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Describe the transformations applied to the parent function f(x) = 1/2 |x - 1| - 1.

a) Vertical compression, horizontal translation to the right, vertical translation downward
b) Vertical compression, horizontal translation to the left, vertical translation upward
c) Vertical stretching, horizontal translation to the right, vertical translation downward
d) Vertical stretching, horizontal translation to the left, vertical translation upward

User Guidoism
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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.

User Shangping
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