For f(x) = x + e^-x
Find, if they exist, the equations of any asymptotes.
How do I do this？Thanks！
First check for vertical asymptotes. Are there any values $x=a$ such that $\displaystyle \lim_{x\to a} f(x)$ does not exist because it approaches positive or negative infinity?
Next, check for horizontal asymptotes. These take the form:
$y=\lim_{x\to \infty} f(x)$
$y=\lim_{x\to -\infty} f(x)$
Finally, you can try
$\lim_{x\to \infty} (f(x)-mx-b) = 0$
$\lim_{x\to -\infty} (f(x)-mx-b) = 0$
If you find valid $m,b$ but you cannot find any value $a$ such that $f(a)=ma+b$ then $y=mx+b$ is an asymptote.
Trying all of these, $y=x$ is the only asymptote.