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
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.
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 <.