Polynomials - Introduction, Zeros and Their Multiplicities, End-Behavior, Graphing

Polynomials - Part 1

Designer curves used in automotive and roller coaster rides, functions modeling human physiology, models analyzing a business's performance, for example, have polynomials in common. A polynomial is a linear combination of basic power functions xk. Linear and quadratic functions are special polynomials. In this module you will learn about graphing a polynomial by studying its end-behavior and the multiplicities of its zeros.

Review:

  • Linear and quadratic equations and be able to solve them with ease
  • Factoring binomials and quadratic expressions

Learning Objectives: By the end of this module you should be able to

  • determine domain and range of a polynomial
  • identify the degree, leading term, leading coefficient and constant term of a polynomial
  • use the graphs of basic power functions to anticipate the graph of a polynomial
  • use factoring to find the zeros or x-intercepts of a polynomial
  • find y-intercept
  • study the end-behavior of a polynomial
  • understand and apply Intermediate Value Theorem to a polynomial
  • make a sign chart for a polynomial using its zeros and their multiplicities
  • sketch the graph of a polynomial without a graphing calculator
  • identify intervals of increase and decrease for a polynomial
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