Question

how do you find the asymptote of f(x) =1/x + x^2?
I know the answer is y=x^2, why?

Answer 1

As x gets very large towards positive infinity 1/x tends towards 0.
Thus 1/x + x^2 can be approximated as x^2 when we make x as large as we like.
Similarly, this result also stands when x tends towards negative infinity.

The graph will look as the sum of 1/x and x^2