Question

How do you find vertical, horizontal and oblique asymptotes for `(x^4 - 8x^2 +16) / x^2`?

Answer 1

The vertical asymptote is `x=0`
No horizontal asymptote
No slant asymptote

Explanation:

Let's rewrite the expression

`(x^4-8x^2+16)/x^2`

Let `f(x)=(x^4-8x^2+16)/x^2`

The domain of `f(x)` is `D_f(x)=RR-{0}`

As you canot divide by `0`, `x!=0`

`lim_(x->+-oo)f(x)=lim_(x->+-oo)x^4/x^2=lim_(x->+-oo)x^2=+oo`

graph{(y-(x^4-8x^2+16)/(x^2))(y-1000x)=0 [-10, 10, -5, 5]}