Final answer:
The function g(x) has been scaled, rather than rotated, by a factor of 3. The correct equation for g(x) after scaling the parent function f(x) = -x + 4 is g(x) = -3x + 4, which corresponds to option a).
Step-by-step explanation:
Regarding the original question about the rotated function, the use of the term "rotated by a factor of 3" appears to be a typo or miscommunication, as functions are not typically described as being rotated by a factor. Instead, functions can be scaled by a factor, which would multiply the function's slope by that factor. Assuming the question meant to use the term "scaled," the equation for the new function g(x) would be obtained by multiplying the slope of the parent function f(x) = -x + 4 by the factor of 3. This would result in the transformed function g(x) = -3x + 4, as the slope is the coefficient of x in the equation. Therefore, the correct answer would be option a) g(x) = -3x + 4.