What is the vertex of the graph of g(x)=|x-3|-3

(3, -3)

Step-by-step explanation:

The vertex of the most general absolute value function is y = |x|, whose vertex is at (0, 0).   Focusing on the " |x - 3| " tells us that the graph of y = |x| is moved 3 units to the right.  Next, focusing on the " -3 " as it tells us that the resulting graph is shifted 3 units down.  Thus, the vertex of g(x)=|x-3|-3 is at (3, -3).