Find all the asymptote of $1-x+\sqrt{2+2x+x^2}$ I find 
$$\lim_{x\rightarrow\infty}1-x+\sqrt{2+2x+x^2}=2,$$ but i'am stuck when $x\rightarrow-\infty$ how to find that $y=-2x$ is an oblique asymptote. Any idea? 

You can use the asymptotic expressions for $f(x)$:
$$f(x) \sim 2 +\frac{1}{2x} + O(x^{-2}) \quad \text{as} \quad x \rightarrow \infty$$
$$f(x) \sim -2x -\frac{1}{2x} + O(x^{-2}) \quad \text{as}\quad  x \rightarrow - \infty$$
and read-off the asymptotes $y=2$ and $y=-2x$.
PS: To get the second expression consider 
$$g(x)=f(-x) = 1+x+\sqrt{2-2x+x^2} \sim 2x + \frac{1}{2x}+O(x^{-2})$$
for $x \rightarrow \infty$.
