Question

write the equation of the translation of y=2/x that has the asymptotes of x=5 and y=-3

Answer 1

$\bf y=\cfrac{2}{x}\implies y=\cfrac{2x^0}{x}$

now, the denominator has a higher degree, a degree of 1, than the numerator's, therefore the horizontal asymptote for this function is at y = 0.

now, the vertical asymptotes of it, are at the zeros of the denominator, namely x = 0, when is x = 0? at 0, so the vertical asymptote for this function is at x = 0, the y-axis.

now, if we want the horizontal asymptote moved over from its position at 0, over to x = 5, simply translate it by 5 units,   $\bf y=\cfrac{2}{x-5}$.

and if we want the vertical asymptote to move down from 0 to -3, simply translate the function vertically 3 units,  $\bf y=\cfrac{2}{x-5}-3$