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# Jaguar Math 106

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This 22 page Class Notes was uploaded by Dazniel Zepeda on Thursday September 1, 2016. The Class Notes belongs to Math 106 at Washington State University taught by Yu in Fall 2016. Since its upload, it has received 16 views. For similar materials see Math 106 in Applied Mathematics at Washington State University.

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Date Created: 09/01/16

MA TH 106: COLLEGE ALGEBRA SECTION07 PROFESSOR:FAITH ZHANG NOTETAKER:DAZNIELZEPEDA *DISCLAIMER* • LET IT BE KNOWN THAT I AM NOT THE INSTRUCTOR OF THIS CLASS, I AM MERELY AN NOTETAKER THROUGH STUDYSOUP AND MY GOAL IS TO MAKE THIS MATERIAL EASIER FOR EVERYONE TO UNDERSTAND. • ALL NOTESWERE TAKEN AND ALTEREDFOR YOUR UNDERSTANDINGFROMPROF. FAITHZHANG INTRODUCTION • Hello!As mentionedearlier, my name is DaznielZepeda.I am currentlya sophomore at WSU retaking thisclassbecause I didn’tfully understandthe contentandfailedto takeadvantageofthe help around me such asthe MathLearningCenter(MLC)or makingfriends withinthe classitselfwho were willingto study anddo homework withme. So I’m here tomake sure that youguys don’thaveto go through what I went throughand my goalis tohelp youguys betterand easierunderstandthe contentbeing taughtin thisclass! FREE NOTES!! • So where tobegin? Well I’m givingyouguys PIECESOF THE FIRST WEEK OF NOTES for free. Yes you heardcorrect ladiesandgerms, FREE. Youget notes, YOUget notes, EVERYBODYGETSNOTES!!And if youlike what yousee, please,please, PLEASE, continueto support me tohelp youguys better understandthisstuff! :D 2.1 THE RECT ANGULAR COORDINA TE SYSTEM Forexample:Plot the point(3, -5) on the RCS Plotting points on Coordinate System (R.C.S) points, (an ‘x’ value Consists of two and a ‘y’ value) put point, an ‘x’ them in this format: coordinate and a ‘y’ (x, y) and plot them. coordinate. ‘y’ coordinates move ‘x’ coordinates move along the “y-axis” along the “x-axis” (up or down (left to right whether or not the whether or not the ‘y’ value is positive ‘x’ value is positive or negative) or negative) *image taken from Coolmath.com 2.1 THE RECT ANGULAR COORDINA TE SYSTEM Forexample:Plot the point(3, -5) on the RCS the Rectangular on Coordinate System (R.C.S) After choosing two Consists of two points, (an ‘x’ value point, an ‘x’ them in this format: coordinate and a ‘y’ (x, y) and plot them. coordinate. ‘y’ coordinates move ‘x’ coordinates move al(up or downaxis” al(left to rights” depending on depending on whether or not the whether or not the Step 1: Start from the Origin (0,0) ‘y’ value is positive ‘x’ value is positive or negative) or negative) Step 2: MoveRight3 units *images taken from Coolmath.com, mathmazement.com 2.1 THE RECT ANGULAR COORDINA TE SYSTEM Forexample:Plot the point(3, -5) on the RCS Plotting points on Coordinate System (R.C.S) After choosing two Consists of two points, (an ‘x’ value point, an ‘x’ them in this format:t coordinate and a ‘y’ (x, y) and plot them. coordinate. ‘y’ coordinates move ‘x’ coordinates move along the “y-axis” along the “x-axis” (up or down (left to right depending on depending on Step 1: Start from the Origin (0,0) ‘y’ value is positive w‘x’ value is positive or negative) or negative) Step 2: MoveRight3 units Step 3: MoveDOWN 5 units *images taken from Coolmath.com, mathmazement.com 2.1 THE RECT ANGULAR COORDINA TE SYSTEM Forexample:Plot the point(3, -5) on the RCS the Rectangular on Coordinate System (R.C.S) points, (an ‘x’ value Consists of two and a ‘y’ value) put coordinate and a ‘y’ them in this format: coordinate. (x, y) and plot them. (3,-5) ‘along the “y-axis”e ‘along the “x-axis”e (up or down (left to right depending on depending on ‘y’ value is positive ‘x’ value is positive Step 1: Start from the Origin (0,0) or negative) or negative) Step 2: MoveRight3 units Step 3: MoveDOWN 5 units *images taken from Coolmath.com, mathmazement.com Step 4: Plot the point! 2.1 THE RECT ANGULAR COORDINA TE SYSTEM • AbsoluteValueEquations: • The absolutevalueofa numberis basicallyitsdistancefrom zero. In the exampleabovewe are given the function:y = lxl. Thismeansthatfor every ‘x’ input,the ‘y’ inputisthe input’s“distancefrom zero” *Image from Wikipiedia 2.1 THE RECT ANGULAR COORDINA TE SYSTEM Lets Practice! Example:Graph the equation:y = I x I + 2 2.1 THE RECT ANGULAR COORDINA TE SYSTEM Lets Practice! Example:Graph the equation:y = I x I + 2 (0,2) Steps: 1) Plot the first pointat the vertex(in thiscase the vertex islocatedatpoint(0,2)) 2.1 THE RECT ANGULAR COORDINA TE SYSTEM Lets Practice! Example:Graph the equation:y = I x I + 2 Steps: 1) Plot the first pointat the vertex(in thiscase the vertex islocatedatpoint(0,2)) 2) Plugin at least5 pointsfor the ‘x’ value(-2,-1,0,1,2 are usuallygood pointsto use) andfigure out what‘y’ equalswhen each ofthose numbersis pluggedin. 2.1 THE RECT ANGULAR COORDINA TE SYSTEM Lets Practice! Example:Graph the equation:y = I x I + 2 Steps: 1) Plot the first pointat the vertex(in thiscase the vertex islocatedatpoint(0,2)) 2) Plugin at least5 pointsfor the ‘x’ value(-2,-1,0,1,2 are usuallygood pointsto use) andfigure out what‘y’ equalswhen each ofthose numbersis pluggedin. Lets practice! When ‘x’ equals“-2” whatdoes ‘y’ equal? y = I -2 I + 2 *Remember, the absolutevalueofa number, positiveornegative,isit’s distanceawayfromzero, And youCAN’T HAVEA NEGATIVEDISTANCE 2.1 THE RECT ANGULAR COORDINA TE SYSTEM Lets Practice! Example:Graph the equation:y = I x I + 2 Steps: 1) Plot the first pointat the vertex(in thiscase the vertex islocatedatpoint(0,2)) 2) Plugin at least5 pointsfor the ‘x’ value(-2,-1,0,1,2 are usuallygood pointsto use) andfigure out what‘y’ equalswhen each ofthose numbersis pluggedin. Lets practice! When ‘x’ equals“-2” whatdoes ‘y’ equal? y = I -2 I + 2 y = 2 + 2 So, y = 4 thisis your‘y’ Valuefor when ‘x’ = -2! 2.1 THE RECT ANGULAR COORDINA TE SYSTEM Lets Practice! Example:Graph the equation:y = I x I + 2 1) Plot the first pointat the vertex(in thiscase the vertex islocatedatpoint(0,2)) 2) Plugin at least5 pointsfor the ‘x’ value(-2,-1,0,1,2 are usuallygood pointsto use) andfigure out what‘y’ equalswhen each ofthose numbersis pluggedin. 3) Now thatyou knowhow to find the ‘y’ valueswhen ‘x’ equals A certain input,findallof the points! 