Question

Which of the following is a transformation of the given equation y = 3|x - 2| + 1?

A. y = 3x - 5
B. y = 3x + 1
C. y = 3|x + 2| - 1
D. y = |3x - 6| + 1

Answer 1

The correct transformation of the equation y = 3|x - 2| + 1 is y = 3|x + 2| - 1, as it maintains the absolute value function and applies the correct shifts.

Step-by-step explanation:

The given equation is y = 3|x - 2| + 1, which is not linear due to the absolute value function. A transformation of this equation would maintain the absolute value characteristic. The correct transformation from the given options is y = 3|x + 2| - 1 (option C). This transformation maintains the absolute value function and simply shifts the graph to the left by 2 units (due to +2 inside the absolute value) and down by 2 units (due to -1 outside the absolute value), as opposed to option A, B, or D, which are either linear equations or alter the absolute value term entirely.