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Thread: problem with polynomial functions (charts)

  1. #1
    Junior Member
    Sep 2008

    problem with polynomial functions (charts)

    i have problems with finding the line of symmetry and the point of symmetry in a polynomial function , and i also have problem on how to find the range and domain for a even or odd polynomial function? can someone explain these concept to me, cause i'm having alot of trouble! thanks
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  2. #2
    MHF Contributor
    Apr 2008
    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 $\displaystyle \frac{f(x)}{g(x)}$ 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 $\displaystyle [inf (f(x)), \infty)$ or $\displaystyle (-\infty, sup (f(x))]$, depending on whether the coefficient of $\displaystyle x^n$, where n is the degree of the polynomial, is positive or negative.
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