Precalculus Chapter 1 Functions and Graphs

Section 1: Modeling and Equation Solving (pages 70 – 85) Objective: Students will be able to use numerical, algebraic, and graphical models to

solve problems and will be able to translate from one model to another.

Self Assessment Exercises: #11, 13, 15, 18, 19, 21, 23, 31, 35, 47, 49, 51, 53, & 55.

Section 2: Functions and Their Properties (pages 86 – 105) Objective: Students will be able to represent functions numerically, algebraically, and

graphically; determine the domain and range for functions, and analyze function

characteristics such as extreme values, symmetry, asymptotes, and end behavior.

Self Assessment Exercises: #3, 5, 11, 17, 21, 33, 37, 41, 49, 57, 65, 70, & 84.

Section 3: Twelve Basic Functions (pages 106 – 116)

Objective: Students will be able to recognize graphs of twelve basic functions, determine

the domains of functions related to the twelve basic functions, and combine the twelve

basic functions in various ways to create new functions.

Self Assessment Exercises: #13, 15, 17, 19, 32, 35, 45, 47, 55, 64, & 67.

Section 4: Building Functions from Functions (pages 117 – 126) Objective: Students will be able to build new functions from basic functions by adding,

subtracting, multiplying, dividing, and composing functions.

Self Assessment Exercises: #3, 6, 12, 15, 17, 25, 31, 35, 37, 51, 52, & 53.

Section 5: Parametric Relations and Inverses (pages 127 – 137) Objective: Students will be able to define functions and relations parametrically and will

be able to find inverses of functions and relations.

Self Assessment Exercises: #3, 5, 7, 9, 15, 17, 23, 27, & 44 – 48.

Section 6: Graphical Transformations (pages 138 – 150) Objective: Students will be able to algebraically and graphically represent translations,

reflections, stretches, and shrinks of functions and parametric relations.

Self Assessment Exercises: #3, 9, 14, 19, 21, 25, 29, 33, 39, 47, 51, 56, & 58.

Section 7: Modeling With Functions (pages 151 – 164)

Objective: Students will be able to identify appropriate basic functions with which to

model real-world problems and be able to produce specific functions to model data,

formulas, graphs, and verbal descriptions.

Self Assessment Exercises: #3, 7, 12, 19, 33, 35, 37, 39, 47, & 52.

Precalculus Chapter 1 Functions and Graphs

Chapter Test: Key Ideas to Know for the Test

Properties, Theorems, & Formulas

The Zero Factor Property (75)

Vertical Line Test (87)

Horizontal Line Test (130)

Tests for Even/Odd Functions (97, 98)

Inverse Reflection Principle (132)

Inverse Composition Rule (133)

Translations of Graphs (139)

Reflections of Graphs across Axes (141)

Stretches and Shrinks of Graphs (144)

Procedures

Root, Zero, x-intercept (76)

Problem Solving (76)

Agreement about Domain (88)

Inverse Notation (130)

Finding the Inverse of a Function (134)

Chapter Project: page 168.