Question

Write a single algebraic rule for the series of transformations: a reflection about the x-axis, a rotation of 90 degrees clockwise, and a translation of 4 units right and 2 units down.

Answer 1

To a point (x,y), a reflection about the x-axis first does this
(x,y) → (x,-y)
A rotation of 90 degrees clockwise
(x,-y) → (-y,-x)
Translating 4 units right and 2 units down
(x,-y) → (-y + 4,-x - 2)
Therefore your answer is (x,y) → (-y + 4,-x - 2)