### 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