Final answer:
The question asks for a function g(x) that is a transformation of f(x) = |4x| + 5. However, none of the options given represent a simple transformation that would shift the graph of f(x) without changing its shape or position. Thus, there is no correct answer to the question as presented.
Step-by-step explanation:
The question asks for a function g(x) whose graph represents a transformation of the function f(x) = |4x| + 5. This transformation must be deciphered from the given options A, B, C, and D. Options A and B do not represent transformations; they are essentially the same as f(x) or a slight variation that doesn't change the graph's shape or position. Option C g(x) = |4x| - 5 is the function f(x) shifted downwards by 5 units. Lastly, option D g(x) = -|4x| - 5 represents a vertical reflection and a downward shift, which are not the transformations we're looking for. Hence, the correct transformation that provides a new function g(x) without changing its shape or position is not present amongst the provided options.
Transformations typically involve shifting the graph horizontally or vertically, reflections across the axes, or stretching and compressing the graph. However, none of the options provided in A through D indicate such a transformation that would simply shift f(x)'s graph without altering its shape or position, as the original function is f(x) = |4x| + 5 and must remain unaltered for this exercise. Therefore, there is no correct answer to the stated question as it is presented.