Chapters 8 & 9 Review for Final


 Beatrix Kelley
 10 months ago
 Views:
Transcription
1 Math Intermediate Algebra Professor Valdez Chapters 8 & 9 Review for Final SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Solve the formula for the indicated letter. 1) A = 1 3 πr2 for r > 0 1) Solve. 2) (9 + 3) 26 = 0 2) 3) = ) Solve the problem. 4) The weekl revenue R of a compan that sells to trucks is given b R = ( ). 4) How man units must be sold so the compan makes a weekl revenue of $60,000? Use the discriminant to determine the number and tpe of solutions for the equation. ) = 0 ) Use the discriminant of the equation to determine the number of intercepts. 6) f() = ) 7) f() = ) Graph the function function. 8) f() = ) Solve the problem. 9) The cost in millions of dollars for a compan to manufacture thousand automobiles is given b the function C() = Find the number of automobiles that must be produced to minimize the cost. 9) 1
2 10) A to rocket is launched straight upward with an initial velocit of 32 feet per second from a 4foot high platform. The height h, in feet, of the rocket above ground t sec after it is launched is modeled b the function h(t) = 16t t ) i) When will the rocket reach its maimum height? What is that height? ii) How man seconds does it take until the rocket hits the ground? Round to the nearest tenth of a second if necessar. Solve the equation. 11) = 0 11) 12) (m + 4) 2/3 + 9(m + 4) 1/ = 0 12) Write a quadratic equation having the given numbers as solutions. 13) 9, onl solution 13) 14)  4, 7 14) 1) 2i, 2i 1) Solve. Then graph the solution. 16) < 0 16) ) ) Graph the function function. 18) f() = (3) 18) Given f() and g(), perform the indicated operation. 19) f() = ; g() = 44 Find (f + g)(). 19) 2
3 20) f() = + 4 ; g() =  4 Find (f g)(). Given f() and g(), find the composition. 21) f() = ; g() = 46 Find (g f)(). 20) 21) 22) f() = 3 ; g() = 21 Find (f g)(13). 22) Evaluate. 23) Find (f/g)(4) given f() = and g() = ) Determine whether the function whose graph is shown is a onetoone function. 24) 24) Given the graph of a onetoone function, sketch the graph of its inverse. 2) 2) Find the inverse of the function represented b the set of ordered pairs. 26) f: {(1, 14), (11, 14), (20, 10)} 26) 3
4 Find the inverse of the following onetoone function. 27) f() = ) 28) f() = ) Decide whether or not the functions are inverses of each other. 29) f() = 9 + 4, g() = ) 30) f() = 3 78, g() = ) Evaluate the function for the given value. 31) f() = 6 1 ; f(4) 31) Solve. 32) = ) Solve the problem. 33) The number of bacteria growing in an incubation culture increases with time according to B() = 900(3), where is time in das. What was the initial number of bacteria in the incubation culture? 34) The halflife of a certain radioactive substance is 14 ears. Suppose that at time t = 0, there are 27 g of the substance. Then after t ears, the number of grams of the substance remaining will be N(t) = 27 1 t/28. How man grams of the 2 33) 34) substance will remain after 70 ears? Round to the nearest tenth. 3) What will be the amount in an account with initial principal $000 if interest is compounded continuousl at an annual rate of 3.2% for 6 ears? 3) Write the logarithmic equation in its equivalent eponential form. 36) log 7 49 = 2 36) 4
5 Write the eponential equation in its equivalent logarithmic form. 37) 12 = 2 37) Solve. Round the answer to three decimal places. 38) 43 = 21 38) Evaluate. 39) log ) 40) log 40) 41) log ) Write the epression as the sum or difference of logarithms. 42) log 4 (16 9) 42) 43) log m m + 16 m ) Evaluate. 44) log 19 44) 4) ln e 9 4) 46) 10 log 9 46) Solve. 47) The formula for the ph of a solution is given b the logarithmic equation ph = log [H + ], where [H + ] is the concentration of hdrogen ions. The concentration of hdrogen ions of a specific solution is Calculate the ph of this solution. Provide an appropriate response. 48) Write the epression as a single logarithm: 47) 48) log b (  3)  6 log b
