Polynomial Functions and Modeling

Polynomial Function
Continuous - No holes or breaks. No sharp corners.
Leading Coefficient - First nonzero coefficient.
Leading Term - The first term, when in descending order.
Degree - highest degree of any of the terms.
Leading-Term Test - Tells end behavior of graph.
Zeros - x-value of the x-intercept.
Multiplicity - odd, then crosses x-axis. Even, then tangent at x-axis.

Algebra Example:
*Find the degree, leading term, and leading coefficient.
*Find the zeros of the polynomial function and state the multiplicity of each.
f(x) = (x+3)^2 (x-1)
f(x) = (x^2 - 9)^3
f(x) = 2x^3 - x^2 - 8x + 4

Application Example: Sales data for vinyl records over the years 2001 to 2014 is modeled by the quartic function f(x) where x is the number of years after 2001 and f(x) is the number of albums in millions. Find the number of vinyl albums sold in 2008.