Trazar todas las asintotas verticales y horizontales de la función racional. \[ f(x)=\frac{7 x+4}{2 x^{2}+8 x+8} \]

Find the vertical asymptotes of \( (7*x+4)/(2*x^2+8*x+8) \). Function by following steps: - step0: Find the vertical asymptotes: \(y=\frac{7x+4}{2x^{2}+8x+8}\) - step1: Evaluate the limit: \(\lim _{x\rightarrow -2}\left(\frac{7x+4}{2x^{2}+8x+8}\right)\) - step2: Evaluate the left-hand and the right-hand limits: \(\begin{align}&\lim _{x\rightarrow -2^{-}}\left(\frac{7x+4}{2x^{2}+8x+8}\right)\\&\lim _{x\rightarrow -2^{+}}\left(\frac{7x+4}{2x^{2}+8x+8}\right)\end{align}\) - step3: Evaluate the left-hand limit: \(\begin{align}&-\infty\\&-\infty\end{align}\) - step4: Calculate: \(-\infty\) - step5: \(x=-2\) is a vertical asymptote\(:\) \(\begin{align}&x=-2\textrm{ }\textrm{is a vertical asymptote}\end{align}\) - step6: List all vertical asymptotes of the function: \(\begin{align}&x=-2\end{align}\) Find the horizontal asymptotes of \( (7*x+4)/(2*x^2+8*x+8) \). Function by following steps: - step0: Find the horizontal asymptotes: \(y=\frac{7x+4}{2x^{2}+8x+8}\) - step1: Evaluate the limits \(\lim _{x\rightarrow +\infty}\left(y\right)\) and \(\lim _{x\rightarrow -\infty}\left(y\right):\) \(\begin{align}&\lim _{x\rightarrow +\infty}\left(\frac{7x+4}{2x^{2}+8x+8}\right)\\&\lim _{x\rightarrow -\infty}\left(\frac{7x+4}{2x^{2}+8x+8}\right)\end{align}\) - step2: Calculate: \(\begin{align}&0\\&0\end{align}\) - step3: The finite values are horizontal asymptotes: \(\begin{align}&y=0\end{align}\) La función racional \( f(x)=\frac{7x+4}{2x^{2}+8x+8} \) tiene una asintota vertical en \( x=-2 \) y una asintota horizontal en \( y=0 \).