The Rule of Four—A Balanced Approach

A principal feature of this text is the balance among the algebraic, numerical, graphical, and verbal methods of representing problems: the rule of four. For instance, we obtain solutions algebraically when that is the most appropriate technique to use, and we obtain solutions graphically or numerically when algebra is difficult to use. We urge students to solve problems by one method and then to support or confirm their solutions by using another method. We believe that students must learn the value of each of these methods or representations and must learn to choose the one most appropriate for solving the particular problem under consideration. This approach reinforces the idea that to understand a problem fully, students need to understand it algebraically as well as graphically and numerically.

 

Twelve Basic Functions

Twelve basic functions are emphasized throughout the text as a major theme and focus.

These functions are

  • The Identity Function
  • The Squaring Function
  • The Cubing Function
  • The Reciprocal Function
  • The Square Root Function
  • The Exponential Function
  • The Natural Logarithm Function
  • The Sine Function
  • The Cosine Function
  • The Absolute Value Function
  • The Greatest Integer Function
  • The Logistic Function
 

One of the most distinctive features of this text is that it introduces students to the full vocabulary of functions early in the course. Students meet the twelve basic functions graphically in Chapter 1 and are able to compare and contrast them as they learn about concepts like domain, range, symmetry, continuity, end behavior, asymptotes, extrema, and even periodicity—concepts that are difficult to appreciate when the only examples a teacher can refer to are polynomials. With this text, students are able to characterize functions by their behavior within the first month of classes. Once students have a comfortable understanding of functions in general, the rest of the course consists of studying the various types of functions in greater depth, particularly with respect to their algebraic properties and modeling applications.

View a sample chapter

 

mathxl tablet

mathxl being shown on a tablet displaying The Cosine Function

 
 

Common Core Success

Align your course for Common Core success with CCSM identified in the Teacher’s edition, and Common Core resources.

Common Core: Student Practice and Review Guide (Download Only)

This resource provides complete daily support for every lesson. The following resources are included: Problem Solving, Practice, and Standardized Test Prep.

Common Core: Implementation Guide (Download Only)

All the support a teacher needs to make the transition to a Common Core curriculum.

Includes:

  • Overview of the Common Core State Standards
  • Standards for Mathematical Practice Observational Protocol
  • Common Core Correlations
  • Common Core assessment resources
 
 

Looking Ahead to Calculus

The Looking Ahead to Calculus icon is found throughout the text next to many examples and topics to point out concepts that students will encounter again in calculus. Ideas that foreshadow calculus, such as limits, maximum and minimum, asymptotes, and continuity, are highlighted. Some calculus notation and language are introduced in the early chapters and used throughout the text to establish familiarity.

convergence of geometric series displayed on a laptop screen

 
 

Graphs of sine and cosine: sinusoids on a tablet

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