Question

How does the graph of the transformed function x= − log3(5x −1)+2 compare to the graph of its parent function compare to the graph of its parent function f(x)= log3 x?

Answer 1

assuming base 3, we have
f(x) = logx
g(x) = -3log(5(x-1/5))+2
so need to transform f(x) as follows:
dilate horizontally by a factor of 1/5:
g(x) = log(5x)
shift right by 1/5:
g(x) = log(5(x - 1/5))
dilate vertically by a factor of 3:
g(x) = 3log(5(x - 1/5))
reflect across the x-axis:
g(x) = -3log(5(x - 1/5))
shift up 2:
g(x) = -3log(5(x - 1/5)) + 2