Question

3 calculate the vertical asymptote(s) of the rational function $f(x)=\frac{x+5}{x^2-2x-8}$
$x=5, x=-8$
$x=-5$
$x=-2, x=4$
$x=-2, x=-8$

Explanation:

Step1: Factor the denominator

$x^2-2x-8=(x+2)(x-4)$

Step2: Set denominator to 0

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

Step3: Solve for x

$x+2=0 \implies x=-2$; $x-4=0 \implies x=4$

Step4: Check numerator at roots

At $x=-2$: $-2+5=3
eq0$; At $x=4$: $4+5=9
eq0$

Answer:

C. $x=-2, x=4$