reply to this like a discusion post Functions are relations but not all relations are functions. A function is special relation when every input has one output. Even when an output has more than one value the relation is not a function. The quadratic function is a parabola it gives a unique vertex which is either has a max or min point of a graph. The Fundamental Algebra Theorem states every single variable with complex coefficients has at least one complex root. It assures that every polynomial equation has a solution. Existence Theorem provides conditions under a solution to a different equation is guaranteed to exist and be unique. Polynomial functions are defined for all real numbers.Because polynomial functions have no undefined points they have no vertical asymptotes and no horizontal asymptotes. Rational function has vertical boundaries but never touch