hi, im having a problem with this question. Im not sure how even go about getting one of these multiple choices.

The graph of , where m and n are real constants, has no vertical asymptotes if

A:

B:

C:

D:

E:

help appreciated.

Printable View

- Sep 24th 2006, 10:40 PMscorpion007graph asymptote question
hi, im having a problem with this question. Im not sure how even go about getting one of these multiple choices.

The graph of , where m and n are real constants, has no vertical asymptotes if

A:

B:

C:

D:

E:

help appreciated. - Sep 24th 2006, 11:46 PMCaptainBlack
<obligatory moan about LaTeX not being working yet>

For f to have a vertical asymtote requires that x^2-mx-n have at least

one real root. This is equivalent to the discriminanat being >=0.

The discriminant is the term under the square root sign in the quadratic

formula, so in this case the disciminant is: m^2+4n, and so f has vetical

asymtots if (and only if):

m^2+4n >=0,

or:

m^2 >= -4n.

RonL - Sep 25th 2006, 03:49 AMscorpion007
hah, sorry about the latex, i wont do it next time.

Also -- i found the answer myself to the problem shortly after posting, lol.

BTW, the question asks for the opposite of what you found. i.e. when the graph has *no* vert asymptotes. But all you have to do is change the >= to <.

Thanks anyway