Answer:
C. reflected in the x-axis, shifted right 4
Explanation:
You want to know the effect on f(x) of the transformation -f(x -4).
Vertical reflection
Multiplying the function value by -1 causes it to be reflected across the x-axis. The image point will be as far from one side of the x-axis as the preimage point is from the other side.
Horizontal shift
Replacing x with (x-4) in the function argument means the value of x must be larger by 4 units to get the same function value. This shifts the graph to the right by 4 units.
Together, the transformations reflect the graph in the x-axis and shift it right by 4 units, moving the vertex to (2, 2).
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Additional comment
In the attachment, the blue graph is the one that has the given transformation. As you can see, it opens downward.
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