The parent function f (x) = log4x has been transformed by reflecting it over the x-axis, stretching it vertically by a factor of three and shifting it down two units. Which function is representative of this transformation?

A.) g (x) = log4 (-3x) - 2

B.) g (x) = log4 (3x) + 2

C.) g (x) = - 3log4 (x) - 2

D.) g (x) = 3log4 (x) + 2

The reflection over the x-axis is given by the transformation:

f₁ (x) = - f (x)

Therefore, the first step is:

f₁ (x) = - log (4x)

Stretching by a factor n along the y-axis is given by the transformation:

f₂ (x) = n · f₁ (x)

Therefore we get:

f₂ (x) = - 3 · log (4x)

Shifting a function down of a quantity n is given by:

f₃ (x) = f₂ (x) - n

Therefore:

f₃ (x) = - 3·log (4x) - 2

Hence, the correct answer is C) g (x) = - 3·log (4x) - 2