Advanced Functions – 12th Grade

Chapter 1: Functions – Characteristics and Properties

1.1: Functions

1.2: Exploring Absolute Value

1.3: Properties of Functions and Graphs

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: Average Rate of Change

2.2: Instantaneous Rate of Change from Tables and Graphs

2.3: Using Rates of Change to make a Graphical Model

2.4: Solving Problems with Rates of Change

Chapter 3: Polynomial Functions

3.1: Exploring Polynomial Functions

3.2: Characteristics of Polynomial Functions

3.3: Characteristics in Factored Form

3.4: Transformations of Cubic and Quartic Functions

3.5: Factoring Polynomials

3.6: Factoring 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: Quotients of Reciprocal Functions

5.3: Graphs of Rational Functions of the form (ax+b)/(cx+d)

5.4: Solving Rational Equations

5.5: Solving Rational Inequalities

5.6: Rates of Change in Rational Functions

Chapter 6: Trigonometric Functions

6.1: Radian Measure

6.2: Radian Measure and Angles on the Cartesian Plane

6.3: Graphs of Trigonometric Functions

6.4: Transformations of Trigonometric Functions

6.5: Graphs of 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: 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 Equations

8.8: Rates of Change in Exponential and Logarithmic Equations

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: Combining Two Functions – Quotients

9.5: Combining Two Functions – Composition of Functions

Extra Practice Problems

Link to Textbook: Advanced Functions 12 by Chris Kirkpatrick