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College Algebra

by: Annamarie Kunze

College Algebra MATH 1340

Annamarie Kunze
University of Texas-Pan American (UTPA)
GPA 3.82

Frances Alvarado

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About this Document

Frances Alvarado
Class Notes
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This 5 page Class Notes was uploaded by Annamarie Kunze on Thursday October 29, 2015. The Class Notes belongs to MATH 1340 at University of Texas-Pan American (UTPA) taught by Frances Alvarado in Fall. Since its upload, it has received 20 views. For similar materials see /class/231311/math-1340-university-of-texas-pan-american--utpa- in Math at University of Texas-Pan American (UTPA).

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Date Created: 10/29/15
ExponenT Rules WriTTen by Frances EM Alvarado OcTober 7 2006 LisTed below are The ExponenT Rules ThaT you will be using all The way Through MaTh 1340 Below each rule is aT leasT one example and a brief exp lanaTion of how They work For This course we will resTricT The exponenTs To whole numbers buT in InTermediaTe Algebra and College Algebra your exponenTs can be any real number including fracTions and decimals ExponenT Rules 1 x m x x mn x3x2x32x5 CondiTions Procedure x m 2 n x quot 39 quot x 5 x 2 x 539 2 x 3 CondiTions x Procedure x m n x mu x 3 2 x 32 x6 CondiTions Procedure 1 2 1 2 2 1 2 1 2 MulTiplicaTion Same Base Add The ExponenTs Keep The base Division Same Base SubTracT The ExponenTs Keep The base Base raised To an ExponenT Then raised To a second exponenT MuITipIy ExponenTs Keep Base 4 5 e 7 CondiTions Procedure CondiTions Procedure CondiTions Procedure CondiTions Procedure 1 MulTiplicaTion inside ParenThesis 1 Raise each base To The EXponenT ouTside This rule is quiTe ofTen combined wiTh Rule 3 1 Division inside ParenThesis 1 Raise each base To The EXponenT ouTside This rule is quiTe ofTen combined wiTh Rule 3 1 Raised To The Zero EXponenT 1 Any Base excepT O raised To The Zero EXponenT is equal To 1 1 Raised To a NegaTive EXponenT 1 Find The Reciprocal of Base raised To The EXponenT I prefer To Think of iT as You are in The wrong place bud if iT39s in The numeraTor iT belongs in The denominaTor and vice versa InequaliTies WriTTen by Frances EM Alvarado February 17 2007 We will discuss Simple InequaliTies Compound InequaliTies AbsoluTe Value InequaliTies and for The momenT Polynomial InequaliTies RaTional InequaliTies will be discussed laTer in The semesTer Simple InequaliTies are noTed by The facT ThaT They have only one InequaliTy Symbol in Them For Example 4X 3 2 27 is a simple inequaliTy The good news is you have The abiIiTy To solve Them if you know how To solve 4X 3 27 The difference comes aT The end when you have To inTerpreT The soluTion seT So To solve The inequaliTy we will subTracT 3 and Then divide by 4 Example 1 4X 3 2 27 4X 3 3 2 27 3 4X 2 24 4X 24 7 Z 7 4 4 X 2 6 Algebraic form of The answer 439H Graphic form of The answer 0 6 10 6 no InTerval form of The answer Be prepared To give all 3 forms of The soluTion To any problem There is one more Thing we should always remember abouT InequaliTies and This rule applies To ALL inequaliTies IT only occurs if you mulTiply or divide by a negaTive number buT iT is eXTremely imporTanT The rule is lisTed below Rule CondiTion If you mulTiply or divide by a negaTive number Procedure you need To flip The inequaliTy symbol Example 2 4X32 27 4X3 3 227 3 4X2 24 4X 24 6 is someTimes called The criTical value 10 6 O 00 6 NexT is Compound InequaliTies These rely on you undersTanding The difference beTween 2 liTTle words quotorquot Si quotandquot One real life comparison would be The idea of promising someone dinner OR a moviequot vs dinner AND a moviequot quotORquot means you have promise To do one or The oTher buT noT boTh quotANDquot means you musT saTisfy boTh or you have lied See examples below Example 3 4X 3 2 27 or 5X 2 lt 18 4x 2 24 or 5x lt 2o X 2 6 or X lt 4 4 and 6 are criTical values 4 6 00 4 or 6oo Example4 4X3527 and 5X2gt 18 4XS24 and 5X gt 20 X s 6 and X gt 4 4 and 6 are criTical values 7 t J 4 6 46 NeXT we will discuss AbsoluTe Value InequaliTies which inTeresTingly enough wind up being a compound inequaliTy Which means eiTher an quotorquot case or an quotandquot case depending on The InequaliTy symbol So here we go firsT we will look aT gt or 2 greaTer Than or greaTer Than and equal As iT Turns ouT if you combine a gt or 2 symbol wiTh The AbsoluTe Value symbol you geT an quotorquot case Oh yeah before I go any farTher This is assuming you have isolaTed The AbsoluTe Value before deTermining wheTher The inequaliTy is greaTer Than or less Than Example5 lZX 1l3216 iZX 1 213 isolaTed Case 1 Case 2 2X 1 213 or 2X 1 S 13 noTe if you negaTe The informaTion ouTside The absoluTe value symbols you musT flip The inequaliTy symbol 2X 2 14 or 2X 3 12 or X s 6 6 Si 7 are criTical values 1 I V e oo 6 or 7oo Example 6 iax 1 3lt 16 iZX 1i lt13 isolaTed Case 1 Case 2 2X 1lt13 and 2X 1gt 13 2X lt14 and 2X gt 12 X lt 7 and X gt 6 6 Si 7 are criTical values 6 7


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