Original Expression: x² // Given expression

Transformation: Shift by 1 to the right:

a. (x-1)² // Shifting the graph of x² one unit to the right

Action on Specific Points:

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

Final Expression: (x-1)² // Final result

Original Expression: x² // Given expression

Transformation: Shift by 1 to the left:

a. (x+1)² // Shifting the graph of x² one unit to the left

b. Note: This is like (x – (-1))², so we add -1 to the x-values

Action on Specific Points:

c. Action on (-1,1): (-1,1) becomes (-2,1) // Shifting the point one unit to the left

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

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

Final Expression: (x+1)² // Final result

Original Expression: f(x) // Given expression

Transformation 1: Shift by 1 to the right:

a. f(x-1) // Shifting the graph of f(x) one unit to the right

b. Note: This transformation adds 1 to the x-values

c. Action on a specific point (a,b): (a,b) becomes (a+1,b) // Shifting the point one unit to the right

Transformation 2: Shift by 1 to the left:

d. f(x+1) // Shifting the graph of f(x) one unit to the left

e. Note: This transformation adds -1 to the x-values

f. Action on a specific point (a,b): (a,b) becomes (a-1,b) // Shifting the point one unit to the left