Question

How do you identify the vertical asymptotes of `f(x) = (10)/(x^2-7x-30)`?

Answer 1

Well, as `x->-3` then `f (x) ->oo`
and as `x->10` then `f(x)->oo`

Explanation:

To get to this answer, you'll first have to factorize the denominator, to see when this gets (closer and closer) to zero.
`x^2-7x-30=(x+3)(x-10)`

Hence `x=-3, x=10` vertical asymptotes.

The graph for `f(x)` is

graph{10/(x^2-7x-30) [-20.27, 20.26, -10.14, 10.13]}