Describe how to transform the graph of g(x)= ln x into the graph of f(x)= ln (3-x) -2.

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.

what is all that apply?