To analyze the transformation from \( f(x) = |x| \) to \( f(-x) + 6 = | -x | + 6 \):
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The expression \( f(-x) \) represents a reflection across the y-axis because replacing \( x \) with \( -x \) in the function flips it horizontally.
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The addition of \( +6 \) indicates a vertical translation upward by 6 units.
Therefore, the transformations undergone can be summarized as:
- Reflected across the y-axis
- Translated up vertically by 6 units
So, the correct response is:
reflected across the y-axis and translated up vertically.