College Algebra (Abridged)

Chapter 1: Introduction to Algebra and Functions Overview Mathematics is a common tool that is used in everyday life. Ranging from simple counting of inventory items to solving complex equations in computer and engineering work, every day involves the use of mathematics. There are a large number of incentives for an individual to study throughout this course to equip him/herself with the knowledge of mathematics in order to excel in their career. Mathematics provides us with a better understanding of the world around us. It helps to hone the individual’s skills in problem solving, logical reasoning and flexible thinking, which is of utmost importance in the modern business world. It is pervasive and useful in almost all the arenas of life, such as business management, predicting stock market prices, safeguarding credit transactions on the internet, science, engineering, and even managing day-to-day financial activities. In this chapter, the introduction to algebra and functions will be presented. The main focus will be on concept building and its application. The building blocks of this chapter will include solving equations, linear inequalities, systems of linear equations by analytical and graphical methods, functions, and linear and exponential growth. The aim of this chapter is to equip you with the knowledge of general algebra that helps in building the foundation of mathematics. Objectives By the end of this chapter, you should be able to recognize, understand, and solve the following: • Algebraic operations • Equations and inequalities • Functions and their properties • Number systems and operations 1.1 Set of Real Numbers Algebra is a tool that is used to solve real life problems in the domains of science, business, architecture, management, space travel, and many other fields. We begin this chapter by understanding the basic notations and symbols used to build and solve algebraic expressions. Sets represent the collection of similar elements, and are denoted by the enclosed brackets {}. The unique characteristic of all elements in a set is that they have some similarity in appearance of purpose. For instance, {2, 4, 6, 8} represents the set of all one-digit even numbers, and {a, e, i, o, u} represents the set of all vowels in English. Sets are denoted by a letter. The set of all positive numbers less than 10 is denoted by S = {1, 2, 3, 4, 5, 6, 7, 8, 9} and the set of all odd numbers less than 10 is denoted by T= {1, 3, 5, 7, 9}. In this case, T is known as the sub-set of S, since all elements in set T are present in set S. Another way to describe a set is by using a set-builder notation. For instance, the set {1, 3, 5} in a set-builder notation is written as {x l x is an odd number between 0 and 6}. Set-builder notation is read as follows:

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