Write a logarithmic function that represents the following transformations applied to the parent function:

Question

Reflection over the y-axis, a vertical stretch by a factor of (5/3) a transformation right 2 units and a transformation down 6 units.

Answer 1

You don't specify the "parent function" so I'll assume it is y = log(x). If its another base, you can make the appropriate changes.

Reflection over the y-axis: y = log(-x)

Vertical stretch by a factor of 5/3: y = 5/3log(-x)

Translate right 2 units: y = 5/3log(-(x - 2))

Translate down 6 units: y = 5/3log(-(x - 2)) - 6

Simplify: y = 5/3log(-x + 2) - 6

Answer 2

y = vertical stretch = (5/3)f(x)

y = -(y) reflection over x-axis

y = x two to the right = (x-2)

y = transformation down 6

Then y = -(5/3)(x-2)-6