5-3: Polynomial Functions

A polynomial function is a function of the form f (x) = a n x n + a n – 1 x n – 1 +· · ·+ a 1 x + a 0 Where a n  0 and the exponents are all whole numbers. A polynomial function is in standard form if its terms are written in descending order of exponents from left to right. For this polynomial function, a n is the leading coefficient, a 0 is the constant term, and n is the degree. a n  0 anan anan leading coefficient a 0a 0 a0a0 constant term n n degree descending order of exponents from left to right. n n – 1

DegreeTypeStandard Form You are already familiar with some types of polynomial functions. Here is a summary of common types of polynomial functions. 4Quartic f (x) = a 4 x 4 + a 3 x 3 + a 2 x 2 + a 1 x + a 0 0Constantf (x) = a 0 3Cubic f (x) = a 3 x 3 + a 2 x 2 + a 1 x + a 0 2Quadratic f (x) = a 2 x 2 + a 1 x + a 0 1Linearf (x) = a 1 x + a 0

One Variable Polynomial, Degrees and Leading Coefficients

Function Values of Variables

Zeros of Even- and Odd-Degree Functions Odd-Degree functions will always have an odd number of real zeros. Even-Degree functions will always have an even number of real zeros or no real zeros at all.

For the graph, Describe the end behavior, Determine if it’s Odd or Even-degree State the number of zeros.

Assignment Pg #17-39 odd