Hello, kishan!
1) Is this statement true or false?
A rational function can never cross one of its asymptotes.
Justify your answer.
A function cannot cross one of its vertical asymptotes.
. . However, it can cross its horizontal asymptote.
Recall that a horizontal asymptote describes the behavior of the graph as
That is, the graph may approach a finite value at the extreme right or extreme left;
. . but anything can happen "locally".
Perhaps the simplest example is a Serpentine Curve: . Code:

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It has a horizontal asymptote: . .(the xaxis)
But it crosses the xaxis at the origin.