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18 August, 01:39

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

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Answers (1)
  1. 18 August, 03:45
    0
    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
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