1. The problem asks to identify the basic function from a list and write an equation for the given transformed graph. 2. The graph is described as a V-shaped absolute value graph with vertex at about (1, -1), opening upward. 3. Among the options, the absolute value function $g(x) = |x|$ has a V-shaped graph. 4. The basic absolute value function is $g(x) = |x|$ with vertex at $(0,0)$. 5. The given graph has vertex at $(1, -1)$, indicating a horizontal shift right by 1 and vertical shift down by 1. 6. The transformation formula for absolute value function is: $$y = |x - h| + k$$ where $(h,k)$ is the vertex. 7. Substituting $h=1$ and $k=-1$ gives: $$y = |x - 1| - 1$$ 8. This matches the described graph shape and vertex. Final answer: The basic function is the absolute value function $g(x) = |x|$. The equation of the transformed graph is: $$y = |x - 1| - 1$$