In the same way that other functions can be combined, a series of transformations can be combined into a single function.

for example, this statement for the function s shows one way to represent the rotation of a point 270° counterclockwise about the origin followed by a translation 3 units to the left and 1 unit up: s(270, o)/< -3,1> (x, y) = (y – 3, -x + 1).

write a function to represent each series of transformations:

rotation of 90 degrees counterclockwise about the origin, point o, then a reflection across the x-axis
reflection across the y-axis, then a translation a units to the right and b units up
translation a units to the right and b units up, then a rotation of 180 degrees
counterclockwise about the origin, then a reflection across the y-axis