Graph all vertical and horizontal asymptotes of the rational function. \[ f(x)=\frac{-10}{-x-5} \]

Find the vertical asymptotes of the function \( f(x)=-\frac{10}{-x-5} \). Function by following steps: - step0: Find the vertical asymptotes: \(f\left(x\right)=\frac{10}{x+5}\) - step1: Evaluate the limit: \(\lim _{x\rightarrow -5}\left(\frac{10}{x+5}\right)\) - step2: Evaluate the left-hand and the right-hand limits: \(\begin{align}&\lim _{x\rightarrow -5^{-}}\left(\frac{10}{x+5}\right)\\&\lim _{x\rightarrow -5^{+}}\left(\frac{10}{x+5}\right)\end{align}\) - step3: Evaluate the left-hand limit: \(\begin{align}&-\infty\\&+\infty\end{align}\) - step4: Limit does not exist: \(\textrm{The limit does not exist}\) - step5: \(x=-5\) is a vertical asymptote\(:\) \(\begin{align}&x=-5\textrm{ }\textrm{is a vertical asymptote}\end{align}\) - step6: List all vertical asymptotes of the function: \(\begin{align}&x=-5\end{align}\) Find the horizontal asymptotes of the function \( f(x)=-\frac{10}{-x-5} \). Function by following steps: - step0: Find the horizontal asymptotes: \(f\left(x\right)=\frac{10}{x+5}\) - step1: Evaluate the limits \(\lim _{x\rightarrow +\infty}\left(f\left(x\right)\right)\) and \(\lim _{x\rightarrow -\infty}\left(f\left(x\right)\right):\) \(\begin{align}&\lim _{x\rightarrow +\infty}\left(\frac{10}{x+5}\right)\\&\lim _{x\rightarrow -\infty}\left(\frac{10}{x+5}\right)\end{align}\) - 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 \( f(x)=-\frac{10}{-x-5} \) is at \( x=-5 \), and the horizontal asymptote is at \( f(x)=0 \).