g. \( y=\frac{1}{2 x+3} \)

Find the vertical asymptotes of the function \( y=\frac{1}{2x+3} \). Function by following steps: - step0: Find the vertical asymptotes: \(y=\frac{1}{2x+3}\) - step1: Evaluate the limit: \(\lim _{x\rightarrow -\frac{3}{2}}\left(\frac{1}{2x+3}\right)\) - step2: Evaluate the left-hand and the right-hand limits: \(\begin{align}&\lim _{x\rightarrow -\frac{3}{2}^{-}}\left(\frac{1}{2x+3}\right)\\&\lim _{x\rightarrow -\frac{3}{2}^{+}}\left(\frac{1}{2x+3}\right)\end{align}\) - step3: Evaluate the left-hand limit: \(\begin{align}&-\infty\\&+\infty\end{align}\) - step4: Limit does not exist: \(\textrm{The limit does not exist}\) - step5: \(x=-\frac{3}{2}\) is a vertical asymptote\(:\) \(\begin{align}&x=-\frac{3}{2}\textrm{ }\textrm{is a vertical asymptote}\end{align}\) - step6: List all vertical asymptotes of the function: \(\begin{align}&x=-\frac{3}{2}\end{align}\) The vertical asymptote of the function \( y=\frac{1}{2x+3} \) is at \( x=-\frac{3}{2} \).