How do you find the asymptotes for #f(x) = (3x + 5) / (2x - 3)#?

1 Answer
Feb 11, 2016

Answer:

Vertical asymptote at #x=3/2#.

Horizontal asymptote at #y=3/2#.

Explanation:

Vertical asymptotes occur when the denominator is zero,
ie when #2x-3=0=>x=3/2#.

Horizontal asymptotes occur at
# lim_(x->+-oo) f(x) = lim_(x->+-oo) (3x+5)/(2x-3)= 3/2#

The graph of the rational function verifies this :

graph{(3x+5)/(2x-3) [-13.3, 18.73, -6.8, 9.22]}