Question

Transformations and Functions

Part A: Write functions for each of the following transformations using function notation. Choose a different letter to represent each function.

A) T_a_b(x, y) = (x + a, y)
B) R_y(x, y) = (-x, y)
C) Ro_90_O(x, y) = (-y, x)
D) Insufficient information to determine.

Answer 1

To write functions for the given transformations: A) T_a_b(x, y) = (x + a, y) shifts the function a units to the right without changing the y-coordinate. B) R_y(x, y) = (-x, y) reflects the graph across the y-axis. C) Ro_90_O(x, y) = (-y, x) rotates the graph 90 degrees counterclockwise.

Step-by-step explanation:

Part A: Write functions for each of the following transformations using function notation:

A) Tab(x, y) = (x + a, y)

B) Ry(x, y) = (-x, y)

C) Ro90O(x, y) = (-y, x)

D) Insufficient information to determine.

To write functions for the given transformations:

A) In the transformation Tab(x, y) = (x + a, y), 'a' represents the horizontal shift of the function and 'b' represents the vertical shift. The function shifts 'a' units to the right and does not change the y-coordinate.

B) In the transformation Ry(x, y) = (-x, y), the function reflects the graph across the y-axis.

C) In the transformation Ro90O(x, y) = (-y, x), the function rotates the graph 90 degrees counterclockwise.

D) The given information is insufficient to determine the transformation.