find all vertical asymptotes of the following function.\n\n$f(x)=\\frac{2 x^{2}+5 x - 12}{3 x +…

find all vertical asymptotes of the following function.\n\n$f(x)=\\frac{2 x^{2}+5 x - 12}{3 x + 12}$\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$f(x)=\\frac{2 x^{2}+5 x - 12}{3 x + 12}$\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 numerator (2x^{2}+5x - 12=(2x - 3)(x + 4))
  • Factor denominator (3x + 12=3(x + 4))

Step2: Simplify the function

[ \begin{align*} f(x)&=\frac{(2x - 3)(x + 4)}{3(x + 4)}\ &=\frac{2x - 3}{3},x\neq - 4 \end{align*} ] Since after simplification, the function (f(x)=\frac{2x - 3}{3}) (a linear function) with a hole at (x=-4) (not a vertical asymptote as the factor ((x + 4)) cancels out).

Answer:

No Vertical Asymptotes