find the dicontinuities of the function. f(x) = (x^2 + 12x + 27)/(x^2 + 4x + 3). there is a removable…

find the dicontinuities of the function. f(x) = (x^2 + 12x + 27)/(x^2 + 4x + 3). there is a removable discontinuity at (-3, -3). complete where is the vertical asymptote(s)? x = -3, x = -1 x = -1 x = -9 x = -9, x = -3 done

find the dicontinuities of the function. f(x) = (x^2 + 12x + 27)/(x^2 + 4x + 3). there is a removable discontinuity at (-3, -3). complete where is the vertical asymptote(s)? x = -3, x = -1 x = -1 x = -9 x = -9, x = -3 done

Answer

Explanation:

Step1: Factor the numerator and denominator

The numerator $x^{2}+12x + 27=(x + 3)(x+9)$. The denominator $x^{2}+4x + 3=(x + 3)(x + 1)$. So $f(x)=\frac{(x + 3)(x + 9)}{(x + 3)(x + 1)}$.

Step2: Identify removable discontinuity

A removable discontinuity occurs when a factor can be canceled from the numerator and denominator. Here, when $x=-3$, the factor $(x + 3)$ can be canceled. After canceling, $f(x)=\frac{x + 9}{x + 1},x\neq-3$.

Step3: Find vertical asymptotes

Vertical asymptotes occur where the denominator of the simplified - function is zero. Set $x+1 = 0$, then $x=-1$.

Answer:

B. $x=-1$