Final answer:
The transformation f(x) ↦ 1/9 f(x) results in a vertical compression by a factor of 9 for the graph of f(x), making it closer to the x-axis while not changing the slope of the line. Option B is the correct answer.
Step-by-step explanation:
The transformation f(x) ↦ 1/9 f(x) applies a vertical scaling to the graph of f(x). In this case, the graph is being scaled by a factor of 1/9, which means every y-value of the original function f(x) is multiplied by 1/9. This operation results in a vertical compression by a factor of 9, as it makes the graph closer to the x-axis, thereby decreasing the vertical size of the graph without altering the horizontal size.
For example, if the original graph had a point at (2, 9), after the transformation, this point would be at (2, 1) because 9 multiplied by 1/9 equals 1. It's important to understand that this transformation does not affect the slope of the line, as the change is uniformly applied in the vertical direction to all points on the graph of f(x).