what is the horizontal asymptote to the rational function f(x)=[1/(x-1)]+4?

Question

so basically the plus 4 is outside of the whole 1/(x-1)
And i thank you

Answer 1

The horizontal asymptote is the value the function approaches as x → ±∞.

y = f(x) = [1/(x-1)] + 4

Limit x → ∞ [1/(x-1)] + 4 = 1/(∞ - 1) + 4 = 0 + 4 = 4

The horizontal asymptote is y = 4.