Course 4 Unit 6 - Polynomial and Rational Functions
1st Edition

Students intending to pursue college majors in the mathematical, physical, and biological sciences and engineering should study this unit. Students intending to pursue programs in social, management, and some of the health sciences or humanities, may omit or reduce the amount of time spent studying this unit and instead study other units from the text. (See the descriptions of Course 4 Units.)

Unit Overview

Polynomial and Rational Functions extends student ability to use polynomial and rational functions to represent and solve problems from real-world situations while focusing on symbolic and graphical patterns.

Unit Objectives
  • To describe and use the concepts of zeroes and end behavior of functions in mathematical, scientific, and everyday situations
  • To use polynomial and rational functions to model data patterns
  • To describe and illustrate the relationship between the graph of a polynomial or rational function and its symbolic representation
  • To develop facility with manipulating and reasoning about polynomial and rational symbolic representations
  • To determine all complex number roots of polynomials and to add, subtract, multiply, and divide complex numbers

Sample Overview

There are two different samples from Polynomial and Rational Functions. The first sample is the first two investigations of Lesson 2 of the unit. In these investigations, students examine nested, standard, and factored forms of polynomials, the effects of the symbolic form on computational efficiency, and the information provided by each form. Students develop skill in factoring polynomials. This work builds the necessary knowledge to introduce complex numbers in the third investigation.

The second sample material is the "Looking Back" lesson for this unit. This lesson is intended to provide students with tasks that will encourage them to look back at the unit as a whole. Students review, synthesize, and apply the knowledge gained during the study of the unit.

Instructional Design

Throughout the curriculum, interesting problem contexts serve as the foundation for instruction. As lessons unfold around these problem situations, classroom instruction tends to follow a common pattern as elaborated under Instructional Design.

View Sample Material

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How the Algebra and Functions Strand Continues

The next unit in Course 4, Functions and Symbolic Reasoning, extends student ability to manipulate symbolic representations of exponential, common and natural logarithmic, and trigonometric functions and to solve exponential, logarithmic, and trigonometric equations. Trigonometric identities are developed and proved or disproved. Geometric representations of complex numbers are used to reason about and to find roots of complex numbers. Algebraic representations of surfaces and conic sections are introduced in Unit 8, Space Geometry.

A unit that develops understanding and skill in the use of standard spreadsheet operations while reviewing and extending many of the basic algebra topics from Courses 1-3 is included for students intending to pursue college programs in social, management, and some of the health sciences or humanities.

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