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    Rational functions, polynomials

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    Explain what makes a function a polynomial. Give an example of a function that is a polynomial and a function that is not a polynomial.

    Given the polynomial f(x) = 2x3 + 5x2 - x - 5, answer the following questions:

    Graph the polynomial. What is the degree of the polynomial?
    Explain the constant in the polynomial and how it relates to the graph.
    Define the x-intercepts of the polynomial.
    Explain the relative maximum and relative minimum of the polynomial in the interval [-3,2]. Is there a different between the relative maximum and minimum and the absolute maximum and minimum?
    Part II:

    What is a rational function? Give an example. For your example, answer or perform the following:

    Graph the rational function.
    Give the domain and range of the rational function.
    Find the vertical and horizontal asymptotes of the rational function.

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    Solution Preview

    A function f(x) is a polynomial if it has the form

    a_0 + a_1 x + a_2 x^2 + ... + a_n x^n

    where a_0, a_1, a_2, .., a_n are numbers.

    Given the polynomial f(x) = 2x^3 + 5x^2 - x - 5

    (a) visit


    and enter 2x^3 + 5x^2 - x - 5

    in the box

    (b) the polynomial has degree 3, because 3 is the largest exponent on x

    (c) the number at the ...

    Solution Summary

    The provides examples of relating functions and polynomials and examples of working with a rational function.