The table of contents below shows the review topics (bulleted text) that are integrated into the MyLabTM Math course. The Integrated Review includes worksheets, videos, and other materials designed to help students master these important topics.

Just-In-Time Review

1. Graphs, Functions, and Models

1.1 Introduction to Graphing

1.2 Functions and Graphs

1.3 Linear Functions, Slope, and Applications

1.4 Equations of Lines and Modeling

1.5 Linear Equations, Functions, Zeros, and Applications

1.6 Solving Linear Inequalities

Integrated Review Topics:

• Graphing Linear Functions
• Operations on the Real Numbers
• Order of operations
• Factoring trinomials: ax² + bx + c
• Factoring trinomial squares and differences of squares
• The principle of zero products
• Interval notation
• Solving linear equations
• Solving linear inequalities

2. More on Functions

2.1 Increasing, Decreasing, and Piecewise Functions; Applications

2.2 The Algebra of Functions

2.3 The Composition of Functions

2.4 Symmetry

2.5 Transformations

2.6 Variation and Applications

Integrated Review Topics:

• Interval Notation
• The Pythagorean Theorem
• Simplifying Rational expressions
• Addition and subtraction of polynomials
• Simplifying complex rational expressions
  

3. Quadratic Functions and Equations; Inequalities

3.1 The Complex Numbers

3.2 Quadratic Equations, Functions, Zeros, and Models

3.3 Analyzing Graphs of Quadratic Functions

3.4 Solving Rational Equations and Radical Equations

3.5 Solving Equations and Inequalities with Absolute Value

Integrated Review Topics:

• Multiplying radical expressions
• Multiplying binomials
• Simplifying radical expressions
• Completing the square
• Factoring trinomials: ax² + bx + c
• Factoring trinomial squares and differences of squares
• The principal of zero products
• Finding the LCM of algebraic expressions
• The principle of powers
  

4. Polynomial Functions and Rational Functions

4.1 Polynomial Functions and Models

4.2 Graphing Polynomial Functions

4.3 Polynomial Division; The Remainder Theorem and the Factor Theorem

4.4 Theorems about Zeros of Polynomial Functions

4.5 Rational Functions

4.6 Polynomial Inequalities and Rational Inequalities

Integrated Review Topics:

• Introduction to polynomials
• Factoring by grouping
• Operations on the Real Numbers
• Interval Notation

5. Exponential Functions and Logarithmic Functions

5.1 Inverse Functions

5.2 Exponential Functions and Graphs

5.3 Logarithmic Functions and Graphs

5.4 Properties of Logarithmic Functions

5.5 Solving Exponential Equations and Logarithmic Equations

5.6 Applications and Models: Growth and Decay; Compound Interest

Integrated Review Topics:

• Integers as exponents
• Finding logarithms without a calculator
  

6. The Trigonometric Functions

6.1 Trigonometric Functions of Acute Angles

6.2 Applications of Right Triangles

6.3 Trigonometric Functions of Any Angle

6.4 Radians, Arc Length, and Angular Speed

6.5 Circular Functions: Graphs and Properties

6.6 Graphs of Transformed Sine and Cosine Functions

Integrated Review Topics:

• The Pythagorean Theorem
• Rationalizing Denominators
• Unit conversion using multiplying by 1
• Determining the domain and range of a function
  

7. Trigonometric Identities, Inverse Functions, and Equations

7.1 Identities: Pythagorean and Sum and Difference

7.2 Identities: Cofunction, Double-Angle, and Half-Angle

7.3 Proving Trigonometric Identities

7.4 Inverses of the Trigonometric Functions

7.5 Solving Trigonometric Equations

Integrated Review Topics:

• Simplifying rational expressions
• Simplifying complex rational expressions
• Adding, subtracting, multiplying and dividing fractions
• Determining the domain and range of a function
• Factoring trinomials: ax² + bx + c
• Factoring trinomial squares and differences of squares
  

8. Applications of Trigonometry

8.1 The Law of Sines

8.2 The Law of Cosines

8.3 Complex Numbers: Trigonometric Notation

8.4 Polar Coordinates and Graphs

8.5 Vectors and Applications

8.6 Vector Operations

Integrated Review Topic:

• Solve proportions
  

9. Systems of Equations and Matrices

9.1 Systems of Equations in Two Variables

9.2 Systems of Equations in Three Variables

9.3 Matrices and Systems of Equations

9.4 Matrix Operations

9.5 Inverses of Matrices

9.6 Determinants and Cramer’s Rule

9.7 Systems of Inequalities and Linear Programming

9.8 Partial Fractions

Integrated Review Topics:

• Graphing Linear Functions
• Operations on the Real Numbers
  

10. Conic Sections

10.1 The Parabola

10.2 The Circle and the Ellipse

10.3 The Hyperbola

10.4 Nonlinear Systems of Equations and Inequalities

10.5 Rotation of Axes

10.6 Polar Equations of Conics

10.7 Parametric Equations

Integrated Review Topic:

• Completing the square
  

11. Sequences, Series, and Combinatorics

11.1 Sequences and Series

11.2 Arithmetic Sequences and Series

11.3 Geometric Sequences and Series

11.4 Mathematical Induction

11.5 Combinatorics: Permutations

11.6 Combinatorics: Combinations

11.7 The Binomial Theorem

11.8 Probability

• Functions are introduced in Chapter 1, starting the course with a new topic rather than a review of equation-solving covered in previous math courses.
  • Students learn the concept of a function by repeated exposure to the language, notation and use of functions throughout.
• Classify the Function exercises in the Skill Maintenance section of the exercise sets ask students to identify a number of functions by their type (linear, quadratic, rational, etc.)
  • Throughout, the variety of functions increases and these exercises become more challenging.
• Technology Connections are optional sections that guide students in the use of the graphing calculator as another way to check problems.
• Zeros, solutions, and x-intercepts are a theme of the text. 

• Just-In-Time Review: Review of prerequisite algebra topics is now presented when students need it most.
  • A set of 25 numbered short review topics creates an efficient review of intermediate algebra topics.
  • This feature is placed at the back of the text. Just-In-Time icons are positioned throughout the text next to the example where review of an intermediate algebra topic would be helpful.
• Data-Informed Exercises: The authors revised exercises for the 5th Edition by analyzing usage data to improve the quality and quantity of exercises that matter the most to instructors and students. For example, the authors adjusted sample homework assignments to ensure usage of the most widely used exercises.
• Symmetry and Transformations: These topics are now presented in two sections rather than one due to reviewer feedback. Separating these concepts into two reasonable amounts of information allows for deeper student understanding.