To find a point on the transformed function y = -2f(x-1), we need to apply the given transformation to the original point (-6,12) on the graph of y = f(x).
Let's start with the original point (-6,12) and apply the transformation:
1. First, we shift the x-coordinate 1 unit to the right.
The new x-coordinate is -6 + 1 = -5.
2. Then, we substitute the new x-coordinate into the original function f(x) to find the y-coordinate.
So, we evaluate f(-5) to find the y-coordinate.
Since the original function f(x) is not given, we can't directly calculate f(-5). However, since the transformed function is y = -2f(x-1), we know that the y-coordinate will be twice the value of f(-5) and have the opposite sign.
If we assume that f(-5) = 6 (which is not given in the question), then multiplying it by -2 gives -2 * 6 = -12.
Therefore, the point on the transformed function is (-5, -12).
Now, let's check which answer choice matches the point (-5, -12):
a) (-7, -24)
b) (-5, -6)
c) (-5, -24)
d) (-7, -6)
The correct answer is (b) (-5, -6) because it matches the point (-5, -12) that we calculated.
It's important to note that without the original function f(x) or more information, we can't definitively determine the exact point on the transformed function. This solution illustrates the process of transforming a given point on a function based on the given transformation.