Select the vertical asymptote(s) of the function f(x)=((x+6)(x-1))/((x-2)(x+6)) A. x=2 B. x=-6 C. x=2, x=-6 D. x=-2

Question

Select the vertical asymptote(s) of the function
`f(x)=((x+6)(x-1))/((x-2)(x+6))`

A. x=2
B. x=-6
C. x=2, x=-6
D. x=-2

Answer 1

A. x = 2

Explanation:

(x+6)(x-1) ÷ (x-2)(x+6)

Since x+6 is common to both, numerator and denominator, it will get cancelled out

And there will be a hole at x = -6

The simplified form would be

(x-1)/(x-2)

There will be a vertical asymptote at x = 2, because the denominator becomes zero at x = 2

Answer 2

As the described function, we want to find vertical asymtotes, we find the value of x so that the denominator is equal to 0.

Here, (x - 2)(x + 6) = 0

=> x = 2, x =-6

=> Option C is correct.

Hope this helps!

:)