Question

what is the horizontal asymptote of the rational function (3x^2 + 4x + 9) / (x^2 + 2x + 1)

Answer 1

For a horizontal asymptote, we're figuring out what happens when x tends to infinity. This means that, in this question, we can ignore all but the highest powers of x, as lower powers will be negligible.
This reduces our equation to 3x^2/x^2 as x->inf which gives a limit of 3.

Answer 2

@djdethclop: @KateLovesPie is correct - the answer is 3.