How do you find the vertical, horizontal and slant asymptotes of: #Y=(3x)/(x^2-x-6) + 3#?

1 Answer
Nov 25, 2016

Horizontal asymptote y=3
Vertical asymptotess x=3 and x=-2
No slant asymptotes.


In case of rational functions, like the one given here, horizontal asymptotes are horizontal lines which the function approaches as #x->oo#. In the present case, as #x->oo# y=3. Hence y=3 is an horizontal asymptote of the given function.

For vertical asymptotes, in case of rational functions, it has to be seen that for what values of x, #y->oo#. In the present case if the denominator is factorised the function can be written as #y=x/((x-3)(x+2)) +3#. For x=3 and x=-2, # y->oo#. Hence vertical asymptotes are x=3 and x=-2.

There are no slant asymptotes.