Where does the graph of the function intersect its asymptote?

Question

anonymous · Answer

$$f(x)= x+1+\frac{ x ^{2}-x }{ x ^{4}+1 }$$

anonymous · Answer

You know the asymptote is the polynomial part of f(x).
So the intersections are at f(x)=x+1

harsimran_hs4 · Answer

well 
1. asymptote never intersect the curve at any point
2. for illustration purpose we can say that the intersect/ asymptote become tangent to the curve at infinity

anonymous · Answer

^^ 
This is never always true. The definition of an asymptote is that when the graph tends to infinity, the other value will tend to the asymptote but never intersect it.

However, it is perfectly alright for the graph to intersect/cut through the asymptote at any other point

anonymous · Answer

The first step to solving this is to find all the asymptotes first. Do you know them?

anonymous · Answer

Found the answer! Thanks guys! (: