Original Expression: |x| // Given expression

Transformation 1: Shift by 1 to the right:

a. |x-1| // Shifting the graph of |x| one unit to the right

b. Action on (-1,1): (-1,1) becomes (0,1) // Shifting the point one unit to the right

c. Action on (0,0): (0,0) becomes (1,0) // Shifting the point one unit to the right

d. Action on (1,1): (1,1) becomes (2,1) // Shifting the point one unit to the right

Transformation 2: Multiply by -2:

a. Note: We’re using the transformed points from Transformation 1 as input for this stage.

b. -2|x-1| // Multiplying the graph of |x-1| by -2

c. Action on (0,1) from Transformation 1: (0,1) becomes (0,-2) // Multiplying the y-coordinate by -2

d. Action on (1,0) from Transformation 1: (1,0) becomes (1,0) // Multiplying the y-coordinate by -2

e. Action on (2,1) from Transformation 1: (2,1) becomes (2,-2) // Multiplying the y-coordinate by -2

Final Expression: -2|x-1| // Final result