Question

Which of the following represents the vertical asymptotes of the function

Answer 1

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

Let me know if you need help.

Answer 2

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