1. 5-3: Polynomial Functions

2. 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

3. 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

4. One Variable Polynomial, Degrees and Leading Coefficients

5. Function Values of Variables

9. 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.

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

11. Assignment Pg. 326-327 #17-39 odd