find all vertical asymptotes of the following function.\n\n$f(x)=\\frac{x^{2}+7x + 12}{2x + 6}$\n\nanswer…

find all vertical asymptotes of the following function.\n\n$f(x)=\\frac{x^{2}+7x + 12}{2x + 6}$\n\nanswer attempt 1 out of 2\n\nno vertical asymptotes\n\nno vertical asymptotes\n\none vertical asymptote\n\ntwo vertical asymptotes

find all vertical asymptotes of the following function.\n\n$f(x)=\\frac{x^{2}+7x + 12}{2x + 6}$\n\nanswer attempt 1 out of 2\n\nno vertical asymptotes\n\nno vertical asymptotes\n\none vertical asymptote\n\ntwo vertical asymptotes

Answer

Explanation:

Step1: Factor numerator and denominator

Factor (x^{2}+7x + 12=(x + 3)(x+4)) and (2x + 6=2(x + 3)). So (f(x)=\frac{(x + 3)(x + 4)}{2(x + 3)}).

Step2: Simplify the function

Cancel out the common factor ((x + 3)) (for (x\neq-3)). (f(x)=\frac{x + 4}{2}), (x\neq-3). Since after simplification, the function is a linear function (a polynomial of degree 1) with a hole at (x=-3) (not a vertical asymptote as vertical asymptotes occur when the simplified function has a denominator that approaches 0 while the numerator does not).

Answer:

No Vertical Asymptotes