In the follow diagram, z=x*y, p=2*y, p has no relation with x.
But according to the set theory definition of function, I can construct the ternary relation $\{(x,y,p)|p=2*y,x\in[0,1],y\in[0,1]\}$ that can satisfy the requirements of a function. So there is a function between p and x,y: p=f(x,y). So is there a function relation between p and x,y or not?