Answer:
A
Step-by-step explanation:
Note the following 3 points with respect to a function given as y = f(x).
1. The function y = f(-x) is a reflection across the y-axis
2. The function y = f(x+a) is a horizontal translation a units left and y = f(x-a) is a horizontal translation a units right
3. the function y = f(x) + a is a vertical translation a units up and y = f(x) - a is a vertical translation a units down
Dissecting the transformed function of f(x) = ln (3-x) -2 w.r.t f(x) = ln x, we see:
1. x is replaced with -x, so reflection across y-axis
2. we have a horizontal shift in left side because the argument of ln is (3-x) or (-x+3)
3. We have vertical shift 2 units down because there is a -2 after the functional part of ln(3-x)
Looking at the choices, A is the right answer.
