+73 Consider the function below. List the answers.
\(\displaystyle{f(x)=\frac{{x^{2}+11x+28}}{{x^{2}-16}}}\)
For what real numbers is the function not continuous?
For which of those is the discontinuity removable?
+128474 The function is not continuous when an x makes the denominator = 0.....so.....
x^2 - 16 = 0
(x + 4) ( x - 4) = 0
Setting each factor to 0 and solving for x produces x = -4 and x = 4
Factor the numerator as ( x + 4) ( x + 7)
We are left with
(x + 4) ( x + 7) ( x + 7)
___________ = _______
(x + 4) ( x - 4) ( x - 4)
The discontinuity is removable at ( x + 4) = 0 ⇒ x = - 4
