Question: Consider a curve of the form $y=f(x)$, where $f(x)$ is a polynomial in $x$ of positive degree $n$. Prove that the curve has exactly one point $P$ at infinity, that it intersects every vertical line exactly $n-1$ times at $P$, and that it intersects the line at infinity exactly $n$ times at $P$. (The case $n=1$ may require separate consideration.)
I have tried many times now but Im completely lost on this one because I want to do it right with no wrongs.
How to do this whole problem step by step?