Final answer:
The transformations applied to the parent function are vertical compression, horizontal translation to the right, and vertical translation downward.
Step-by-step explanation:
The parent function given is f(x) = 1/2 |x - 1| - 1, and we can describe the transformations that have occurred from the basic absolute value function f(x) = |x|. The coefficient 1/2 in front of the absolute value indicates a vertical compression because it's a fractional value between 0 and 1, which compresses the graph vertically downward in the coordinate system. The |x - 1| suggests a horizontal translation because of the subtraction within the absolute value; according to algebra rules, f(x - d) translates the function horizontally to the right side of the coordinate system by a distance d, in this case, the translation is by 1 unit. Lastly, the -1 at the end of the expression represents a vertical translation downward by 1 unit.