let the real function 
f(x)=(2-sqrt(x+1))/(x-3)

Sage has no difficulty finding the limits at x=-1 and x=3. However, I am 
unable to get plot to detect these singularities :
plot((2-sqrt(x+1))/(x-3),[x,-1,6],figsize=4,detect_poles=True)
gives me a continuous curve between -1 and 6 with no marking whatsoever at 
-1 and 6.

Can someone suggest a more-or-less automated way to get
1) a curve segment between abcissae -1 and 3 with some marker excluding the 
point at abcissa 3?
2) a curve segment between 3 an 6 with a marker at abcissa 3

I want to emphasize that the function is not defined at 3 and (for real 
values), not defined for x<0

Bonus points (just kidding :-) for the representation of the complex 
(multivalued) function
f(z)=(2-sqrt(z+1))/(z-3)
where sqrt(t) is a root r of r^2=t....

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