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College Algebra with Intermediate Algebra: A Blended Course, 1st edition

  • Judith A. Beecher, 
  • Judith A. Penna, 
  • Barbara L. Johnson, 
  • Marvin L. Bittinger

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Overview

Precalculus: A Right-Triangle Approach helps you prepare, visualize and ultimately succeed in your precalculus course. You'll learn to “see the math” through a focus on visualization and early introduction to functions, which allows for the use of graphs to provide a visual aspect to solving equations and inequalities. Specific features help you visualize and make connections between concepts. The 5th Edition expands and enhances instruction  on review topics needed for corequisite courses or simply for students who start the course needing additional preparation. Ongoing review features throughout reinforce the concepts and help build understanding.

Published by Pearson (August 15th 2021) - Copyright © 2022

ISBN-13: 9780137417445

Subject: Precalculus, College Algebra & Trigonometry

Category: College Algebra

Overview

R. Review of Basic Algebra

Part 1 Operations

  • R.1 The Set of Real Numbers
  • R.2 Operations with Real Numbers
  • R.3 Exponential Notation and Order of Operations

Part 2 Manipulations

  • R.4 Introduction to Algebraic Expressions
  • R.5 Equivalent Algebraic Expressions
  • R.6 Simplifying Algebraic Expressions
  • R.7 Properties of Exponents and Scientific Notation

1. Solving Linear Equations and Inequalities

  • 1.1 Solving Equations
  • 1.2 Formulas and Applications
  • 1.3 Applications and Problem Solving
  • 1.4 Sets, Inequalities, and Interval Notation
  • 1.5 Intersections, Unions, and Compound Inequalities
  • 1.6 Absolute-Value Equations and Inequalities

2. Graphs, Functions, and Applications

  • 2.1 Graphs of Equations
  • 2.2 Functions and Graphs
  • 2.3 Finding Domain and Range
  • 2.4 The Algebra of Functions
  • 2.5 Linear Functions: Graphs and Slope
  • 2.6 More on Graphing Linear Equations
  • 2.7 Finding Equations of Lines; Applications

3. Systems of Equations

  • 3.1 Systems of Equations in Two Variables
  • 3.2 Solving by Substitution
  • 3.3 Solving by Elimination
  • 3.4 Solving Applied Problems: Two Equations
  • 3.5 Systems of Equations in Three Variables
  • 3.6 Solving Applied Problems: Three Equations
  • 3.7 Systems of Inequalities and Linear Programming

4. Polynomials and Polynomial Functions

  • 4.1 Introduction to Polynomials and Polynomial Functions
  • 4.2 Multiplication of Polynomials
  • 4.3 Introduction to Factoring
  • 4.4 Factoring Trinomials: x2 + bx + c
  • 4.5 Factoring Trinomials: ax2 + bx + c, a _1
  • 4.6 Special Factoring
  • 4.7 Factoring: A General Strategy
  • 4.8 Applications of Polynomial Equations and Functions

5. Rational Expressions, Equations, and Functions

  • 5.1 Rational Expressions and Functions: Multiplying, Dividing, and Simplifying
  • 5.2 LCMs, LCDs, Addition, and Subtraction
  • 5.3 Division of Polynomials
  • 5.4 Complex Rational Expressions
  • 5.5 Solving Rational Equations
  • 5.6 Applications and Proportions
  • 5.7 Formulas and Applications
  • 5.8 Variation and Applications

6. Radical Expressions, Equations, and Functions

  • 6.1 Radical Expressions and Functions
  • 6.2 Rational Numbers as Exponents
  • 6.3 Simplifying Radical Expressions
  • 6.4 Addition, Subtraction, and More Multiplication
  • 6.5 More on Division of Radical Expressions
  • 6.6 Solving Radical Equations
  • 6.7 Applications Involving Powers and Roots
  • 6.8 Increasing, Decreasing, and Piecewise Functions; Applications

7. Quadratic Functions and Equations

  • 7.1 Symmetry
  • 7.2 Transformations
  • 7.3 The Complex Numbers
  • 7.4 Quadratic Equations, Functions, Zeros, and Models
  • 7.5 Analyzing Graphs of Quadratic Functions

8. Polynomial Functions and Rational Functions

  • 8.1 Polynomial Functions and Models
  • 8.2 Graphing Polynomials Functions
  • 8.3 Polynomial Division; The Remainder Theorem and the Factor Theorem
  • 8.4 Theorems about Zeros of Polynomial Functions
  • 8.5 Rational Functions
  • 8.6 Polynomial Inequalities and Rational Inequalities

9. Exponential Functions and Logarithmic Functions

  • 9.1 The Composition of Functions
  • 9.2 Inverse Functions
  • 9.3 Exponential Functions and Graphs
  • 9.4 Logarithmic Functions and Graphs
  • 9.5 Properties of Logarithmic Functions
  • 9.6 Solving Exponential Equations and Logarithmic Equations
  • 9.7 Applications and Models: Growth and Decay; Compound Interest

10 Matrices

  • 10.1 Matrices and Systems of Equations
  • 10.2 Matrix Operations
  • 10.3 Inverses of Matrices
  • 10.4 Determinants and Cramer's Rule

11. Conic Sections

  • 11.1 The Parabola
  • 11.2 The Circle and the Ellipse
  • 11.3 The Hyperbola
  • 11.4 Nonlinear Systems of Equations and Inequalities

12. Sequences, Series, and Combinatorics

  • 12.1 Sequences and Series
  • 12.2 Arithmetic Sequences and Series
  • 12.3 Geometric Sequences and Series
  • 12.4 Mathematical Induction
  • 12.5 Combinatorics: Permutations
  • 12.6 Combinatorics: Combinations
  • 12.7 The Binomial Theorem
  • 12.8 Probability

Appendix

  • A.1 Partial Fractions

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