Final answer:
The transformations of the given equation y = 3|x-2|+1 are: option A, which reflects and shifts the graph on the x-axis, and option D, which shifts the graph 1 unit to the right.
Step-by-step explanation:
The student asked which of the options is a transformation of the given equation y = 3|x-2|+1. A transformation involves changing the graph's position, shape, or size. We'll examine each option:
- A. y = 3|x+2|+1: This reflects the graph across the y-axis and shifts it 2 units to the left.
- B. y = -3|x-2|+1: This reflects the graph across the x-axis (since the coefficient of the absolute value term is negative).
- C. y = 3|x-2|+2: This shifts the graph 1 unit up (since the constant term is increased by 1).
- D. y = 3|x-3|+1: This shifts the graph 1 unit to the right (since the absolute value expression is changed from |x-2| to |x-3|).
The correct transformations of the given equation are option A and D.