Question

Where are the asymptotesame for the following function located? f (x)=7/x^2-2x-24

Answer 1

1) given function:  

      7
---------------
x^2 - 2x - 24

2) Vertical asymptotes are at the values ox x for which the function is not defined. These are the roots of the denominator polynomial.

You can factor the denominator to find those roots:

x^2 - 2x - 24 = 0 = (x - 6)(x + 4) => x = 6 and x = - 4

Therefore, the two vertical asymptotes are x = 6 and x = - 4

3) The function also has one horizontal asymptote:

Lim f(x) when x → +/- ∞ is 0, so y = 0 is also an asymptote.