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

1 Answer
Jul 16, 2015

Answer:

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#