“Why so serious?”

3.2 Polynomial Functions and Models

Polynomial Functions A polynomial function is a function of the form where are real numbers and n is a nonnegative integer. The domain consists of all real numbers. The degree of the function is the largest power of x.

Polynomial Functions Determine which of the following are polynomial functions. For those that are, state the degree.

Polynomial Functions Determine which of the following are polynomial functions. For those that are, state the degree.

Power Functions A power function is of the form If n is odd… If n is even… The end behavior of a polynomial function can be related to the power function of the same degree.

Zeroes of Polynomials Find the degree, the end behavior, zeroes, and multiplicity each. If a zero has an odd multiplicity, the function crosses at the zero. If a zero has an even multiplicity, the function touches at the zero.

Zeroes of Polynomials Find the degree, the end behavior, zeroes, and multiplicity each.

Zeroes of Polynomials Find the polynomial whose zeroes are given. 1) Zeroes: 0, -4, 2 (all multiplicity 1) 2) Zeroes: -3, multiplicity 2; 5, multiplicity 1 3) Zeroes: 0, multiplicity 2; 6, multiplicity 3; -2, multiplicity 4

Zeroes of Polynomials Given the polynomial a) Find the degree and end behavior of the polynomial. b) Find the x- and y-intercepts of the graph. c) Determine whether the graph crosses or touches at each x-intercept. d) Graph f using a graphing utility. e) Determine any local maxima or minima.

Zeroes of Polynomials Given the polynomial f) Graph by hand. g) Determine the domain and range. h) Determine intervals of increasing and decreasing Degree = 6 y-intercept: (0,0) x-intercepts: (0,0) crosses, (4,0) touches; (-3,0) crosses Local minima: (-2.321,-402.176) and (4,0) Local maxima: (2.451,224.636)

3.2 Polynomial Functions and Models Homework #28: p.183 #39-43 odd, 47-79 EOO