question\nfind all vertical asymptotes of the following function.\n f(x)=\frac{3 x^{2}+9 x - 162}{3 x - 7}…

question\nfind all vertical asymptotes of the following function.\n f(x)=\frac{3 x^{2}+9 x - 162}{3 x - 7} \nanswer attempt 2 out of 2\none vertical asymptote

question\nfind all vertical asymptotes of the following function.\n f(x)=\frac{3 x^{2}+9 x - 162}{3 x - 7} \nanswer attempt 2 out of 2\none vertical asymptote

Answer

Explanation:

Step1: Find the zero of the denominator

Set the denominator (3x - 7=0). Solving for (x), we get (x=\frac{7}{3}).

Step2: Check if the numerator is non - zero at this (x) value

Substitute (x = \frac{7}{3}) into the numerator (3x^{2}+9x - 162). [ \begin{align*} 3\times(\frac{7}{3})^{2}+9\times\frac{7}{3}-162&=3\times\frac{49}{9}+21 - 162\ &=\frac{49}{3}+21-162\ &=\frac{49 + 63-486}{3}\ &=\frac{112 - 486}{3}\ &=\frac{- 374}{3}\neq0 \end{align*} ]

Answer:

The vertical asymptote is (x = \frac{7}{3})