THE ASYMPTOTIC VALUES OF A POLYNOMIAL FUNCTION ON THE REAL PLANE

Let a polynomial function f of two real variables be given. We prove t he existence of a finite number of unbounded regions of the real plane along which the tangent planes to the graph of f tend to horizontal p osition, when moving away from the origin. The real limit values of th is function on these regions are called asymptotic values. We also def ine the real critical values at infinity off and prove the theorem of local trivial fibration at infinity, away from these values.