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

1 Answer
Gió
Dec 26, 2014

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:
#1-x# must be #>0#
Let us see what this condition tells us about the "permitted" values of #x# for our function:
#1-x>0#
#-x> -1#
and finally:
#x<1#
This means that I can choose only values in the interval between #1# and #-oo#.

I then try to use values of #x# starting from 1 and going towards -1 to see a possible tendency of my curve.

I then test what is going to happen when #x->-oo#.

Choosing #x# very big negatively I have in my function a situation like this:
#f(-1,000,000)=-1,000,000+sqrt(1,000,001)=(-1,000,000+1000)=-999000#
This is to say that #-oo# will always win and even if in your function you have a positive part (#sqrt(1-x#) it does not interfere too much with the #-oo# tendency of the complete function.

Finally, the graph should look like this:
enter image source here

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