help with graphs

If you were to graph this equation, you might notice that the line  y = x  is a line of symmetry.

 

Combining the two equations  y  =  3/x  and  y  =  x,  we get:  x  =  3/x   --->   x²  =  3

 

So:  either  x = sqrt(3)  or  x = - sqrt(3).

Therefore, the points  ( sqrt(3), sqrt(3) )  and  ( - sqrt(3), - sqrt(3) )  are closest to the origin.