Final answer:
The transformation that gives the function g(x) = -5x is a vertical transformation with no shift in this case.
Step-by-step explanation:
The function g(x) = -5x is a linear function. A linear function has the form y = mx + b, where m is the slope and b is the y-intercept. Since g(x) = -5x has no constant term (b = 0), the y-intercept is 0. Therefore, the transformation that gives the function g(x) = -5x is a vertical transformation.
The transformation that shifts a linear function vertically is represented by the equation g(x) = mx + b + c, where c is the amount of vertical shift. In this case, c is 0, so the correct transformations are A and D.