State the transformations needed to go from the graph of the basic function f (x ) = ln(x ) to the graph of the function f (x ) = -ln(x - 4).

Question

A. Reflect across the y-axis and shift left 4

B. Reflect across the x-axis and shift right 4

C. Reflect across the x-axis and shift left 4

D. Reflect across the y-axis and shift down 4

E. None of the above

Answer 1

B. Reflect across the x-axis and shift right 4  ⇐ reflecting across x-axis because the y values are changed to opposites, due to leading minus; replacement of argument x by (x-4) means that the usual vertical asymptote of ln x, namely when x=0, is moved to the right such that the argument now is zero when x = 4.  (Of course, the domain of the new function is (4,infinity).