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Given g(x) = -2|x – 1 + 2, describe the transformation from the graph of f(x) = |x| to the graph of g.

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The description of the transformation is

  • horizontal shift of 1 unit to the right
  • vertical stretch of 2 units
  • reflection over the x-axis
  • shift 2 units upward

How to describe the transformation

The transformation from the graph of f(x) = |x| to the graph of g(x) = -2|x - 1| + 2 is described as follows

Horizontal Shift:

Shown by the expression |x - 1| inside the absolute value represents a horizontal shift of 1 unit to the right.

Vertical Stretch and reflection

The coefficient -2 outside the absolute value indicates a vertical stretch by a factor of 2 (since it's negative, it's also a reflection about the x-axis).

Vertical Shift

The constant term +2 outside the absolute value represents a vertical shift 2 units upward.

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