Question

Where are the asymptotes for the following function located? f(x)= 7/ x^2-2x-24

Answer 1

Factor the demoniator:-

x^2 -2x - 24 = (x - 6)(x + 4)

the asymptotes occurs when denominator = 0

so here they are  the vertical lines x = 6 and x = -4

Answer 2

Answer: Hence, the asymptotes of f(x) located at x=6 and x=-4.

Step-by-step explanation:

Since we have given that

$f(x)= \frac{7}{x^2-2x-24}$

We need to find the asymptotes for the above function:

Asymptotes occur when denominator becomes zero.

$x^2-2x-24=0\\\\x^2-6x+4x-24=0\\\\x(x-6)+4(x-6)=0\\\\(x-6)(x+4)=0\\\\x=6,-4$

Hence, the asymptotes of f(x) located at x=6 and x=-4.