Question

Find the vertical asymptotes of the following function:

y=x+2
_______
x^2 +2x−8

Select the appropriate response:

A) horizontal asymptotes x = −4, 5

B) horizontal asymptotes x = −4, 4

C) vertical asymptotes x = −8, 4

D) vertical asymptotes x = −4, 2

Help please! 50 points!

Answer 1

D) vertical asymptotes x = −4, 2

Explanation:

x² + 2x - 8 = 0

x² + 4x - 2x - 8 = 0

x(x + 4) - 2(x + 4) = 0

(x + 4)(x - 2) = 0

x = 2, -4

Answer 2

D) vertical asymptotes x = −4, 2

Explanation:

First you factor the denominator: x^2 +2x−8

Find factors of -8(c) that add together to give 2(b): 4 and -2

Rewrite the equation: x^2+4x-2x-8

Factor out common variables: x(x+4)-2(x+4)

Group the things inside and outside the parentheses together: (x-2)(x+4)

Solve: x-2=0 so x=2 and x+4=0 so x=-4