question find all vertical asymptotes of the following function. f(x) = (x^2 + 7x + 12)/(2x + 8) answer no…

question find all vertical asymptotes of the following function. f(x) = (x^2 + 7x + 12)/(2x + 8) answer no vertical asymptotes submit answer

question find all vertical asymptotes of the following function. f(x) = (x^2 + 7x + 12)/(2x + 8) answer no vertical asymptotes submit answer

Answer

Explanation:

Step1: Factor the numerator and denominator

Factor $x^{2}+7x + 12=(x + 3)(x+4)$ and $2x + 8=2(x + 4)$. So, $f(x)=\frac{(x + 3)(x + 4)}{2(x + 4)}$.

Step2: Simplify the function

Cancel out the common factor $(x + 4)$ (for $x\neq - 4$), we get $f(x)=\frac{x + 3}{2},x\neq - 4$. The function is a linear - function with a removable discontinuity at $x=-4$ and no vertical asymptotes.

Answer:

No Vertical Asymptotes