I have some questions , first : in college Algebra course I didn't used to prove that y is a function of x for example must I prove that polynomials are function (I did by mathematical induction but I see that this is useless) , now I don't know why I am thinking different I want to prove somethings I am not used to even think to prove., is that a good thing to think by this way .??? I think I am stupid in someway than I was during reading the college algebra text-book . second : how must I understand if and only if part in fundamental graphing principle of equations and functions. The Fundamental Graphing Principle The graph of an equation is the set of points which satisfy the equation. That is, a point (x,y) is on the graph of an equation if and only if x and y satisfy the equation. I used to not to concentrate at these points , but now after I began to read in other branches of mathematics , I began to think by another ways I don't know why . Here I understand that that if (x,y) is on the graph then x and y will satisfy the equation until now we are assuming that it is possible that there exists some x and y which satisfy the eq. but (x,y) is not on the graph . the second implication is saying that if x and y satisfying the equation then (x,y) lies on the graph , which also says that it is possible to have (x,y) on the graph but x and y doesn't satisfy the equation here the first implication says that x and y satisfy the equation so all x and y which satisfy the equation corresponds to all (x,y) on the graph. so in this way I understand why the equation of circle for example describe only the set of all points on the circle and so with ellipse , hyperbola , parabola , lines , ...... I think this way I think is a stupid so please help me. thanks .