Write an equation for the translation of y= 4/x that has the asymptotes​ x=7 and​ y=6.

Question

Write an equation for the translation of

y=4/x

that has the asymptotes​ x=7 and​ y=6.

Answer 1

4/x has asymptotes of x = 0 and y = 0

Thus,

y = 6 + 4/(x-7) translates the original equation 7 to the right and 6 up, resulting in the desired asymptotes.

You may write this y = (6x - 38)/(x-7) if you prefer

Answer 2

The graph of y = 4/x has vertical asymptote x = 0 (the y-axis) and horizontal asymptote y = 0 (the x-axis).

So, translating 7 units to the right and 6 units upward translates the vertical asymptote to x = 7 and the horizontal asymptote to y = 6.

The translated equation is y = 4 / (x-7) + 6