Question

How do you find the vertical, horizontal and slant asymptotes of: `f(x)= x^(1/3)`?

Answer 1

No vertical asymptotes as all values of `x` are valid in `f(x)`

No slant asymptotes as not a quotient.

No horizontal asymptote.

Explanation:

Our function `f` is continuous and therefore has no vertical asymptotes.

No slant asymptotes as not a quotient.

Horizontal asymptote when `lim_(x->-oo)= k lim_(x->oo)=k` where`k cancel= -oo,oo`

`lim_(x->00) x^(1/3)=oo`

No horizontal asymptote.