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.