Question

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

Answer 1

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]}