Functions as models of change

Units

Units 1 to 3 are on the AP Exam. Unit 4 is a set of additional topics a school may choose to teach, and it is not assessed on the AP Exam.

1. Unit 1 Polynomial and Rational Functions 30–40% of the multiple-choice section · 14 topics

   1. 1.1Change in Tandem
   2. 1.2Rates of Change
   3. 1.3Rates of Change in Linear and Quadratic Functions
   4. 1.4Polynomial Functions and Rates of Change
   5. 1.5Polynomial Functions and Complex Zeros
   6. 1.6Polynomial Functions and End Behavior
   7. 1.7Rational Functions and End Behavior
   8. 1.8Rational Functions and Zeros
   9. 1.9Rational Functions and Vertical Asymptotes
   10. 1.10Rational Functions and Holes
   11. 1.11Equivalent Representations of Polynomial and Rational Expressions
   12. 1.12Transformations of Functions
   13. 1.13Function Model Selection and Assumption Articulation
   14. 1.14Function Model Construction and Application

   Unit 1 overviewUnit 1 check

2. Unit 2 Exponential and Logarithmic Functions 25–40% of the multiple-choice section · 15 topics

   1. 2.1Change in Arithmetic and Geometric Sequences
   2. 2.2Change in Linear and Exponential Functions
   3. 2.3Exponential Functions
   4. 2.4Exponential Function Manipulation
   5. 2.5Exponential Function Context and Data Modeling
   6. 2.6Competing Function Model Validation
   7. 2.7Composition of Functions
   8. 2.8Inverse Functions
   9. 2.9Logarithmic Expressions
   10. 2.10Inverses of Exponential Functions
   11. 2.11Logarithmic Functions
   12. 2.12Logarithmic Function Manipulation
   13. 2.13Exponential and Logarithmic Equations and Inequalities
   14. 2.14Logarithmic Function Context and Data Modeling
   15. 2.15Semi-log Plots

   Unit 2 overviewUnit 2 check

3. Unit 3 Trigonometric and Polar Functions 30–35% of the multiple-choice section · 15 topics

   The lessons for this unit are still being written. Ready now:

   1. 3.5Sinusoidal FunctionsPractice
   2. 3.6Sinusoidal Function TransformationsPractice
   3. 3.13Trigonometry and Polar CoordinatesPractice

   • LabFunction Grapher

   Unit 3 overview

4. Unit 4 Functions Involving Parameters, Vectors, and Matrices Not assessed on the AP Exam · 14 topics

   The lessons for this unit are still being written.

   Unit 4 overview

Labs

The function grapher draws a parent function and its transformation together, for polynomial, rational, exponential, logarithmic and sinusoidal functions.

• Topics 1.12, 2.3, 2.4, 2.7, 2.11, 2.12 and 3.6 Function Grapher Move a, b, c and d in g(x) = a f(b(x + c)) + d and watch a polynomial, rational, exponential, logarithmic or sine graph transform.
• Topics 1.14, 2.5, 2.6 and 2.14 Model Builder Fit a linear, quadratic, cubic, quartic, exponential or logarithmic regression to a small data set, then read the residual plot to decide whether the model is appropriate.