

Course 3, Unit 5  Polynomial and Rational Functions
Overview
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) = a_{n}x^{n} + a_{n − 1}x^{n − 1} + … + a_{2}x^{2} + a_{1}x + a_{0}

Rational functions of the form: g(x) = p(x)/q(x) = (a_{m}x^{m} + a_{m − 1}x^{m − 1} + … + a_{2}x^{2} + a_{1}x + a_{0})/(b_{n}x^{n} + b_{n − 1}x^{n − 1} + … + b_{2}x^{2} + b_{1}x + b_{0})

Vertex form of a quadratic function: f(x) = a(x − h)^{2} + k (See
pages 348352.)

Completing the square: (See pages 350352.)

Arithmetic of polynomial and rational expressions: (See
pages 319345 and 364388.)

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