6 Write the epression as the sum or difference of logarithms. 49) log b 4 9 b ) Solve. 0) log 4 = 3 0) 1) log 8 2 = 1) 2) log 2 ( + 4) + log 2 (  2) = 4 2) Use a calculator to approimate the logarithm to four decimal places. 3) log ) Solve the problem. 4) The size P of a rabbit population at time t (in ears) is modeled b the function P(t) = 600e 0.16t. 4) After how man ears will the population reach 3000? Round to the nearest hundredth. ) $600 is invested at 4% compounded quarterl. In how man ears will the account have grown to $8000? Round our answer to the nearest tenth of a ear. ) 6
7 Answer Ke Testname: CHAPTERS 8 AND 9 REVIEW 1) r = 3A π 2) , ) 2 + i 38 6, 2  i ) 2340 units ) Two realnumber solutions 6) One intercept 7) No intercepts 8) Verte: (1,4); ais of sm: = 1; intercepts: (1,0), (3,0); intercept: (0,3) ) 4 thousand automobiles 10) i) 20 ft in 1 sec ii) 2.1 sec 11) ±1, ± 3 12) 129, ) = 0 14) = 0 1) = 0 16) (3, ) )  7 4,
8 Answer Ke Testname: CHAPTERS 8 AND 9 REVIEW 18) ) , 4, ) ) (g f)() = ) 3 23) ) Not onetoone 2) ) f 1 : {(14, 1), (14, 11), (10, 20)} 27) f 1 () = ) f 1 () = ) Not inverses 30) Inverses 8
9 Answer Ke Testname: CHAPTERS 8 AND 9 REVIEW 31) ) 3 33) ) 4.8 g 3) $ ) 7 2 = 49 37) log 1/ 2 = 2 38) ) 2 40) ) 0 42) 2 + log ) log m (m + 16 )  log m (m + 13 ) 44) 19 4) 9 46) 9 47) 6 48) log b (  3) 6 49) 9 4 log b + 22log b 0) 64 1) 1 3 2) 4 3) ) r ).2 ears 9
MAT 1033C  MartinGay Intermediate Algebra Chapter 8 (8.1, 8.2, 8.5, 8.6) Practice for the Exam
MAT 33C  MartinGa Intermediate Algebra Chapter 8 (8.1 8. 8. 8.6) Practice for the Eam Name Date Da/Time: SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
More informationM122 College Algebra Review for Final Exam
M1 College Algebra Review for Final Eam Revised Fall 017 for College Algebra  Beecher All answers should include our work (this could be a written eplanation of the result, a graph with the relevant feature
More informationSHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Spring 0 Math 08 Eam Preparation Ch Dressler Name SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Solve the quadratic equation b the square root propert.
More informationC)not a function. B) function domain: {3, 2, 4, 6} range: {7, 4, 2, 1}
Name Spring Semester Final Review (Dual) Precalculus MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Determine whether the relation represents a function.
More informationMath125 Exam 5 (Final) Review Name. Do the following as indicated. 17) log 17x = 1.2 (Round answer to four decimal places.)
Math12 Eam (Final) Review Name Do the following as indicated. For the given functions f and g, find the requested function. 1) f() =  6; g() = 92 Find (f  g)(). 2) f() = 33 + 1; g() = 22 Find (f g)().
More information121D Practice Test #
D Practice Test # College Algebra / Math D GARAGE (Prof. Vasan) Student Name/ID:. Write the epression as a single logarithm. 5log 8 w + 5 log 8 3log 8 z. Solve for. log + 3 = log + 6 ALEKS D Practice Test
More informationMath Chapter 5  More Practice MUST SHOW WORK IN ALL PROBLEMS  Also, review all handouts from the chapter, and homework from the book.
Math 101  Chapter  More Practice Name MUST SHOW WORK IN ALL PROBLEMS  Also, review all handouts from the chapter, and homework from the book. Write the equation in eponential form. 1) log 2 1 4 = 2
More informationThe speed the speed of light is 30,000,000,000 m/s. Write this number in scientific notation.
