Which statement is true about f(x)+2=1/6|x-3|?
a. the graph of f(x) has a vertex of (-3,2).
b. the graph of f(x) is horizontally compressed.
c. the graph of f(x) opens downward.
d. the graph of f(x) has range of f(x)_> -2.

The  range of f(x) is and option D is correct.

Step-by-step explanation:

The given function is

It can be written as

         .... (1)

The function is in the form of

                    ....(2)

Where, a is scale factor and (h,k) is vertex of the graph.

On comparing (1) and (2), we get

Therefore the vertex of f(x) is (3,-2). Option A is incorrect.

The value of a is  . So, the graph compressed vertically. The value of a is positive, therefore the graph of f(x) opens upward.

We know the absolute value is always greater than or equal to 0.

Therefore the range of f(x) is and option D is correct.