The domain of any polynomial function is the set of real numbers. Zero is a real number, therefore for any polynomial function , is defined and exists. The -intercept of a polynomial function is the point .
-intercepts of the graph of a polynomial function are points of the form where is a real number zero of the polynomial function. Since complex roots always occur in conjugate pairs, that is to say if is a root, then must also be a root, and the number of zeros of a polynomial function is equal to the degree of the function (Fundamental Theorem of Algebra) it is possible to have a polynomial function of even degree with no real number zeros, and therefore no -intercepts. Polynomial functions of odd degree are guaranteed to have at least one real zero and therefore at least one -intercept.
John
My calculator said it, I believe it, that settles it