Chapter 1 Section 1.1 Scientific Notation Powers of Ten 1 1 1.1.1.1.1 Standard Scientific Notation N n where 1 N and n is an integers Eamples of numbers in scientific notation. 8.17 11 Using Scientific
More informationSHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Math 03 CFair College Departmental Final Eamination Review SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Graph the linear equation b the method of
More informationMA Lesson 14 Notes Summer 2016 Exponential Functions
Solving Eponential Equations: There are two strategies used for solving an eponential equation. The first strategy, if possible, is to write each side of the equation using the same base. 3 E : Solve:
More information6. The braking distance (in feet) for a car traveling 50 miles per hour on a wet uphill road is given by
MATH 34  College Algebra Review for Test 3 Section 4.6. Let f ( ) = 3 5 + 4. (a) What is the domain? (b) Give the intercept(s), if an. (c) Give the intercept(s), if an. (d) Give the equation(s) of the
More informationMTH 112 Practice Test 3 Sections 3.3, 3.4, 3.5, 1.9, 7.4, 7.5, 8.1, 8.2
MTH 112 Practice Test 3 Sections 3.3, 3., 3., 1.9, 7., 7., 8.1, 8.2 Use properties of logarithms to epand the logarithmic epression as much as possible. Where possible, evaluate logarithmic epressions
More information3.1 Exponential Functions and Their Graphs
.1 Eponential Functions and Their Graphs Sllabus Objective: 9.1 The student will sketch the graph of a eponential, logistic, or logarithmic function. 9. The student will evaluate eponential or logarithmic
More informationName Please print your name as it appears on the class roster.
Berkele Cit College Practice Problems Math 1 Precalculus  Final Eam Preparation Name Please print our name as it appears on the class roster. SHORT ANSWER. Write the word or phrase that best completes
More informationPreCalculus Exponential/Logarithm Quiz 3A Name Date Period Part 1: NonCalculator 1. Determine which graph below is the graph of the function.
PreCalculus Exponential/Logarithm Quiz A Name Date Period Part : NonCalculator. Determine which graph below is the graph of the function. E). Identif the operation that will transform the graph of (
More informationInstructor: Imelda Valencia Course: A3 Honors Pre Calculus
Student: Date: Instructor: Imelda Valencia Course: A3 Honors Pre Calculus 01 017 Assignment: Summer Homework for those who will be taking FOCA 017 01 onl available until Sept. 15 1. Write the epression
More informationFinal Exam Review Part 2 #4
Final Eam Review Part # Intermediate Algebra / MAT 135 Fall 01 Master (Prof. Fleischner) Student Name/ID: 1. Solve for, where is a real number. + = 8. Solve for, where is a real number. 9 1 = 3. Solve
More informationPRACTICE FINAL EXAM. 3. Solve: 3x 8 < 7. Write your answer using interval notation. Graph your solution on the number line.
MAC 1105 PRACTICE FINAL EXAM College Algebra *Note: this eam is provided as practice onl. It was based on a book previousl used for this course. You should not onl stud these problems in preparing for
More informationLast modified Spring 2016
Math 00 Final Review Questions In problems 6, perform the indicated operations and simplif if necessar.. 8 6 8. 7 6. ( i) ( 4 i) 4. (8 i). ( 9 i)( 7 i) 6. ( i)( i) In problems 7, solve the following applications.
More informationSTANDARD FORM is a QUADRATIC FUNCTION and its graph is a PARABOLA. The domain of a quadratic function is the set of all real numbers.
EXERCISE 23 Things to remember: 1. QUADRATIC FUNCTION If a, b, and c are real numbers with a 0, then the function f() = a 2 + b + c STANDARD FORM is a QUADRATIC FUNCTION and its graph is a PARABOLA. The
More informationf 0 ab a b: base f
Precalculus Notes: Unit Eponential and Logarithmic Functions Sllabus Objective: 9. The student will sketch the graph of a eponential, logistic, or logarithmic function. 9. The student will evaluate eponential
More informationName Class Date. Quadratic Functions and Transformations. 4 6 x
 Quadratic Functions and Transformations For Eercises, choose the correct letter.. What is the verte of the function 53()? D (, ) (, ) (, ) (, ). Which is the graph of the function f ()5(3) 5? F 6 6 O
More informationFind the distance between the pair of points. 2) (7, 7) and (3, 5) A) 12 3 units B) 2 5 units C) 6 units D) 12 units B) 8 C) 63 2
Sample Departmental Final  Math 9 Write the first five terms of the sequence whose general term is given. 1) a n = n 2  n 0, 2,, 12, 20 B) 2,, 12, 20, 30 C) 0, 3, 8, 1, 2 D) 1,, 9, 1, 2 Find the distance
More informationMth 95 Module 4 Chapter 8 Spring Review  Solving quadratic equations using the quadratic formula
Mth 95 Module 4 Chapter 8 Spring 04 Review  Solving quadratic equations using the quadratic formula Write the quadratic formula. The NUMBER of REAL and COMPLEX SOLUTIONS to a quadratic equation ( a b
More information9 (0, 3) and solve equations to earn full credit.
