y2=6/x is the same as x=6/y2, which can be written f(y)=6/y2. Therefore f(x)=6/x2, whose parent is p(x)=1/x2, known as the reciprocal squared function. It could also be considered to belong to the exponential function family, because 1/x2=x-2 may be considered to belong to exp(x)=xn.
Effectively, graphically y2=6/x is x2=6/y (y=f(x)=6/x2) rotated clockwise 90° so that (x,y) becomes (y,-x). For example, the point (1,6) on x2=6/y becomes (6,-1) on y2=6/x; and (-1,6) on x2=6/y becomes (6,1) on y2=6/x; and vice versa.