Question

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

Answer 1

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