How do you sketch the curve #f(x)=x+sqrt(1-x)# ?
First I would check the square root. What I want to avoid is to have a negative argument. This is because I cannot find a Real Number that is solution of a negative square root.
So I say that:
Let us see what this condition tells us about the "permitted" values of
This means that I can choose only values in the interval between
I then try to use values of
I then test what is going to happen when
This is to say that
Finally, the graph should look like this: