Can a polynomial form any one to one and continuous graph?

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Hello I was wondering if it was possible to right any one to one and continuous graph as a polynomial with real co-efficient s. If this is not so why? It seems like it would possible to just write a piecewise function that would make it impossible for it to be represented by a polynomial but I am curious on to why that is mathematically. Or in other words what characteristics do polynomials contain that allow or don't allow them to represent such a graph.