Final answer:
The question involves applying transformations to the reciprocal parent function and finding the new asymptotes. After a reflection, translation, and stretching, the new function is f(x) = -2/x + 5, with vertical asymptote x = 0 and horizontal asymptote y = 5.
Step-by-step explanation:
The question is asking to apply a series of transformations to the reciprocal parent function, identify the asymptotes, and analyze reflections and stretches.
The reciprocal parent function is f(x) = 1/x. When we reflect this function across the x-axis, it changes to f(x) = -1/x. Then, translating it 5 units up gives us f(x) = -1/x + 5.
Vertically stretching by a factor of 2 would then result in f(x) = -2/x + 5. The asymptotes of the reciprocal function are the lines x = 0 (vertical asymptote) and y = 0 (horizontal asymptote).
After the transformations, we still have a vertical asymptote at x = 0, and the horizontal asymptote moves to y = 5 due to the vertical translation.