The parent function f (x) = log3x has been transformed by reflecting it over the x-axis, stretching it vertically by a factor of two and shifting it up three units. Which function is representative of this transformation? g (x) = log3 (2x) - 3 g (x) = log3 (-2x) + 3 g (x) = 2log3 (x) - 3 g (x) = - 2log3 (x) + 3

The transformation from f (x) to g (x) using

g (x) = a*f (x-h) + k

will stretch f (x) by a scale factor of a (>0), translates to the right by h, and translates upwards of k.

Similarly, the transformation from f (x) to g (x) using

g (x) = - a*f (x-h) + k

will stretch f (x) by a scale factor of a (>0) AND reflects over the x-axis, translates to the right by h, and finally translates upwards of k.

For the given problem,

f (x) = log_3 (x)

a=-2 (dilates with scale factor of 2, AND with reflection over the x-axis)

h=0 (no horizontal translation)

k=3 (translates UPwards by 3 units)

Put into the above formula,

g (x) = - 2f (x) + 3=-2log_3 (x) + 3.

You should be able to find the correct answer option.