The description of the transformation is
- horizontal shift of 1 unit to the right
- vertical stretch of 2 units
- reflection over the x-axis
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.