ok. My teacher wants our class to graph (*being sq root) f(x)=*x . And we have to have some negatives. which means there will be imaginary numbers. so how do you graph those?
Are you sure you have understood the directions correctly? Just graphing a complex number, a+ ib, requires two dimensions. Graphing a function, y= f(x), where both x and y are complex numbers, requires two dimensions for both variables- you would need a four dimensional graph! If you take x to be real only, you would need a three dimensional graph which is at least possible. If you take the x-axis to be the real x variable, you can let the y-axis be the real part of f(x), and the z axis be the imaginary part.
Now for $\displaystyle y= \sqrt{x}$, with x real, y is real for $\displaystyle x\ge 0$, pure imaginary for x< 0. So for $\displaystyle x\ge 0$ you will have just the graph of $\displaystyle y= \sqrt{x}$ in the xy-plane. For x< 0, [tex]\sqrt{x}= \sqrt{-1|x|}= i\sqrt{|x|}. The graph will be turned 90 degrees at x= 0 and will be the graph of $\displaystyle z= \sqrt{|x|}$ in the xz- plane.