How can "$y = \sqrt{-x}$ " be sketched on the x-y plane? I was reading James Stewart's book Calculus 5th edition (international student edition) and I came across an example that seemed wrong to me. In chapter 1 section 3, he talks about transformations of functions (i.e., vertical and horizontal shifts, vertical and horizontal stretching and reflecting). 
In example 1, the function $y=\sqrt{x}$ is provided and it is asked to graph its transformation $y=\sqrt{-x}$. The solution is provided as below.
My question is, shouldn't such a function be in the realm of imaginary/complex numbers? If so, then how is it graphed on the x-y plane?

 A: Do you see "$-x$" as a negative number? That's understandable, given the negative sign. But $-x$ can be positive, when $x$ itself is negative. And then $\sqrt{-x}$ is something that is real, like $\sqrt{-(-4)}=2$. And that is why the graph of $y=\sqrt{-x}$ is only appearing on the left side of the coordinate plain, where $x$ is negative.
A: Not if x < 0, user. Notice carefully that the domain of f(x) lies to the left of the positive y axis, meaning that x < 0. Since x< 0, -x> 0 and the square root is perfectly valid. In fact,you can think of f as taking the square root of the absolute value of negative reals. Now if $x \geq 0$, you'd be completely correct. 
Of course, the important question in that case is-what does it mean to graph a complex valued function? Turns out this isn't as easy to answer as it looks at first: Since f: C $\rightarrow$ C is a function of 2 variables i.e. z = x+ iy for every z$\in$ C , the graph of such a map lies in a four dimensional space. So how to do you graph such mappings? 
An interesting question for your first week of complex variables.............    
