Graphs of absolute value functions with various transformations.

- The function `y = -|x - 4| + 3` is a transformation of the basic absolute value function `y = |x|`.
- The negative sign in front of the absolute value, `-|x - 4|`, flips the graph vertically, creating a "V" shape that opens downwards.
- The term `(x - 4)` inside the absolute value shifts the graph 4 units to the right. The vertex, which was at (0, 0) for `y = |x|`, is now at x = 4.
- The `+ 3` outside the absolute value shifts the entire graph 3 units up. So, the vertex moves from (4, 0) to (4, 3).
- Therefore, the correct graph is the one with its vertex at the point (4, 3) and opening downwards.
- Looking at the provided options, the graph in the top-right position matches this description: its peak (vertex) is at (4, 3), and the lines slope down to the left and right.