(Abut the final) [COLLEGE ALGEBRA EXAM I REVIEW TOPICS] ( u s e t h i s t m a k e s u r e y u a r e r e a d y ) The department writes the final exam s I dn't really knw what's n it and I can't very well tell yu what t study. Yu shuld be prepared fr everything that we've cvered this term, which is Chapters 1-5 minus the things that we skipped Knw hw t determine if a given relatin is a functin (input vs. utput, vertical line test) The exam will fcus n chapters 4 &5 (abut 75% f the exam), s there still will be sme things frm chapters 1-3. Stry prblems and being able t make sense f an answer using wrds is an imprtant part f the curse, and smewhere between 50-65% f the exam will be wrd prblems (at least, that s been true in past exams) Yu may use a duble sided 3X5 ntecard fr the final scratch paper will als be prvided Yu will need yur calculatr, but yu are expected t shw all f yur wrk, unless explicitly stated therwise make sure yur batteries are wrking. I will nt be lending ut my calculatr n the exam day. There may be a ptin where yu may nt use yur calculatr, and instructin will be iven at the time f the final exam. N scantrn/bluebk needed Belw are the tpics we have cvered in the curse s far listed by chapter. (chapter 1) Intr t Functins and Their Graphs (1.3) functins and their representatins (page 26) Understand the definitin f a functin. Knw hw t determine if a given relatin is a functin (input vs. utput, vertical line test) Knw hw t find dmain and range f a functin (via graph, equatin, blb diagram, table) (1.4) types f functins (page 42) Knw hw t find the slpe f a line given: Tw pints, A perpendicular/parallel slpe and a pint Knw the 3 different types f functins (linear, nnlinear, cnstant) Knw discrete vs. cntinuus Difference qutient. (chapter 2) Linear Functins and Equatins (2.1) Equatins f lines (page 68) Knw hw t find the equatin f a line using pint-slpe r slpe-intercept frm Knw hw t use the standard frm f a linear equatin t find the x and y-intercepts Understand hw t set up and slve direct variatin prblems. (2.2) Linear Equatins (page 86) Knw hw t set up and slve linear equatins given a paragraph f infrmatin (this was the sectin with the velciraptr prblem, as well as the prblem with the radiatr!) Knw hw t slve frmulas fr specific variables (i.e. slve fr h: )
(2.4) Mre Mdeling With Functins (page 118) Knw hw t set up and mdel situatins using linear functins give by: Knw hw t use the LinReg (ax+b) functin n ur calculatr Understand hw t graph and evaluate piecewise functins Knw direct variatin ( ) Be cmfrtable with graphing, evaluating, and finding the dmains f piecewise functins (chapter 3) Quadratic Functins and Equatins (3.1) Quadratic Functins and Mdels (page 156) Knw the basic anatmy f a parabla Understand hw t find the vertex f a quadratic functin either vertex f standard frm Knw hw t find the maximum r minimum values f quadratic functins (by finding the vertex) Knw hw t set up quadratic functins that mdel specific situatins Knw hw t use the QuadReg functin n ur calculatr t find best fit parablas Knw the general frm f prjectile mtin ( ) (3.2) Quadratic Equatins and Prblem Slving (page 172) Knw the main ways t slving quadratic equatins (sans cmpleting the square) Knw hw t set up and slve quadratic equatins that mdel specific situatins. (3.3) Cmplex Numbers (page 188) Will nt be n first exam ran ut f time due t sickness. (3.5) Transfrmatins (page 206) Knw hw t use the 10 transfrmatins t manipulate graphs and their tables. (chapter 4) Mre Nnlinear Functins And Equatins (4.1) Mre Nnlinear Functins and their graphs (page 232) Knw and understand the definitin f a plynmial functin Knw hw t find lcal and abslute extrema Be able t identify if functins are dd r even by examining the graph f the equatins and checking its symmetry; r using the definitins f dd and even ( and respectively) (4.2) Plynmial Functins and Mdels (page 243) Knw hw t determine a plynmials functin s end behavir (falls t left, rises t right, etc ) knw hw an even degree ply functin behaves knw hw an dd degree ply functin behaves be familiar with limit ntatin ( etc ) Knw hw t determine a functins minimum degree by lking at the graph (using turning pints and x-intercepts) Knw hw t determine whether a ply functin s leading cefficient is psitive r negative (4.3) Divisin f Plynmials (page 260) Knw hw t divide plynmials using lng divisin synthetic divisin Understand hw dividing plynmials is useful in determining the zers f a ply functin
