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