Final answer:
The new function is y = 2/(x - 1) + 7. The vertical asymptote remains at x = 0.
Step-by-step explanation:
The reciprocal parent function is represented by the equation y = 1/x. To vertically stretch the function by a factor of 2, we multiply the y-coordinate by 2, resulting in y = 2/(x). To translate the function 7 units up, we add 7 to the y-coordinate, giving us y = 2/(x) + 7. Finally, to translate the function 1 unit left, we subtract 1 from the x-coordinate, giving us y = 2/(x - 1) + 7.
The vertical asymptote of the original reciprocal function is x = 0. Since there is no horizontal shift in the transformation, the vertical asymptote remains at x = 0.