Question

Which of the following represents the vertical asymptotes of the function

Answer 1

The expression in the denominator is $\displaystyle{ x^2-2x-8$.

We can use this expression by completing the square, and the difference of squares as follows:

$\displaystyle{ x^2-2x-8=(x^2-2x+1)-9=(x-1)^2-3^2$

$=(x-1-3)(x-1+3)=(x-4)(x+2)$.

So, the zeros of the polynomial $\displaystyle{ P(x)=x^2-2x-8$ are x=4 and x=-2.


Thus, the asymptotes are the lines x=-2, and x=4.


Answer: D

Answer 2

The answer would be D, x = -2, and x = 4

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