Graph all asymptotes of the rational function. $$ f(x)=\frac{-x^{2}-3 x+3}{x+1} $$

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Find the horizontal asymptotes of $$ (-x^2-3x+3)/(x+1) $$.
Function by following steps:
- step0: Find the horizontal asymptotes:
  $$y=\frac{-x^{2}-3x+3}{x+1}$$
- step1: Evaluate the limits $$\lim _{xightarrow +\infty}\left(yight)$$ and $$\lim _{xightarrow -\infty}\left(yight):$$
  $$\begin{align}&\lim _{xightarrow +\infty}\left(\frac{-x^{2}-3x+3}{x+1}ight)\&\lim _{xightarrow -\infty}\left(\frac{-x^{2}-3x+3}{x+1}ight)\end{align}$$
- step2: Calculate:
  $$\begin{align}&-\infty\&+\infty\end{align}$$
- step3: The function has no horizontal asymptotes:
  $$	extrm{No horizontal asymptotes}$$
Find the vertical asymptotes of $$ (-x^2-3x+3)/(x+1) $$.
Function by following steps:
- step0: Find the vertical asymptotes:
  $$y=\frac{-x^{2}-3x+3}{x+1}$$
- step1: Evaluate the limit:
  $$\lim _{xightarrow -1}\left(\frac{-x^{2}-3x+3}{x+1}ight)$$
- step2: Evaluate the left-hand and the right-hand limits:
  $$\begin{align}&\lim _{xightarrow -1^{-}}\left(\frac{-x^{2}-3x+3}{x+1}ight)\&\lim _{xightarrow -1^{+}}\left(\frac{-x^{2}-3x+3}{x+1}ight)\end{align}$$
- step3: Evaluate the left-hand limit:
  $$\begin{align}&-\infty\&+\infty\end{align}$$
- step4: Limit does not exist:
  $$	extrm{The limit does not exist}$$
- step5: $$x=-1$$ is a vertical asymptote$$:$$
  $$\begin{align}&x=-1	extrm{ }	extrm{is a vertical asymptote}\end{align}$$
- step6: List all vertical asymptotes of the function:
  $$\begin{align}&x=-1\end{align}$$
Find the oblique asymptotes of $$ (-x^2-3x+3)/(x+1) $$.
Function by following steps:
- step0: Find the oblique asymptotes:
  $$y=\frac{-x^{2}-3x+3}{x+1}$$
- step1: Evaluate the limits $$\lim _{xightarrow +\infty}\left(\frac{y}{x}ight)$$ and $$\lim _{xightarrow -\infty}\left(\frac{y}{x}ight):$$
  $$\begin{align}&\lim _{xightarrow +\infty}\left(\frac{\frac{-x^{2}-3x+3}{x+1}}{x}ight)\&\lim _{xightarrow -\infty}\left(\frac{\frac{-x^{2}-3x+3}{x+1}}{x}ight)\end{align}$$
- step2: Calculate:
  $$\begin{align}&-1\&-1\end{align}$$
- step3: Evaluate the limit $$\lim _{xightarrow +\infty}\left(y-axight):$$
  $$\begin{align}&\lim _{xightarrow +\infty}\left(\frac{-x^{2}-3x+3}{x+1}+xight)\&\lim _{xightarrow -\infty}\left(\frac{-x^{2}-3x+3}{x+1}+xight)\end{align}$$
- step4: Calculate:
  $$\begin{align}&-2\&-2\end{align}$$
- step5: Write the oblique asymptote according to limits value:
  $$\begin{align}&y=-x-2	extrm{ }	extrm{is an oblique asymptote}\&y=-x-2	extrm{ }	extrm{is an oblique asymptote}\end{align}$$
- step6: The function has one oblique asymptote:
  $$y=-x-2$$
The rational function $$ f(x)=\frac{-x^{2}-3x+3}{x+1} $$ has the following asymptotes:
- No horizontal asymptotes
- Vertical asymptote at $$ x=-1 $$
- Oblique asymptote at $$ y=-x-2 $$
No horizontal asymptotes, vertical asymptote at $$ x=-1 $$, oblique asymptote at $$ y=-x-2 $$

Graph all asymptotes of the rational function.

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