Final answer:
The coordinates of the turning point of the function g(x) are (5, 6), which is found by shifting the turning point of the original function f(x) = -2|x-2| + 7 by 3 units to the right and 1 unit down.
Step-by-step explanation:
To find the coordinates of the turning point of the function g(x), we must first understand how it was transformed from the function f(x). The given function f(x) = -2|x-2| + 7 is a V-shaped graph since it involves an absolute value. The vertex of this graph is the turning point of f(x), which is at (2, 7) because the absolute value expression is equal to zero at x = 2, giving us the maximum value of the function.
To transform f(x) into g(x), the rule g(x) = f(x-3)-1 tells us that the graph of f(x) is shifted 3 units to the right and 1 unit down. Therefore, to find the turning point of g(x), we add 3 to the x-coordinate and subtract 1 from the y-coordinate of the turning point of f(x). This gives us the coordinates of the turning point of g(x) as (5, 6).