You might have to be more specific about the function you're trying to find a line of symmetry for. For example, a parabola has a line of symmetry passing through its vertex and perpendicular to the tangent line to the curve at that point.
As for calculating a function's range and domain, the domain of a polynomial with real coefficients is all real numbers. If the function is of the form where both f(x) and g(x) are polynomials, then the domain is all real numbers except the roots of g(x) (values of x that make g(x) = 0). The range of a function is equal to all real numbers that can be output by the function. Polynomials with odd degree have a range of all real numbers. Polynomials with positive even degree have a range equal to either or , depending on whether the coefficient of , where n is the degree of the polynomial, is positive or negative.