5-1 Polynomial Functions

Objectives

To classify polynomials

To graph polynomial functions and describe end behavior

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The sequence of numbers in the first column above are values of a particular polynomial function. For such a sequence, you can use patterns of 1st differences, 2nd differences, 3rd differences, and so on, to learn more about the polynomial function.

Essential Understanding A polynomial function has distinguishing “behaviors.” You can look at its algebraic form and know something about its graph. You can look at its graph and know something about its algebraic form.

A monomial is a real number, a variable, or a product of a real number and one or more variables with whole-number exponents. The degree of a monomial in one variable is the exponent of the variable. A polynomial is a monomial or a sum of monomials. The degree of a polynomial in one variable is the greatest degree among its monomial terms.

A polynomial with the variable x defines a polynomial function of x. The degree of the polynomial function is the same as the degree of the polynomial.

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