Whats a function that has a hole at (6, 11), no horizontal asymptote and resembles the line y = 3x - 7.
You don't say anything about a vertical asymptote, so let's assume there is none. To get the asymptote of y=3x+7, we could use
y = 3x+7 + (ax+b)/(x^2+1)
To have y(6) = 11 we can use
y = 3x+7 - (70x+98)/(x^2+1) = (3x^3+7x^2-67x-91)/(x^2+1)
Now, to get the hole at x=6, just add a factor of (x-6) top and bottom
y = (3x^3+7x^2-67x-91)(x-6) / (x^2+1)(x-6)
= (3x^4 - 11x^3 - 109x^2 - 311x + 546) / (x^3 - 6x^2 + x - 6)