Where are the asymptotes for the following function located? f(x)=14/(x-5)(x+1)
a. x=-1 and x=5
b. x=-1 and x=14
c. x=1 and x=-5
d. x=14 and x=5

Option a is correct.

x=-1 and x=5

Step-by-step explanation:

To find the asymptotes for the rational function:

The vertical asymptotes for this function is to set the denominator equals to 0.

The horizontal asymptotes for this given fucntion is 0.

Denominator of the given function is:

By definition of asymptotes;

By zero product property:

and

⇒x = 5 and x= -1

Therefore, the asymptotes for the following function located are: x = -1 and x =5