Write the equation for g (x) if f (x) = x3 had a reflective over the x-axis, a horizontal compression of 1/2 and vertically translated up 9 units

  g(x) = -8x^3 +9

Step-by-step explanation:

The form ...

  -f(ax) +b

represents the function f(x) reflected over the x-axis (-f(x)), compressed horizontally by a factor of "a" (f(ax)), and translated up by "b" units (f(x)+b).

Your sequence of transformations results in ...

  g(x) = -f(2x) +9 = -(2x)^3 +9

  g(x) = -8x^3 +9