Why do the asymptotes of y = x^2 + 1/x include y=x^2 and y=1/x?
x = 0 is a vertical asymptote. It's the line through the value of x that makes the function undefined.
y = x^2 is an oblique asymptote. It's the curve that the function approaches as x --> +oo and x --> -oo. Note: Horizontal asymptotes are a special case of oblique asymptote.