1: Basic Algebra Review
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”Failure is the foundation of success, and the means by which it is achieved.” - Lao Tzu
Because this book is targeted at a wide range of different student audiences, it is natural to ask where to begin. Many students attempting calculus have a strong foundation in algebra and trigonometry (the elements of precalculus ), while others may be lacking in one or the other. The first chapter of this book is dedicated to students who may not have the strongest background in algebra, but may be a worthy brush up for students of all skill levels. Chapter one begins with a review of solving basic linear equations Ax+By=C, which we then use to help us draw the graphs of lines on the Cartesian plane. We will also discuss the three different equations of a line which we will use throughout the rest of the book. We also review solving linear inequalities and putting our answer into interval notation.
This chapter continues to discuss the topic of relationships vs. functions and function notation. We cover the family of power functions f(x)=xp, and how to solve basic linear equations involving them. Alongside this exploration of the power functions are radical functions and quadratic functions. We talk about how to sketch the parabola represented by a given quadratic function as well as methods for solving quadratic equations. A student who has mastered the topics in this chapter should feel confident solving an assortment of equations from a first algebra course, linear inequalities, using function notation, and graphing a line or parabola given in a variety of different possible forms. All of these skills will be expanded as we progress through the book, but they are ultimately the building blocks of mathematics.