Final answer:
The parent function f(x) = 4x is transformed to g(x) = 0.15(4x) by a vertical scaling, specifically a vertical compression by the factor of 0.15.
Step-by-step explanation:
The transformation that changes the parent function f(x) = 4x to g(x) = 0.15(4x) is a vertical scaling. The factor 0.15 is applied to the original function, resulting in a reduction in the steepness of the graph.
This type of transformation is referred to as a vertical compression by the factor of 0.15. In other words, each y-value of the parent function is multiplied by 0.15 in the transformed function g(x).