Final answer:
To find the corresponding point on the graph of y=g(x), we must apply the transformation g(x)=-f(x+3) to the point (2,6). This results in a new point of (-1, -6) after reflecting over the x-axis and shifting left by three units, which matches choice (B).
Step-by-step explanation:
The student is asking about transformation of functions, specifically how a transformation affects points on the graph of the original function. Since the original function f(x) has a point (2,6), we want to find where this point will be mapped on the function g(x), which is defined as g(x) = -f(x+3). This involves a horizontal shift to the left by 3 units (since we're adding 3 inside the function) and a reflection across the x-axis (because of the negative sign in front of the function).
The point (2,6) on f(x) means that f(2)=6. Using the definition of g(x), we find that g(x) = -f(x+3) = -f(2) when x=-1 because -1 + 3 = 2. Since f(2)=6, g(-1) = -6, so the point on the g(x) function will be (-1, -6), which corresponds to answer choice (B).