AP Calculus AB‎ > ‎Previous Units‎ > ‎PreCalc Review‎ > ‎

2-Functions

Important Concepts for This Unit

Functions are a core concept in mathematics. Most the the theory and mathematical operations you will learn this year and next year require that you're working with a function. Understanding what a function is and its properties are crucial as we move forward. The standards that will be assessed in this chapter are

2.5 Can graph and solve problems related to linear functions and models.
2.6 Can solve problems involving translation and dilation transformations to functions.
2.7 Can solve problems involving composition of functions (nested functions).




 

u2.1 - Introduction to Functions

  • The idea of function, viewed as the dependence of one quantity on a different quantity.
  • The notation associated with piecewise-defined functions.
  • Domains and ranges from an algebraic perspective.
  • Four different representations of functions (verbal, algebraic, visual, and numeric)

 

Core Exercises: 3, 15, 20, 33, 37, 50, 58, 68, 80, 89, 94

Recommended: 1, 3, 8, 13, 15, 17, 20, 25, 29, 32, 33, 35, 37, 42, 43, 50, 53, 57, 58, 64, 68, 73, 76, 80, 83, 86, 89, 947



u2.2 Graphs of Functions

  • The Vertical Line Test.
  • Graphs of piecewise-defined functions.
  • The greatest integer function.

Core Exercises: 3, 7, 22, 34, 42, 47, 52, 60, 70, 78, 83
Recommended: 3, 4, 7, 8, 16, 22, 25, 31, 34, 38, 42, 45, 47, 50, 52, 56, 60, 64, 66, 70, 73, 76, 78, 81, 83, 87

 



u2.3 Getting Information from the Graph of a Function

  • Gaining information about a function from its graph, including finding function values, domain and range. 
  • Algebraic and geometric definitions of increasing and decreasing. 
  • Finding local extrema of a function from its graph. 

Core Exercises: 3, 8, 13, 22, 32, 37, 45, 48, 52, 59, 66, 67

Recommended:
 1, 3, 7, 8, 9, 13, 15, 20, 22, 32, 34, 36, 37, 41, 44, 45, 48, 52, 56, 57, 59, 62, 65, 66, 67, 69

 



u2.5  Linear Functions and Models

  • Definition of a linear function.
  • The relationship between slope and rate of change, including units.
  • Creating linear models in an applied context.

Core Exercises: 3, 9, 14, 17, 21, 29, 35, 42, 46, 52

Recommended: 1, 3, 5, 7, 9, 13, 14, 15, 17, 18, 21, 22, 25, 27, 29, 32, 35, 36, 38, 42, 43, 45, 46, 49, 52


u1.10 Lines

Core Exercises: 4, 7, 17, 34, 52

Recommended: 4, 6, 7, 16, 17, 22, 24, 34, 36, 40, 51, 52, 54

 



u2.4 Average Rate of Change of a Function

  • Using slope to model the average rate of change of a function or measurable

Core Exercises: 3, 10, 16, 24, 31, 36, 40

Recommended:
 3, 4, 8, 10, 11, 15, 16, 22, 24, 26, 29, 31, 33, 36, 38, 40 103




u2.6 Transformations of Functions

  • Transforming a given function to a different one by shifting, stretching, and reflection.
  • Using the technique of reflection to better understand the concepts of even and odd functions.

Core Exercises: 3, 9, 14, 17, 21, 29, 35, 42, 46, 52

Sample Assignment:
 1, 3, 5, 7, 9, 13, 14, 15, 17, 18, 21, 22, 25, 27, 29, 32, 35, 36, 38, 42, 43, 45, 46, 49, 52 112




  u2.7 Combining Functions

  • Addition, subtraction, multiplication, and division of functions.
  • Composition of functions.
  • Finding the domain of a function based on analysis of the domain of its components.

Core Exercises: 4, 10, 15, 20, 26, 34, 38, 49, 57, 64, 71, 75, 79, 86, 92, 104

 

Recommended: 2, 4, 6, 7, 10, 13, 15, 20, 22, 24, 26, 27, 29, 34, 36, 38, 45, 49, 52, 55, 57, 61, 64, 67, 69, 71, 73, 75, 77, 79, 82, 85, 86, 92, 93, 95, 98, 104



 
  u2.8 One-to-One Functions and their Inverses

  • One-to-one functions: their definition and the Horizontal Line Test.
  • Algebraic and geometric properties of inverse functions.
  • Finding inverse functions.

 

Core Exercises: 3, 8, 14, 20, 24, 35, 48, 54, 57, 64, 67, 79, 71

Recommended:
 1, 3, 8, 10, 14, 15, 18, 20, 22, 24, 25, 29, 31, 35, 38, 41, 46, 47, 48, 54, 56, 57, 60, 64, 66, 67, 70, 71, 73, 77, 79, 81, 82


Showing 0 items
AssignmentDue DateNotes
Sort 
 
Sort 
 
Sort 
 
AssignmentDue DateNotes
Showing 0 items
Ċ
Nikhil Joshi,
Dec 1, 2016, 12:12 PM
Ċ
Nikhil Joshi,
Oct 21, 2016, 11:09 AM
Ċ
Nikhil Joshi,
Nov 4, 2016, 11:54 AM
Ċ
Nikhil Joshi,
Nov 4, 2016, 11:54 AM
Ĉ
Nikhil Joshi,
Oct 25, 2016, 10:49 AM