state the vertical asymptotes of f(x)= 1/x^2 - 4x - 12
To find the vertical asymptotes of a function, we must determine the values of x that make the function undefined. In this case, the function is f(x) = 1/(x^2 - 4x - 12).
The function becomes undefined when the denominator is equal to zero. So, we need to find the values of x that make x^2 - 4x - 12 = 0.
The quadratic equation x^2 - 4x - 12 = 0 can be factored as (x - 6)(x + 2) = 0.
Setting each factor equal to zero, we have x - 6 = 0 and x + 2 = 0. Solving these equations, we find x = 6 and x = -2.
Therefore, the vertical asymptotes of f(x) = 1/(x^2 - 4x - 12) are x = 6 and x = -2.