Math 0 Intermediate Algebra II Final Eam Review Page of Instructions: (6, ) Use our own paper for the review questions. For the final eam, show all work on the eam. (6, ) This is an algebra class do not
More informationSHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Practice for the Final Eam MAC 1 Sullivan Version 1 (2007) SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Find the distance d(p1, P2) between the points
More informationBARUCH COLLEGE MATH 2205 FALL 2007
BARUCH COLLEGE MATH 05 FALL 007 MANUAL FOR THE UNIFORM FINAL EXAMINATION Joseph Collison, Warren Gordon, Walter Wang, April Allen Materowski, Sarah Harne The final eamination for Math 05 will consist of
More informationMath 125 Practice Problems for Test #3
Math Practice Problems for Test # Also stud the assigned homework problems from the book. Donʹt forget to look over Test # and Test #! Find the derivative of the function. ) Know the derivatives of all
More information71. Exploring Exponential Models. Vocabulary. Review. Vocabulary Builder. Use Your Vocabulary. 1. Cross out the expressions that are NOT powers.
71 Eploring Eponential Models Vocabular Review 1. Cross out the epressions that are NOT powers. 16 6a 1 7. Circle the eponents in the epressions below. 5 6 5a z Vocabular Builder eponential deca (noun)
More informationExam practice Disclaimer. The actual test does not mirror this practice. This is meant as a means to help you understand the material.
Eam 3 24 practice Disclaimer. The actual test does not mirror this practice. This is meant as a means to help ou understand the material. Graph the function. 1) f() = 2 2 + 4 + 3 1) Sketch the graph of
More informationMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
MAC 0 Module Test 8 Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the function value. ) Let f() = . Find f(). 8 6 C) 8 6 Objective:
More informationHW 5 Date: Name Use Scantron 882E to transfer the answers. Graph. 1) y = 5x
HW 5 Date: Name Use Scantron 88E to transfer the answers. Graph. ) = 5 ) A)             C) D)             Differentiate. ) f() = e8 A) e8 8e8 C) 8e D) 8 e 8 ) 3) = e9/ A) 9 e 9/
More informationMath 3201 Chapter 6 Review
Math 0 Chapter 6 Review Multiple Choice Identif the choice that best completes the statement or answers the question.. Which of the following is an exponential function? A. f(x) = x B. g(x) = ( ) x C.
More informationTO THE STUDENT: To best prepare for Test 4, do all the problems on separate paper. The answers are given at the end of the review sheet.
MATH TEST 4 REVIEW TO THE STUDENT: To best prepare for Test 4, do all the problems on separate paper. The answers are given at the end of the review sheet. PART NONCALCULATOR DIRECTIONS: The problems
More informationPrecalculus Fall Final Exam REVIEW Evaluate the function at the specified value(s) of the independent variable and simplify.
Precalculus Fall Final Eam EVIEW 016017 1. Model the following situation with a linear equation in slopeintercept form. 4 The gas tank in a truck holds 15 gallons. The truck uses gallon per mile. 7.
More informationFind the integral. 12) 15)
Find the location of the indicated absolute etremum within the specified domain. ) Minimum of f() = / /; [0, ] 8) Maimum h() ) Minimum of f() =  +  ; [, ] ) Minimum of f() = ( + )/; [, ] ) Maimum
More informationMath Want to have fun with chapter 4? Find the derivative. 1) y = 5x2e3x. 2) y = 2xex  2ex. 3) y = (x22x + 3) ex. 9ex 4) y = 2ex + 1
Math 160  Want to have fun with chapter 4? Name Find the derivative. 1) y = 52e3 2) y = 2e  2e 3) y = (22 + 3) e 9e 4) y = 2e + 1 5) y = e  + 1 e e 6) y = 32 + 7 7) y = e31 5 Use calculus to find
More informationlim a, where and x is any real number. Exponential Function: Has the form y Graph y = 2 x Graph y = 2 x Graph y = Graph y = 2
Precalculus Notes Da 1 Eponents and Logarithms Eponential Function: Has the form a, where and is an real number. Graph = 2 Graph = 2 +2 + 1 1 1 Graph = 2 Graph = 3 1 2 2 2 The Natural Base e (Euler s
More informationFunctions. Essential Question What are some of the characteristics of the graph of an exponential function? ) x e. f (x) = ( 1 3 ) x f.
