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

To get y = ln(x-4) from y = ln(x), you need to translate (shift) the graph 4 units to the right.

 

To get y = -ln(x-4) from y = ln(x-4), you reflect in the x-axis.

 

You can do these transformations in either order, because they do not undo each other.

 

The correct answer is B.

Answer 2

"-4" shifts four units to the right

"-" in front of ln reflects across the abscissa.