Question

What is the discontinuity of the function f(x)= x^2-4x-12/x+2. PLEASE ASAP WILL GIVE BRAINLIEST!

Answer 1

Hello!

$\large\boxed{\text{Infinite discontinuity at x = 2}}$

$f(x) = \frac{x^{2} - 4x - 12}{x - 2}$

Recall that in a rational function, the denominator contains the vertical asymptote (an infinite discontinuity).

If terms can be canceled from the denominator and the numerator, then the function contains a hole. We can check whether this function contains such by factoring:

$f(x) = \frac{(x - 6)(x + 2)}{x - 2}$

There is no common factor, so the function only contains a discontinuity at its vertical asymptote.

Find the vertical asymptote by setting the denominator equal to 0:

x - 2 = 0

x = 2.