(4.4) Real Zers f Plynmial Functins (page 267) Understand the imprtance f the factr therem Knw hw t write a plynmial in cmplete factred frm Knw hw t find the multiplicities f a functin given it s graph and hw t write multiplicities in the cmplete factred frm Knw hw t use the ratinal zers test t find the ratinal zers f a plynmial functin Knw hw t find the number f pssible psitive zers and the number f pssible negative zers using Descartes Rule f Signs (4.5) The Fundamental Therem f Algebra (page 283) Knw what the fundamental therem f algebra says, and why it is s imprtant Understand that ANY plynmial functin can be written in cmplete factred frm using cmplex numbers Be able t find the cmplete factred frm f plynmials This may require using the ratinal zers test t find any real zers, then dividing thrugh using that zer t simplify the riginal plynmial int smething yu may be able t factr Be able t write cmplete factred frm given the leading cefficient and a few zers Knw the cmplex cnjugate zers therem (4.6) Ratinal Functins and their Mdels (page 289) Knw what a ratinal functin is and hw t find it s dmain Knw hw t find vertical and hrizntal asympttes given the functins graph the equatin f the functin (dn t frget hidden step #1!!!) Knw hw t graph ratinal functins by hand (using the 7 step prcess) remember that ratinal functins tend twards their asympttes (4.8) Radical Equatins and Pwer Functins (page 322) Knw hw t use the prperties f ratinal expnents t simplify radical expressins Knw hw t slve radical equatins (using mck s strategy fr slving radical eq s ) Knw what pwer functins and rt functins are and hw t find their dmains Knw hw t slve equatins with ratinal r negative expnents Understand hw t find the best fit curve f data using Pwer Regressin (chapter 5) Expnential and Lgarithmic Functins (5.1) Cmbining Functins (page 349) Knw hw t perfrm the fur basic peratins n functins ( ) and knw hw t evaluate thse functins at specific values analytically, numerically (given a table), and graphically (given a graph). Knw hw t find cmpsite functins given each functin, a table f values, r a graph f each functin. Be able t find the dmain f cmpsite functins. (5.2) Inverse Functins and Their Representatins (page 365) Knw hw t check if a functin is ne-t-ne (and further, knw what ne-t-neness means). Be able t find the inverse functin f ne-t-ne functins (use the step by step prcess we went ver in class with switching the x and y) Understand what it means fr tw functins t be inverses (knw what inverse means) Knw that when yu cmpse a functin with its inverse (and vice-versa) yu get the input x. Understand what it means fr tw functins t be inverses in relatin t their graphs (they are reflectins acrss the line y=x)
(5.3) Expnential Functins and Mdels (page 380) Knw hw t find the equatin f an expnential functin f the frm given a table f data. Knw the frmulas fr: Cmpund interest Cntinuus cmpund interest Radiactive decay Knw hw t use the abve frmulas (examples are given in the chapter sectin) (5.4) Lgarithmic Functins and Mdels (page 399) Knw the basic facts/prperties abut lgarithms (i.e. they are the inverse f expnential functins,,, etc ) Understand what a lgarithm is asking yu ( is asking: t what pwer must be raised in rder t get ). Knw hw t slve simple lgarithmic and expnential equatins (using the fact that lg functins and expnential functins are inverses). Be able t cnvert frm expnential frm t lgarithmic frm (5.5) Laws f Lgarithms (LLs) (page 415) Knw the 4 LL s and hw t use them t expand r cmbine expressins. (5.6) Expnential and Lgarithmic Equatins (page 423) Knw hw t slve mre cmplex lgarithmic equatins Knw hw t slve mre cmplex expnential equatins Essentially, sectin 5.6 is all abut slving equatins utilizing the laws f lgarithms in cmbinatin with the slving skills yu learned in sectin 5.4 (by using the inverse functin t get (5.7) Cnstructing Nnlinear Mdels (page 460) Knw hw t make a scatterplt f given data and determine which mdel t use (Additinal Thughts) There is n in-class review that I have fr yu guys. I dn t want t write a reviw and have students think that if I study nly this, I will be ready fr the final exam, because that isn t true and in fact I have n idea what s n the final. That being said, I have made an nline review (which is basically all ur past nline reviews crammed int ne review assignment) that yu guys can lk thrugh. There are five main ways I suggest reviewing: Lking ver past exams The nline review Lking thrugh yur ntes Ging thrugh the bk t sectins yu struggle with and ding sme f the prblems ut f that sectins hmewrk sectin Ging ver past hmewrk assignments Make sure yu get enugh sleep Sunday night befre the final! がんばってください