7. TEXAS ESSENTIAL KNOWLEDGE AND SKILLS A..A Eponential Growth and Deca Functions Essential Question What are some of the characteristics of the graph of an eponential function? You can use a graphing
More informationAlgebra 22nd Semester Exam Review 11
Algebra 22nd Semester Eam Review 11 Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Determine which binomial is a factor of. a. 14 b. + 4 c. 4 d. + 8
More information4. Sketch the graph of the function. Ans: A 9. Sketch the graph of the function. Ans B. Version 1 Page 1
Name: Online ECh5 Prep Date: Scientific Calc ONLY! 4. Sketch the graph of the function. A) 9. Sketch the graph of the function. B) Ans B Version 1 Page 1 _ 10. Use a graphing utility to determine which
More information3.1Quadratic Functions & Inequalities
3.1Quadratic Functions & Inequalities Quadratic Functions: Quadratic functions are polnomial functions of the form also be written in the form f ( ) a( h) k. f ( ) a b c. A quadratic function ma Verte
More informationMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. B) x y =
Santa Monica College Practicing College Algebra MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Write the standard equation for the circle. 1) Center
More informationUnit 5: Exponential and Logarithmic Functions
71 Rational eponents Unit 5: Eponential and Logarithmic Functions If b is a real number and n and m are positive and have no common factors, then n m m b = b ( b ) m n n Laws of eponents a) b) c) d) e)
More informationExponential and Logarithmic Functions
7 Eponential and Logarithmic Functions 7.1 Eponential Growth and Deca Functions 7. The Natural Base e 7.3 Logarithms and Logarithmic Functions 7. Transformations of Eponential and Logarithmic Functions
More informationNonlinear Systems. No solution One solution Two solutions. Solve the system by graphing. Check your answer.
810 Nonlinear Sstems CC.91.A.REI.7 Solve a simple sstem consisting of a linear equation and a quadratic equation in two variables algebraicall and graphicall. Objective Solve sstems of equations in two
More informationEvaluate Logarithms and Graph Logarithmic Functions
TEKS 7.4 2A.4.C, 2A..A, 2A..B, 2A..C Before Now Evaluate Logarithms and Graph Logarithmic Functions You evaluated and graphed eponential functions. You will evaluate logarithms and graph logarithmic functions.
More informationAP Calculus Summer Homework MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
AP Calculus Summer Homework 20152016 Part 2 Name Score MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the distance d(p1, P2) between the points
More informationMath 102 Final Exam Review
. Compute f ( + h) f () h Math 0 Final Eam Review for each of the following functions. Simplify your answers. f () 4 + 5 f ( ) f () + f ( ). Find the domain of each of the following functions. f( ) g (
More informationMath 1050 REVIEW for Exam 1. Use synthetic division to find the quotient and the remainder. 1) x3  x2 + 6 is divided by x + 2
Math 0 REVIEW for Eam 1 Use snthetic division to find the quotient and the remainder. 1) 32 + 6 is divided b + 2 Use snthetic division to determine whether  c is a factor of the given polnomial. 2) 332
More informationSummary, Review, and Test
45 Chapter Equations and Inequalities Chapter Summar Summar, Review, and Test DEFINITIONS AND CONCEPTS EXAMPLES. Eponential Functions a. The eponential function with base b is defined b f = b, where b
More informationAlgebra II. Chapter 8 Notes. Exponential and Logarithmic Functions. Name
Algebra II Chapter 8 Notes Eponential and Logarithmic Functions Name Algebra II 8.1 Eponential Growth Toda I am graphing eponential growth functions. I am successful toda when I can graph eponential growth
More informationQuadratic Function. Parabola. Parent quadratic function. Vertex. Axis of Symmetry
Name: Chapter 10: Quadratic Equations and Functions Section 10.1: Graph = a + c Quadratic Function Parabola Parent quadratic function Verte Ais of Smmetr Parent Function =  1 0 1 1 Eample 1: Make a table,
More informationLinear and Nonlinear Systems of Equations. The Method of Substitution. Equation 1 Equation 2. Check (2, 1) in Equation 1 and Equation 2: 2x y 5?
