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Dynamic College Algebra : Chapter 3 : Introduction to Functions (Student/Teacher)

Marsha Davis, Gary Froelich and Gary Simundza

 Mathematics Topic:Algebra Application Areas:College Algebra Prerequisites:Adobe Acrobat Adobe AIR Software Volume Weight Image Processing Excel

| ©2014 by COMAP, Inc. | DynaMAP | 108 pages |

Dynamic College Algebra

Dynamic College Algebra uses a modeling approach built around applications from technical fields such as semiconductor manufacturing and biotechnology. Each chapter begins with an engaging contextual problem that students explore in class or on their own via an Adobe Air simulation. Reflecting the realities of modern technical careers, Dynamic College Algebra integrates data analysis and spreadsheet technology throughout.

Chapter 1: Measurement/Data Analysis
Chapter 2: Variation
Chapter 3: Introduction to Functions
Chapter 4: Linear Relationships
Chapter 5: Systems of Equations
Chapter 6: Exponential and Logarithmic Functions
Chapter 7: Polynomial Functions
Chapter 8: Trigonometric Functions

CHAPTER 3: Introduction to Functions

This chapter begins with the definition and properties of functions, which were introduced informally in Chapter 2. A detailed examination of linear functions is followed by a look at a basic catalog of simple function types, along with vertical transformations—shifts and stretches—of these functions. (Horizontal transformations are delayed until the study of exponential and other function types.) A section on creating other functions includes algebraic combinations, piecewise-defined functions, and composite and inverse functions. The chapter concludes with an introduction to matrices, with matrix addition and scalar multiplication paving the way for a return to linear functions in the guise of operations on matrices. The introductory activity allows students to examine essential characteristics of linear functions through a simulated data collection experiment in a chemical/biological context.

Career Feature: Chemical Technicians
Introductory Activity: Laboratory Automation
Section 3.1: Linear Models
Section 3.2: Function Toolkit
Section 3.3: Building Other Functions
Section 3.4: Matrices
Chapter 3: Review
Chapter 3: Instructor’s Notes