Question

How to find the equation of vertical and horizontal asymptotes?

Answer 1

Please find some specific examples of functions for which you want to find vert. or horiz. asy. and their equations.  This is a broad topic.

Very generally, vert. asy. connect only to rational functions; if the function becomes undef. at any particular x-value, that x-value, written as x = c, is the equation of one vertical asy.

Very generally, horiz. asy. pertain to the behavior of functions as x grows increasingly large (and so are often associated with rational functions).  To find them, we take limits of the functions, letting x grow large hypothetically, and see what happens to the function.  Very often you end up with the equation of a horiz. line, your horiz. asy., which the graph usually (but not always) does not cross.