# Chapter 1: Equations and Functions

**At Grade**Created by: CK-12

## Introduction

Equations and functions are the basic building blocks of algebra. You will use the concepts you learn in this chapter not only in the chapters to follow but also in your everyday life. Every time you encounter a situation with an unknown value, like the amount of interest your bank account is earning, you can write and manipulate an equation to find that value. Likewise, when you encounter mathematical rules, graphs, and tables, you can use a function to represent the relationships explained by them. Chemists, teachers, lab technicians, computer programmers, insurance professionals, and engineers are just some of the many professions that make use of equations and functions.

Throughout this chapter, you will learn the language of algebra, you will evaluate expressions, you will write equations and inequalities, you will check your solutions, you will write function rules and graph functions, and you will devise problem-solving strategies for real-world situations.

## Chapter Outline

- 1.1. Definition of Variable
- 1.2. Expressions with One or More Variables
- 1.3. Algebra Expressions with Exponents
- 1.4. Order of Operations
- 1.5. Algebra Expressions with Fraction Bars
- 1.6. Patterns and Expressions
- 1.7. Words that Describe Patterns
- 1.8. Checking Solutions to Equations
- 1.9. Checking Solutions to Inequalities
- 1.10. Domain and Range of a Function
- 1.11. Functions that Describe Situations
- 1.12. Functions on a Cartesian Plane
- 1.13. Graphs of Functions based on Rules
- 1.14. Function Rules based on Graphs
- 1.15. Algebraic Functions
- 1.16. Problem-Solving Models
- 1.17. Comparison of Problem-Solving Models

### Chapter Summary

## Summary

This chapter first deals with with writing expressions and equations using variables. It then moves on to evaluating algebraic expressions. Building on this knowledge, you will next write, solve, and check the solution of equations and inequalities. Functions are then covered in detail, with special emphasis given to writing function rules and graphing functions from both rules and tables. From there, you will learn how to determine if a given relation is a function. Finally, the chapter concludes by pulling all this knowledge together into techniques for devising and selecting a problem-solving strategy for real-world scenarios.