Answer:-
A vertical asymptote occurs where a function approaches infinity or becomes undefined. For rational functions, vertical asymptotes happen where the denominator equals zero, provided the numerator doesn’t cancel it out. Given a function ???? ( ???? ) = ???? ( ???? ) ???? ( ???? ) f(x)= q(x) p(x) ? , set ???? ( ???? ) = 0 q(x)=0 and solve for ???? x to find the vertical asymptote equation. For logarithmic functions like ???? ( ???? ) = log ? ( ???? − ???? ) f(x)=log(x−a), the vertical asymptote is at ???? = ???? x=a. Identifying these points helps determine the function's behavior as it approaches certain values on the graph.
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