Finding Asymptotes of a Function: Example with Vertical and Slant Asymptotes

[Dell]

if i am given a function y=f(x) for example,

f(x)=[tex]\frac{x<sup>3/SUP]{x2/SUP]-1tex]

and i am asked to find all asymptotes, i find

vertical asymptotes : x=1 x=-1

slant asymptote: y=x

am i expected to write y=infinity as well since

Lim
x->inf = infinity

or is this just understood since i do not have another horizontalasymptote</sup>

 

[Mark44]

I fixed up your LaTeX tags. I think this is what you meant.

if i am given a function y=f(x) for example,

f(x)=$$\frac{x^3}{x^2-1}$$

and i am asked to find all asymptotes, i find

vertical asymptotes : x=1 x=-1

slant asymptote: y=x

am i expected to write y=infinity as well since

Lim
x->inf = infinity

or is this just understood since i do not have another horizontalasymptote

Everything looks fine. I wouldn't expect that you'd need to add that f(x) is unbounded for large or very negative x.

 

[Dell]

thanks, that's exactly it, not that it really matters, more of a general question than this specific case