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Course 3, Unit 5 - Polynomial and Rational Functions

The lessons of this unit extend students' knowledge and skill in work with algebraic functions and expressions in three ways. First they learn how to use polynomial functions and expressions to model data and graph patterns that are more complex than the familiar linear and quadratic patterns. They revisit quadratic functions and expressions in more depth and also study the properties and applications of rational functions.

New Key Ideas from Course 3, Unit 5

  • Polynomial functions of the form: f(x) = anxn + an − 1xn − 1 + … + a2x2 + a1x + a0

  • Rational functions of the form: g(x) = p(x)/q(x) = (amxm + am − 1xm − 1 + … + a2x2 + a1x + a0)/(bnxn + bn − 1xn − 1 + … + b2x2 + b1x + b0)

  • Vertex form of a quadratic function: f(x) = a(x − h)2 + k (See pages 348-352.)

  • Completing the square: (See pages 350-352.)

  • Arithmetic of polynomial and rational expressions: (See pages 319-345 and 364-388.)

  • The shapes of polynomial and rational function graphs, especially the number of local maximum and minimum points, the number of zeroes, and asymptotes

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