# How do you sketch the curve #f(x)=x+sqrt(1-x)# ?

##### 1 Answer

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

and finally:

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

Choosing

This is to say that

Finally, the graph should look like this: