Write an equation for the translation of y = 5/x that has the asymptotes x = 6 and y = 7

Solution:

Given, y = 5/x

Asymptotes x = 6 and y = 7.

We have to write an equation for the translation.

The function has a vertical asymptote at x = 0, at x = 0 the denominator is 0, so the function becomes undefined.

To have the vertical asymptote at x = 6, the denominator has to  be

x = x - 6

So, the function y = 5/x-6 has vertical asymptote at x = 6.

Since, the function y = 5/x-6 has a horizontal asymptote at y = 0.

To get the horizontal asymptote at y = 7, we have to add 7 to the function.

So, the function becomes y = 5/x-6 + 7

Therefore, the function y = 5/x-6 + 7 has a vertical asymptote at x = 6 and a horizontal asymptote at y = 7.

Write an equation for the translation of y = 5/x that has the asymptotes x = 6 and y = 7

Summary:

An equation for the translation of y = 5/x that has the asymptotes x = 6 and y = 7 is y = 5/x-6 + 7.