asymptotes and discontinuities of F(x)= |x|(x-3)/(9-x^2)

[Cuddles]

Consider the function F(x)= |x|(x-3)/(9-x^2)

Determine all vertical and horizontal asymptotes and nonremovable discontinuities of f.

I think I got the horizontal asymptote. I just can't remember how to find vertical asymptotes without the graph.

 

[o_O]

Vertical asymptotes occur at non-permissible values of x (values that you cannot have). So for what x values can you NOT have?

 

[Cuddles]

3 or negative 3, but according to the graph positive 3 is a removable discontinuity

 

[o_O]

Oh right! Sorry, didn't see you had to find the discontinuities. For removable discontinuities, the left and right hand limits exist but aren't DEFINED at that particular point, i.e.
\(\displaystyle \lim_{x \to a} f(x)\) exists but f(a) does not exist.

 

[Cuddles]

Oh! Wow, I feel dumb for forgetting that now! Thanks!