Final answer:
The function f(x) = g(x-3)-2 is a horizontal shift to the right by 3 units and a vertical shift downward by 2 units from the original function g(x). These transformations move the position of g(x) on the plane but do not change its shape.
Step-by-step explanation:
The function f(x) = g(x-3)-2 represents a transformation of the function g(x) on the coordinate plane. Considering transformations in algebra, the term (x-3) indicates a horizontal translation to the right by 3 units, since it takes the form of f(x-d) where d is the distance of translation. Additionally, the constant term -2 at the end of the function represents a vertical translation downward by 2 units.
In simpler terms, if you were to sketch the graph of f(x) in comparison to g(x), every point on g(x) would be shifted 3 units to the right and 2 units down to form the graph of f(x). It's important to note that these transformations do not affect the shape of g(x), but merely shift its position on the plane.