A resource written specifically for the University Functions (MCR 3U) course. Functions 11 addresses and supports the diverse needs of students and teachers and integrates mathematical process expectations into all areas of the student text.
Preface
Chapter 1 Functions
Prerequisite Skills
1.1 Functions, Domain, and Range
1.2 Functions and Function Notation
1.3 Maximum or Minimum of a Quadratic Function
Use Technology
Use a TI-Nspire™ CAS Graphing Calculator to Find Maximum or Minimum and the Zeros of a Quadratic Function
1.4 Skills You Need: Working With Radicals
Use Technology
Use a TI-Nspire™ CAS Graphing Calculator to Explore Operations With Radicals
1.5 Solve Quadratic Equations
1.6 Determine a Quadratic Equation Given its Roots
1.7 Solve Linear-Quadratic Systems
Chapter 1 Review
Chapter 1 Practice Test
Task: Laser Beams
Chapter 2 Transformations of Functions
Prerequisite Skills
2.1 Functions and Equivalent Algebraic Expressions
Use Technology
Graph Functions Using a TI-Nspire™ CAS Graphing Calculator
2.2 Skills You Need: Operations With Rational Expressions
2.3 Horizontal and Vertical Translations of Functions
2.4 Refl ections of Functions
2.5 Stretches of Functions
Use Technology
Use The Geometer’s Sketchpad® to Explore Transformations
2.6 Combinations of Transformations
2.7 Inverse of a Function
Chapter 2 Review
Chapter 2 Practice Test
Task: Functions in Design
Chapter 3 Exponential Functions
Prerequisite Skills
3.1 The Nature of Exponential Growth
Use Technology
Use Lists and Trace Features on a TI-Nspire™ CAS Graphing Calculator
3.2 Exponential Decay: Connecting to Negative Exponents
3.3 Rational Exponents
3.4 Properties of Exponential Functions
3.5 Transformations of Exponential Functions
3.6 Making Connections: Tools and Strategies for Applying Exponential Models
Chapter 3 Review
Chapter 3 Practice Test
Chapters 1 to 3 Review
Task: Radioactive Isotopes
Chapter 4 Trigonometry
Prerequisite Skills
4.1 Special Angles
4.2 Co-terminal and Related Angles
Use Technology
Use a Computer Algebra System to Find Exact Trigonometric Ratios and Angles
4.3 Reciprocal Trigonometric Ratios
4.4 Problems in Two Dimensions
Use Technology
Use Geometry Software to Test for the Ambiguous Case
4.5 Problems in Three Dimensions
4.6 Trigonometric Identities
Chapter 4 Review
Chapter 4 Practice Test
Task: Pyramids and Angles of Elevation
Chapter 5 Trigonometric Functions
Prerequisite Skills
5.1 Modelling Periodic Behaviour
5.2 The Sine Function and the Cosine Function
Use Technology
Dynamically Unwrap theUnit Circle
5.3 Investigate Transformations of Sine and Cosine Functions
5.4 Graphing and Modelling with y = asin[k(x - d)] + c and y = acos[k(x - d)] + c
5.5 Data Collecting and Modelling
5.6 Use Sinusoidal Functions to Model Periodic Phenomena Not Involving Angles
Use Technology
Create a Scatter Plot and a Function Using a TI-Nspire™ CAS Graphing Calculator
Chapter 5 Review
Chapter 5 Practice Test
Chapters 4 and 5 Review
Task: Modelling a Rotating Object
Chapter 6 Discrete Functions
Prerequisite Skills
6.1 Sequences as Discrete Functions
Use Technology
Use a TI-Nspire™ CAS Graphing Calculator to Write Terms in a Sequence
6.2 Recursive Procedures
6.3 Pascal’s Triangle and Expanding Binomial Powers
6.4 Arithmetic Sequences
6.5 Geometric Sequences
6.6 Arithmetic Series
6.7 Geometric Series
Chapter 6 Review
Chapter 6 Practice Test
Task: Mathematics in Media Studies
Chapter 7 Financial Applications
Prerequisite Skills
7.1 Simple Interest
7.2 Compound Interest
7.3 Present Value
7.4 Annuities
7.5 Present Value of an Annuity
Chapter 7 Review
Chapter 7 Practice Test
Chapters 6 and 7 Review
Task: Loans and Annuities Due
Course Review
Prerequisite Skills Appendix
Technology Appendix
Answers
Glossary
Index
Credits
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