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

You must solve this first: x^2-2x-24=0

You should now that we cannot devide by 0 but there are wierd things happening near that value.

After that think about what happens if x is really big (goes to positive infinity) or if x goes to negative infinity.

Factor the demoniator:-

x^2 - 2x - 24 = (x - 6) (x + 4)

the asymptotes occurs when denominator = 0

so here they are the vertical lines x = 6 and x = - 4