Write  an  equation  for  the  translation  of  y  = 6/x  that  has  the  asymptotes  x  =  4  and  y  = 5. a.) y = 6/x+4 + 5 b.) y = 6/x-4 + 5 c.) y = 6/x+5 + 4 d.) y = 6/x-5 + 4

otpion b. y = 6/(x + 4) + 5

Explanation:

1) The given equation is  y = 6 / x

2) The vertical asympote is  x = 0, since the function is not defined at x = 0, and the limits of f(x) when x → 0 from the right is ∞, and the limit from the left is - ∞.

3) The horizontal asympotes are the value of the limits of f(x) when x → +/- ∞.

The limit of 6 /x when x → ∞ or - ∞ is 0, so the asymptote is y = 0.

4) Now you want the new asymptotes be x = 4 and y = 5. Then you have to translate the function 4 units to the right and 5 units upward.

That means that the function has to be undefined at x = 4, which leads to make the denominator of the function x - 4.

And to translate the horizontal asympotote 5 units upward you have to add 5 to the function.

That is: y = 6/(x - 4) + 5, which is the option b.