i
Table of Contents
Introduction .................................................................................................... i–v
What is Engaging Mathematics, Volume I: Precalculus? ....................................... iv
What is found in an Engaging Mathematics TEKS-based activity? ........................... v
Functions .................................................................................................. 1–102
Solving Problems with Composition of Functions, Activity 1 P(2)(A) ...................... 1
Solving Problems with Composition of Functions, Activity 2 P(2)(A) ...................... 3
Solving Problems with Composition of Functions, Activity 3 P(2)(A) ...................... 5
Commutative Property and Composition of Functions P(2)(B) .............................. 9
Composition of Functions, Activity 1 P(2)(C) ................................................... 11
Composition of Functions, Activity 2 P(2)(C) ................................................... 13
Even and Odd Functions, Activity 1 P(2)(D) .................................................... 17
Even and Odd Functions, Activity 2 P(2)(D) ..................................................... 19
Inverse of a Function, Activity 1 P(2)(E) .......................................................... 21
Inverse of a Function, Activity 2 P(2)(E) .......................................................... 25
Graphing Functions, Activity 1 P(2)(F) ............................................................. 27
Graphing Functions, Activity 2 P(2)(F) ............................................................. 29
Graphing Functions, Activity 3 P(2)(F) ............................................................. 31
Graphing Functions, Activity 4 P(2)(F) ............................................................. 33
Graphing Functions, Activity 5 P(2)(F) ............................................................. 35
Functions and Their Transformations, Activity 1 P(2)(G) .................................... 37
Functions and Their Transformations, Activity 2 P(2)(G) .................................... 39
Functions and Their Transformations, Activity 3 P(2)(G) .................................... 43
Functions and Their Transformations, Activity 4 P(2)(G) .................................... 45
Functions and Their Transformations, Activity 5 P(2)(G) .................................... 49
Transformations of Periodic Functions, Activity 1 P(2)(G) ................................... 53
Transformations of Periodic Functions, Activity 2 P(2)(G) ................................... 55
Transformations of Periodic Functions, Activity 3 P(2)(G) ................................... 57
Arcsine and Arccosine, Activity 1 P(2)(H) ......................................................... 59
Arcsine and Arccosine, Activity 2 P(2)(H) ......................................................... 61
Key Features of Functions, Activity 1 P(2)(I) .................................................... 63
Key Features of Functions, Activity 2 P(2)(I) .................................................... 65
Key Features of Functions, Activity 3 P(2)(I) .................................................... 67
Key Features of Functions, Activity 4 P(2)(I) .................................................... 71
End Behaviors of Functions, Activity 1 P(2)(J) .................................................. 73
End Behaviors of Functions, Activity 2 P(2)(J) .................................................. 75
Asymptotes P(2)(K) ...................................................................................... 77
Discontinuities P(2)(L) .................................................................................. 79
Behaviors around Discontinuities, Activity 1 P(2)(M) ......................................... 83
Behaviors around Discontinuities, Activity 2 P(2)(M) ......................................... 85
Analyzing Contextual Situations, Activity 1 P(2)(N) ........................................... 87
Analyzing Contextual Situations, Activity 2 P(2)(N) ........................................... 91
Sinusoidal Functions, Activity 1 P(2)(O) ........................................................... 93
Sinusoidal Functions, Activity 2 P(2)(O) ........................................................... 95
Trigonometric Functions at Special Angles, Activity 1 P(2)(P) .............................. 97
Trigonometric Functions at Special Angles, Activity 2 P(2)(P) ............................ 101
Relations and Geometric Reasoning ...................................................... 103–140
Graphing Parametric Equations, Activity 1 P(3)(A) .......................................... 103
Graphing Parametric Equations, Activity 2 P(3)(A) .......................................... 105
Table of Contents
Introduction .................................................................................................... i–v
What is Engaging Mathematics, Volume I: Precalculus? ....................................... iv
What is found in an Engaging Mathematics TEKS-based activity? ........................... v
Functions .................................................................................................. 1–102
Solving Problems with Composition of Functions, Activity 1 P(2)(A) ...................... 1
Solving Problems with Composition of Functions, Activity 2 P(2)(A) ...................... 3
Solving Problems with Composition of Functions, Activity 3 P(2)(A) ...................... 5
Commutative Property and Composition of Functions P(2)(B) .............................. 9
Composition of Functions, Activity 1 P(2)(C) ................................................... 11
Composition of Functions, Activity 2 P(2)(C) ................................................... 13
Even and Odd Functions, Activity 1 P(2)(D) .................................................... 17
Even and Odd Functions, Activity 2 P(2)(D) ..................................................... 19
Inverse of a Function, Activity 1 P(2)(E) .......................................................... 21
Inverse of a Function, Activity 2 P(2)(E) .......................................................... 25
Graphing Functions, Activity 1 P(2)(F) ............................................................. 27
Graphing Functions, Activity 2 P(2)(F) ............................................................. 29
Graphing Functions, Activity 3 P(2)(F) ............................................................. 31
Graphing Functions, Activity 4 P(2)(F) ............................................................. 33
Graphing Functions, Activity 5 P(2)(F) ............................................................. 35
Functions and Their Transformations, Activity 1 P(2)(G) .................................... 37
Functions and Their Transformations, Activity 2 P(2)(G) .................................... 39
Functions and Their Transformations, Activity 3 P(2)(G) .................................... 43
Functions and Their Transformations, Activity 4 P(2)(G) .................................... 45
Functions and Their Transformations, Activity 5 P(2)(G) .................................... 49
Transformations of Periodic Functions, Activity 1 P(2)(G) ................................... 53
Transformations of Periodic Functions, Activity 2 P(2)(G) ................................... 55
Transformations of Periodic Functions, Activity 3 P(2)(G) ................................... 57
Arcsine and Arccosine, Activity 1 P(2)(H) ......................................................... 59
Arcsine and Arccosine, Activity 2 P(2)(H) ......................................................... 61
Key Features of Functions, Activity 1 P(2)(I) .................................................... 63
Key Features of Functions, Activity 2 P(2)(I) .................................................... 65
Key Features of Functions, Activity 3 P(2)(I) .................................................... 67
Key Features of Functions, Activity 4 P(2)(I) .................................................... 71
End Behaviors of Functions, Activity 1 P(2)(J) .................................................. 73
End Behaviors of Functions, Activity 2 P(2)(J) .................................................. 75
Asymptotes P(2)(K) ...................................................................................... 77
Discontinuities P(2)(L) .................................................................................. 79
Behaviors around Discontinuities, Activity 1 P(2)(M) ......................................... 83
Behaviors around Discontinuities, Activity 2 P(2)(M) ......................................... 85
Analyzing Contextual Situations, Activity 1 P(2)(N) ........................................... 87
Analyzing Contextual Situations, Activity 2 P(2)(N) ........................................... 91
Sinusoidal Functions, Activity 1 P(2)(O) ........................................................... 93
Sinusoidal Functions, Activity 2 P(2)(O) ........................................................... 95
Trigonometric Functions at Special Angles, Activity 1 P(2)(P) .............................. 97
Trigonometric Functions at Special Angles, Activity 2 P(2)(P) ............................ 101
Relations and Geometric Reasoning ...................................................... 103–140
Graphing Parametric Equations, Activity 1 P(3)(A) .......................................... 103
Graphing Parametric Equations, Activity 2 P(3)(A) .......................................... 105
