Question

The function f(x) = x was transformed to create a graph g(x) = f(x- 1) – 2.

Answer 1

To get the graph of g(x) = f(x-1) -2, you'd shift the graph of f right 1 unit and down 2 units.

The "x-1" in f(x-1) is a horizontal shift (left/right) and those are the opposite of what you'd think.  Subtraction moves right, addition moves left.

The "-2" at the end is a vertical shift and that is what you'd expect with subtraction moving you down.

Go with the second answer:

The graph of f is shifted to the right 1 unit and down 2 units to create the graph of g.