Final answer:
To find the corresponding point on the graph of g, we must apply the transformation g(x) to the original x-value of the point (8,5) on f, which involves scaling, shifting, and inversing operations. The point (8,-6) is the result of the transformation, making option D the correct choice.
Step-by-step explanation:
To solve this problem, we need to apply the given transformation g(x) = -2(3x - 1) + 4 to the x-coordinate of the point (8,5), which belongs to the graph of the function f. This transformation scales the x-coordinate by a factor of 3, shifts it by -1, scales the resulting y-value by -2, and then shifts it upwards by 4 units. Let's apply this step-by-step:
- First, scale and shift the x-coordinate: 3(8) - 1 = 24 - 1 = 23.
- Then, apply the -2 scale to the y-coordinate of f: -2(5) = -10.
- Finally, add the upward shift of 4 to the y-value: -10 + 4 = -6.
Now, we use the transformed x-value (23) as the input to our function g. However, we typically look for an x-value that is within the domain of normal function representation, so we need to find the original x-value before the transformation was applied to it. To find this, we do the inverse of the transformation to the x-value: (23+1)/3 = 24/3 = 8. Thus, the point on the graph of g corresponding to the original x-value of 8 will have the coordinates (8,-6), meaning that option D is the correct answer.