Final answer:
The transformation of f(x) = cos(x) to g(x) = (1/4)cos(x) is a vertical scaling by a factor of 1/4, resulting in a new function with one-fourth the amplitude of the original cosine function without affecting its period or phase shift.
Step-by-step explanation:
The function f(x) = cos(x) undergoing a transformation to become g(x) = (1/4)cos(x) represents a vertical scaling transformation in mathematics. This transformation affects the amplitude of the cosine function. The new function, g(x), will have an amplitude that is one-fourth the amplitude of the original function, f(x), which means the maximum and minimum values that g(x) can take on have been scaled down by a factor of 1/4.
In the context of graphing the functions, the graph of g(x) will appear to be compressed vertically when compared to the graph of f(x). For example, while f(x) oscillates between +1 and -1, the transformed function g(x) will oscillate between +1/4 and -1/4. This change does not affect the period or the horizontal position of the graph, which means there is no phase shift or horizontal translation involved in this particular transformation.