How do you find the Vertical, Horizontal, and Oblique Asymptote given #f(x)= (3x + 5) /( x - 2)#?

1 Answer
Nov 11, 2016

Answer:

The vertical asymptote is #x=2#
There is no oblique asymptote.
The horizontal asymptoteis #y=3#

Explanation:

As you cannot divide by #0#, the vertical asymptote is #x=2#

The degree of the numerator is #=# to the degree of the denominator, there is no oblique asymptote.

#lim_(x->+-oo)f(x)=3x/x=3#

Therefore #y=3# is a horizontal asymptote
graph{(y-(3x+5)/(x-2))(y-3)=0 [-25.65, 25.65, -12.83, 12.84]}