A resource written specifically for the University, Advanced Functions (MHF4U) course.
Preface
Chapter 1 Polynomial Functions
Prerequisite Skills
1.1 Power Functions
1.2 Characteristics of Polynomial Functions
1.3 Equations and Graphs of Polynomial Functions
1.4 Transformations
1.5 Slopes of Secants and Average Rate of Change
1.6 Slopes of Tangents and Instantaneous Rate of Change
Review
Practice Test
Task: Create Your Own Water Park
Chapter 2 Polynomial Equations and Inequalities
Prerequisite Skills
2.1 The Remainder Theorem
2.2 The Factor Theorem
2.3 Polynomial Equations
2.4 Families of Polynomial Functions
2.5 Solve Inequalities Using Technology
2.6 Solve Factorable Polynomial Inequalities Algebraically
Review
Practice Test
Task: Can You Tell Just by Looking?
Chapter 3 Rational Functions
Prerequisite Skills
3.1 Reciprocal of a Linear Function
Extension: Asymptotes and the TI-83 Plus or TI-84 Plus Graphing Calculator
3.2 Reciprocal of a Quadratic Function
3.3 Rational Functions of the Form
f(x) = ax + b
cx + d
3.4 Solve Rational Equations and Inequalities
3.5 Making Connections With Rational Functions and Equations
Review
Practice Test
Chapters 1 to 3 Review
Task: ZENN and Now
Chapter 4 Trigonometry
Prerequisite Skills
4.1 Radian Measure
4.2 Trigonometric Ratios and Special Angles
4.3 Equivalent Trigonometric Expressions
4.4 Compound Angle Formulas
4.5 Prove Trigonometric Identities
Extension: Use The Geometer’s Sketchpad® to Sketch and Manipulate Three-Dimensional Structures in a Two-Dimensional Representation
Review
Practice Test
Task: Make Your Own Identity
Chapter 5 Trigonometric Functions
Prerequisite Skills
5.1 Graphs of Sine, Cosine, and Tangent Functions
5.2 Graphs of Reciprocal Trigonometric Functions
5.3 Sinusoidal Functions of the Form
f(x) = a sin [k(x - d)] + c and
f(x) = a cos [k(x - d)] + c
Extension: Use a Graphing Calculator to Fit a Sinusoidal Regression to Given Data
5.4 Solve Trigonometric Equations
5.5 Making Connections and Instantaneous Rate of Change
Review
Practice Test
Chapters 4 and 5 Review
Task: Predators and Prey
Chapter 6 Exponential and Logarithmic Functions
Prerequisite Skills
6.1 The Exponential Function and Its Inverse
6.2 Logarithms
6.3 Transformations of Logarithmic Functions
6.4 Power Law of Logarithms
6.5 Making Connections: Logarithmic Scales in the Physical Sciences
Review
Practice Test
Task: Not Fatal
Chapter 7 Tools and Strategies for Solving Exponential and Logarithmic Equations
Prerequisite Skills
7.1 Equivalent Forms of Exponential Equations
7.2 Techniques for Solving Exponential Equations
7.3 Product and Quotient Laws of Logarithms
7.4 Techniques for Solving Logarithmic Equations
7.5 Making Connections: Mathematical Modelling With Exponential and Logarithmic Equations
Review
Practice Test
Task: Make Your Own Slide Rule
Chapter 8 Combining Functions
Prerequisite Skills
8.1 Sums and Differences of Functions
8.2 Products and Quotients of Functions
8.3 Composite Functions
8.4 Inequalities of Combined Functions
8.5 Making Connections: Modelling With Combined Functions
Review
Practice Test
Chapters 6 to 8 Review
Task: Modelling a Damped Pendulum
Course Review
Prerequisite Skills Appendix
Technology Appendix
Answers
Glossary
Index
Credits