x) = |x|$, so $a = 1$. 7. Therefore, the function rule is: $$g(x) = 1|x - 0| + 6 = |x| + 6$$ Final answer: $$g(x) = |x| + 6$$