Answer
True.
Work Step by Step
Refer to example 5, where the rational function $y=\displaystyle \frac{2x^{2}+7x-4}{x^{2}+x-2}$
crosses the line $y=2$, which is a horizontal asymptote.
The reason for this statement being true is that horizontal asymptotes are defined because of the behavior of the graph at the far left and far right ends of the graph (when $x\rightarrow\pm\infty)$, so for values of x relatively near 0, the line may be crossed.
