Question

Describe transformations of f(x)=-f(2-x)

Answer 1

suppose we use an example:
e.g.
f(x) = (x-5)^2 + 3 , which is a parabola with vertex (5,3), opening upwards

f(2-x) = (2-x - 5)^2 + 3
f(2-x) = (-x - 3)^2 + 3
f(2-x) = (x+3)^2 + 3 , (just like (-9)^2 = 9^2 )
-f(2-x) = -(x+3)^2 - 3

so we have a reflection in the x-axis, and a horizontal shift of 8 units to the left

http://www.wolframalpha.com/input/?i=plot+y+%3D+(x-5)%5E2+%2B+3

http://www.wolframalpha.com/input/?i=plot+y+%3D+-(x%2B3)%5E2+-+3

Answer 2

best describes the combination of transformations that must be applied to the graph of f(x) = x ^ 2 the graph of g(x) = - x ^ 2 + 1