Question

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

Answer 1

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]}