A graph can cross through a horizontal asymptote when it is near the middle. In order for the graph to cross the horizontal asymptote it must be towards the middle it can’t be towards the right or the left. If it's a slant asymptote the graph can sometimes cross through an asymptote as well. For a slant asymptote it must be near the middle of the graph. Vertical asymptotes, in the other hand, the graphs can't cross through the vertical asymptotes.
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