Question

How do you identify the vertical asymptotes of `f(x) =2/(x^2+3x-10)`?

Answer 1

Find the zeros of the denominator and make sure they are not also zeros of the numerator. (If any of them are: factor, reduce the quotient and try again.)

Explanation:

`f(x) =2/(x^2+3x-10)`

The denominator is `0` when

`x^2+3x-10=0`

`(x+5)(x-2)=0`

The zeros are `-5` and `2`

(For a quadratic equation, I always try factoring first, because it's fast. But don't spend a lot of time on factoring, because you can use the quadratic formula to get zeros.)

Obviously, neither of these numbers is a zero of the numerator so:

The vertical asymptotes are the lines whose equations are:

`x=-5` and `x=2`