Graph all vertical and horizontal asymptotes of the rational function. \[ f(x)=\frac{-5}{-4 x+2} \]

Find the vertical asymptotes of the function \( f(x)=-\frac{5}{-4x+2} \). Function by following steps: - step0: Find the vertical asymptotes: \(f\left(x\right)=-\frac{5}{-4x+2}\) - step1: Evaluate the limit: \(\lim _{x\rightarrow \frac{1}{2}}\left(-\frac{5}{-4x+2}\right)\) - step2: Rewrite the fraction: \(\lim _{x\rightarrow \frac{1}{2}}\left(\frac{-5}{-4x+2}\right)\) - step3: Evaluate the left-hand and the right-hand limits: \(\begin{align}&\lim _{x\rightarrow \frac{1}{2}^{-}}\left(\frac{-5}{-4x+2}\right)\\&\lim _{x\rightarrow \frac{1}{2}^{+}}\left(\frac{-5}{-4x+2}\right)\end{align}\) - step4: Evaluate the left-hand limit: \(\begin{align}&-\infty\\&+\infty\end{align}\) - step5: Limit does not exist: \(\textrm{The limit does not exist}\) - step6: \(x=\frac{1}{2}\) is a vertical asymptote\(:\) \(\begin{align}&x=\frac{1}{2}\textrm{ }\textrm{is a vertical asymptote}\end{align}\) - step7: List all vertical asymptotes of the function: \(\begin{align}&x=\frac{1}{2}\end{align}\) Find the horizontal asymptotes of the function \( f(x)=-\frac{5}{-4x+2} \). Function by following steps: - step0: Find the horizontal asymptotes: \(f\left(x\right)=-\frac{5}{-4x+2}\) - step1: Evaluate the limits \(\lim _{x\rightarrow +\infty}\left(f\left(x\right)\right)\) and \(\lim _{x\rightarrow -\infty}\left(f\left(x\right)\right):\) \(\begin{align}&\lim _{x\rightarrow +\infty}\left(-\frac{5}{-4x+2}\right)\\&\lim _{x\rightarrow -\infty}\left(-\frac{5}{-4x+2}\right)\end{align}\) - step2: Calculate: \(\begin{align}&0\\&0\end{align}\) - step3: The finite values are horizontal asymptotes: \(\begin{align}&f\left(x\right)=0\end{align}\) The vertical asymptote of the rational function \( f(x)=-\frac{5}{-4x+2} \) is \( x=\frac{1}{2} \), and the horizontal asymptote is \( f(x)=0 \).