Question

How do you find the Vertical, Horizontal, and Oblique Asymptote given `g(x)= (x+2 )/( 2x^2)`?

Answer 1

The vertical asymptote is `x=0`
No oblique asymptote.
The horizontal asymptote is `y=0`

Explanation:

The domain of `g(x)` is `D_g(x)=RR-{0}`

As we cannot divide by `0`, `x!=0`

The vertical asymptote is `x=0`

The degree of the numerator is `<` than the degree of the denominator, so there is no oblique asymptote.

`lim_(x->-oo)g(x)=lim_(x->-oo)(x/(2x^2))=lim_(x->-oo)1/(2x)=0^-`

`lim_(x->+oo)g(x)=lim_(x->+oo)(x/(2x^2))=lim_(x->+oo)1/(2x)=0^+`

The horizontal asymptote is `y=0`

graph{(y-(x+2)/(2x^2))(y)(y-100x)=0 [-7.02, 7.024, -3.51, 3.51]}