Advanced Functions

hapter 1: Functions: Characteristics and Properties

1.1 Functions

1.2 Exploring Absolute Value

1.3 Properties of Graphs of Functions

1.4 Sketching Graphs of Functions

1.5 Inverse Relations

1.6 Piecewise Functions

1.7 Exploring Operations with Functions

Chapter 2: Functions: Understanding Rates of Change

2.1 Determining Average Rate of Change

2.2 Estimating Instantaneous Rates of Change from Tables

2.3 Exploring Instantaneous Rates of Change from Graphs

Chapter 3: Polynomial Functions

3.1 Exploring Polynomial Functions

3.2 Characteristics of Polynomial Functions

3.3 Characteristics of Polynomial Functions in Factored form

3.4. Transformations of Cubic and Quartic Functions

3.5 Dividing Polynomials

3.6 Factoring Polynomials

3.7 Factoring a Sum or Difference of Cubes

Chapter 4: Polynomial Equations and Inequalities

4.1 Solving Polynomial Equations

4.2 Solving Linear Inequalities

4.3 Solving Polynomial Inequalities

4.4 Rates of Change in Polynomial Functions

Chapter 5: Rational Functions, Equations, and Inequalities

5.1 Graphs of Reciprocal Functions

5.2 Exploring Quorients of Polynomial Functions

5.3 Graphs of Rational Functions

5.4 Solving Rational Equations

5.5 Solving Rational Inequalities

5.6 Rates of Changes in Rational Functions

Chapter 6: Trigonometric Functions

6.1 Radian Measure

6.2 Angle on the Cartesian Plane

6.3 Exploring Graphs of the primary trigonometric functions

6.4 Transformations of Trigonometric Functions

6.5 Exploring Graphs of the Reciprocal Trigonometric Functions

6.6 Modelling with Trigonometric Functions

6.7 Rates of Change in Trigonometric Functions

Chapter 7: Trigonometric Identities and Equations

7.1 Exploring Equivalent Trigonometric Functions

7.2 Compound Angle Formulas

7.3 Double Angle Formulas

7.4 Proving Trigonometric Identities

7.5 Solving Linear Trigonometric Equations

7.6 Solving Quadratic Trigonometric Equations

Chapter 8: Exponential and Logarithmic Functions

8.1 Exploring the Logarithmic Function

8.2 Transformations of Logarithmic Functions

8.3 Evaluating Logarithms

8.4 Laws of Logarithms

8.5 Solving Exponential Equations

8.6 Solving Logarithmic Equations

8.7 Solving Problems with Exponential and Logarithmic Functions

8.8 Rate of Change in Exponential and Logarithmic Functions

Chapter 9: Combinations of Functions

9.1 Exploring Combinations of Functions

9.2 Combining Two functions: Sums and Differences

9.3 Combining Two Functions: Products

9.4 Exploring Quotients of Functions

9.5 Composition of functions

9.6 Techniques for Solving Equations and Inequalities

9.7 Modelling with Functions