Thread: graph 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.

Originally Posted by scorpion007

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.

<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

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