To find the vertical asymptote, take the denominator and set it equal to zero:
To find the horizontal asymptote, note the degrees of the polynomials in the numerator and denominator. Since they are the same (1), take the ratio of the leading coefficients:
Thus the product would be
Edit: Beaten to it by mr fantastic!
Sorry for my terrible handwriting but I did the long division polynomial method and as a final answer I get: -ct/p and that is not even one of the multiple choice!
In my country at least, the standard form of the rational function is:
f(x) = (a/(b(x-h))) + k
First of all, remember that asymptotes are equations of lines, not numbers. So it doesn't make sense to write them as an ordered pair like . Second, is the horizontal asymptote, but where did the come from? If that's supposed to be the vertical asymptote, that's wrong. It's as mr fantastic and I both explained.
When the problem asked to find the "product of the parameters that defines its vertical and horizontal asymptotes," I took it to mean that you multiply by , getting the answer I stated above.