2.1 THE RECT ANGULAR COORDINA TE SYSTEM Lets Practice! Example:Graph the equation:y = I x I + 2 Steps: 1) Plot the first pointat the vertex(in thiscase the vertex islocatedatpoint(0,2)) 2) Plugin at least5 pointsfor the ‘x’ value(-2,-1,0,1,2 are usuallygood pointsto use) andfigure out what‘y’ equalswhen each ofthose numbersis pluggedin. 3) Now thatyou knowhow to find the ‘y’ valueswhen ‘x’ equals A certain input,findallof the points! If youdid yourmath right, youshouldend up with pointsthatare: (-2, 4), (-1, 3), (0, 2), (1, 3), (2, 4) 2.1 THE RECT ANGULAR COORDINA TE SYSTEM Lets Practice! Example:Graph the equation:y = I x I + 2 Steps: 1) Plot the first pointat the vertex(in thiscase the vertex islocatedatpoint(0,2)) 2) Plugin at least5 pointsfor the ‘x’ value(-2,-1,0,1,2 are usuallygood pointsto use) andfigure out what‘y’ equalswhen each ofthose numbersis pluggedin. 3) Now thatyou knowhow to find the ‘y’ valueswhen ‘x’ equals A certain input,findallof the points! 4) Now thatyou haveyourpoints: (-2, 4), (-1, 3), (0, 2), (1, 3), (2, 4) Plot them! 2.1 THE RECT ANGULAR COORDINA TE SYSTEM Lets Practice! Example:Graph the equation:y = I x I + 2 Steps: 1) Plot the first pointat the vertex(in thiscase the vertex islocatedatpoint(0,2)) 2) Plugin at least5 pointsfor the ‘x’ value(-2,-1,0,1,2 are usuallygood pointsto use) andfigure out what‘y’ equalswhen each ofthose numbersis pluggedin. 3) Now thatyou knowhow to find the ‘y’ valueswhen ‘x’ equals A certain input,findallof the points! 4) Now thatyou haveyourpoints: (-2, 4), (-1, 3), (0, 2), (1, 3), (2, 4) Plot them! 2.1 THE RECT ANGULAR COORDINA TE SYSTEM Lets Practice! Example:Graph the equation:y = I x I + 2 Steps: 1) Plot the first pointat the vertex(in thiscase the vertex islocatedatpoint(0,2)) 2) Plugin at least5 pointsfor the ‘x’ value(-2,-1,0,1,2 are usuallygood pointsto use) andfigure out what‘y’ equalswhen each ofthose numbersis pluggedin. 3) Now thatyou knowhow to find the ‘y’ valueswhen ‘x’ equals A certain input,findallof the points! 4) Now thatyou haveyourpoints: (-2, 4), (-1, 3), (0, 2), (1, 3), (2, 4) Plot them! 5) After the pointsare plotted,draw yourgraph! 2.1 THE RECT ANGULAR COORDINA TE SYSTEM Lets Practice! Example:Graph the equation:y = I x I + 2 Steps: 1) Plot the first pointat the vertex(in thiscase the vertex islocatedatpoint(0,2)) 2) Plugin at least5 pointsfor the ‘x’ value(-2,-1,0,1,2 are usuallygood pointsto use) andfigure out what‘y’ equalswhen each ofthose numbersis pluggedin. 3) Now thatyou knowhow to find the ‘y’ valueswhen ‘x’ equals A certain input,findallof the points! 4) Now thatyou haveyourpoints: (-2, 4), (-1, 3), (0, 2), (1, 3), (2, 4) Plot them! 5) After the pointsare plotted,draw yourgraph! 6) Alldone! END OF THE DEMO • Well I hope youenjoyedmy “note taking”style!I planonmakingallofthe notesassimple and hopefullyeasy to follow likethose were! I willalso post studyguideson Study soup about4 daysbefore each test, so fear not, I got you guyscovered. Here isthe linktosee allof my future uploads! • https://studysoup.com/note/2309867/wsu-math-106-week-1-fall-2016

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