A. write functions for the following transformations using function notation. choose a different letter to represent each function. for example, you can use r to represent rotations. assume that a positive rotation occurs in the counterclockwise direction.
•translation of a units to the right and b units up
•reflection across the y-axis
•reflection across the x-axis
•rotation of 90 degrees counterclockwise about the origin, point o
•rotation of 180 degrees counterclockwise about the origin, point o
•rotation of 270 degrees counterclockwise about the origin, point o

1. f( x - a ) + b

2. g ( -x )

3. - h ( x )

4. (x,y) = ( -y,x )

5.(x,y) = ( -x,-y )

6.(x,y) = ( y,-x )

Step-by-step explanation:

1. We know that, 'Translation shifts the figure in any direction'.

As, the function f(x) is translated 'a' units to the right, the new form of function is f(x-a).

Again, the function is translated 'b' units up, the final form of the function is f(x-a)+b.

2 and 3. We know that, ' Reflection flips the image over a line'.

As the function g(x) is reflected over y-axis, the new form of the function is g(-x).

As the function h(x) is reflected over x-axis, the new form of the function is -h(x).

4 , 5 and 6. We know that, 'Rotation turns the image around a point to a certain degree'.

Let us assume the function to be a point (x,y).

As the function is rotated by 90° counterclockwise about the origin, the new function becomes ( y,-x ) i.e. (x,y) = ( -y,x ).

As the function is rotated by 180° counterclockwise about the origin, the new function becomes ( y,-x ) i.e. (x,y) = ( -x,-y ).

As the function is rotated by 2700° counterclockwise about the origin, the new function becomes ( y,-x ) i.e. (x,y) = ( y,-x ).

rounding to the nearest thousandth would be 452,000