SAMPLE College Math

‭Chapter 1:‬ ‭Introduction to Algebra and Functions‬

‭Overview‬ ‭Mathematics‬ ‭is‬‭a‬‭common‬‭tool‬‭that‬‭is‬‭used‬‭in‬‭everyday‬‭life.‬‭Ranging‬‭from‬‭simple‬‭counting‬‭of‬‭inventory‬ ‭items‬ ‭to‬ ‭solving‬ ‭complex‬ ‭equations‬ ‭in‬ ‭computer‬ ‭and‬ ‭engineering‬ ‭work,‬ ‭every‬ ‭day‬ ‭involves‬ ‭the‬ ‭use‬‭of‬ ‭mathematics.‬‭There‬‭are‬‭a‬‭large‬‭number‬‭of‬‭incentives‬‭for‬‭an‬‭individual‬‭to‬‭study‬‭throughout‬‭this‬‭course‬‭to‬ ‭equip‬ ‭him/herself‬ ‭with‬ ‭the‬ ‭knowledge‬ ‭of‬ ‭mathematics‬ ‭in‬ ‭order‬ ‭to‬ ‭excel‬ ‭in‬ ‭their‬ ‭career.‬ ‭Mathematics‬ ‭provides‬‭us‬‭with‬‭a‬‭better‬‭understanding‬‭of‬‭the‬‭world‬‭around‬‭us.‬‭It‬‭helps‬‭to‬‭hone‬‭the‬‭individual’s‬‭skills‬‭in‬ ‭problem‬ ‭solving,‬ ‭logical‬ ‭reasoning‬ ‭and‬ ‭flexible‬ ‭thinking,‬ ‭which‬ ‭is‬ ‭of‬‭utmost‬‭importance‬‭in‬‭the‬‭modern‬ ‭business‬‭world.‬‭It‬‭is‬‭pervasive‬‭and‬‭useful‬‭in‬‭almost‬‭all‬‭the‬‭arenas‬‭of‬‭life,‬‭such‬‭as‬‭business‬‭management,‬ ‭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 ‭algebra‬‭and‬‭functions‬‭will‬‭be‬‭presented.‬‭The‬‭main‬‭focus‬‭will‬‭be‬‭on‬ ‭concept‬ ‭building‬ ‭and‬ ‭its‬ ‭application.‬‭The‬‭building‬‭blocks‬‭of‬‭this‬‭chapter‬‭will‬‭include‬‭solving‬‭equations,‬ ‭linear‬‭inequalities,‬‭systems‬‭of‬‭linear‬‭equations‬‭by‬‭analytical‬‭and‬‭graphical‬‭methods,‬‭functions,‬‭and‬‭linear‬ ‭and‬ ‭exponential‬ ‭growth.‬‭The‬‭aim‬‭of‬‭this‬‭chapter‬‭is‬‭to‬‭equip‬‭you‬‭with‬‭the‬‭knowledge‬‭of‬‭general‬‭algebra‬ ‭that helps in building the foundation of mathematics.‬ ‭Objectives‬ ‭A. Set of Real Numbers‬ ‭Algebra‬‭is‬‭a‬‭tool‬‭that‬‭is‬‭used‬‭to‬‭solve‬‭real‬‭life‬‭problems‬‭in‬‭the‬‭domains‬‭of‬‭science,‬‭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 ‭unique‬‭characteristic‬‭of‬‭all‬‭elements‬‭in‬‭a‬‭set‬‭is‬‭that‬‭they‬‭have‬‭some‬‭similarity‬‭in‬‭appearance‬‭of‬‭purpose.‬ ‭For‬‭instance,‬‭{2,‬‭4,‬‭6,‬‭8}‬‭represents‬‭the‬‭set‬‭of‬‭all‬‭one-digit‬‭even‬‭numbers,‬‭and‬‭{a,‬‭e,‬‭i,‬‭o,‬‭u}‬‭represents‬‭the‬ ‭set‬‭of‬‭all‬‭vowels‬‭in‬‭English.‬‭Sets‬‭are‬‭denoted‬‭by‬‭a‬‭letter.‬‭The‬‭set‬‭of‬‭all‬‭positive‬‭numbers‬‭less‬‭than‬‭10‬‭is‬ ‭denoted‬‭by‬‭S‬‭=‬‭{1,‬‭2,‬‭3,‬‭4,‬‭5,‬‭6,‬‭7,‬‭8,‬‭9}‬‭and‬‭the‬‭set‬‭of‬‭all‬‭odd‬‭numbers‬‭less‬‭than‬‭10‬‭is‬‭denoted‬‭by‬‭T=‬‭{1,‬ ‭3,‬‭5,‬‭7,‬‭9}.‬‭In‬‭this‬‭case,‬‭T‬‭is‬‭known‬‭as‬‭the‬‭sub-set‬‭of‬‭S,‬‭since‬‭all‬‭elements‬‭in‬‭set‬‭T‬‭are‬‭present‬‭in‬‭set‬‭S.‬ ‭Another‬ ‭way‬ ‭to‬ ‭describe‬ ‭a‬ ‭set‬ ‭is‬ ‭by‬ ‭using‬ ‭a‬ ‭set-builder‬ ‭notation.‬ ‭For‬ ‭instance,‬ ‭the‬ ‭set‬ ‭{1,‬ ‭3,‬ ‭5}‬ ‭in‬ ‭a‬ ‭set-builder‬‭notation‬‭is‬‭written‬‭as‬‭{x‬‭l‬‭x‬‭is‬‭an‬‭odd‬‭number‬‭between‬‭0‬‭and‬‭6}.‬‭Set-builder‬‭notation‬‭is‬‭read‬ ‭as follows:‬ ‭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

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