3330_070.qd 96 /5/05 Chapter 7 7. 9:39 AM Page 96 Sstems of Equations and Inequalities Linear and Nonlinear Sstems of Equations What ou should learn Use the method of substitution to solve sstems of linear
More informationUnit 3 Exam Review Questions MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Unit Eam Review Questions MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Some Useful Formulas: Compound interest formula: A=P + r nt n Continuously
More informationFair Game Review. Chapter 8. Graph the linear equation. Big Ideas Math Algebra Record and Practice Journal
Name Date Chapter Graph the linear equation. Fair Game Review. =. = +. =. =. = +. = + Copright Big Ideas Learning, LLC Big Ideas Math Algebra Name Date Chapter Fair Game Review (continued) Evaluate the
More informationMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Stud Guide for Test II Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Graph the linear inequalit. 1) 3 + 6 1)     A) B)        
More information3.1 Graph Quadratic Functions
3. Graph Quadratic Functions in Standard Form Georgia Performance Standard(s) MMA3b, MMA3c Goal p Use intervals of increase and decrease to understand average rates of change of quadratic functions. Your
More informationSAMPLE. Exponential and logarithmic functions
Objectives C H A P T E R 5 Eponential and logarithmic functions To graph eponential and logarithmic functions. To graph transformations of the graphs of eponential and logarithmic functions. To introduce
More informationName: Period: SM Starter on Reading Quadratic Graph. This graph and equation represent the path of an object being thrown.
SM Name: Period: 7.5 Starter on Reading Quadratic Graph This graph and equation represent the path of an object being thrown. 1. What is the ais measuring?. What is the yais measuring? 3. What are the
More informationExponential and Logarithmic Functions, Applications, and Models
86 Eponential and Logarithmic Functions, Applications, and Models Eponential Functions In this section we introduce two new tpes of functions The first of these is the eponential function Eponential Function
More informationPreCalculus Final Exam Review Revised Spring 2014
PreCalculus Final Eam Review Revised Spring 0. f() is a function that generates the ordered pairs (0,0), (,) and (,). a. If f () is an odd function, what are the coordinates of two other points found
More informationMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Eam Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Determine from the graph whether the function has an absolute etreme values on the interval
More informationTwoYear Algebra 2 A Semester Exam Review
Semester Eam Review TwoYear Algebra A Semester Eam Review 05 06 MCPS Page Semester Eam Review Eam Formulas General Eponential Equation: y ab Eponential Growth: A t A r 0 t Eponential Decay: A t A r Continuous
More information3.2 LOGARITHMIC FUNCTIONS AND THEIR GRAPHS
Section. Logarithmic Functions and Their Graphs 7. LOGARITHMIC FUNCTIONS AND THEIR GRAPHS Ariel Skelle/Corbis What ou should learn Recognize and evaluate logarithmic functions with base a. Graph logarithmic
More informationUnit 5: Quadratic Functions
Unit 5: Quadratic Functions LESSON #2: THE PARABOLA APPLICATIONS AND WORD PROBLEMS INVERSE OF A QUADRATIC FUNCTION DO NOW: Review from Lesson #1 (a)using the graph shown to the right, determine the equation
More informationSections 4.1 & 4.2 Exponential Growth and Exponential Decay
8 Sections 4. & 4.2 Eponential Growth and Eponential Deca What You Will Learn:. How to graph eponential growth functions. 2. How to graph eponential deca functions. Eponential Growth This is demonstrated
More informationMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Exam Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) Rationalize the denominator and simplify. 1 1) B) C) 1 D) 1 ) Identify the pair of like
More informationExponential and Logarithmic Functions
Eponential and Logarithmic Functions 6 Figure Electron micrograph of E. Coli bacteria (credit: Mattosaurus, Wikimedia Commons) CHAPTER OUTLINE 6. Eponential Functions 6. Logarithmic Properties 6. Graphs
More informationHonors Algebra 2 ~ Spring 2014 Name 1 Unit 3: Quadratic Functions and Equations
Honors Algebra ~ Spring Name Unit : Quadratic Functions and Equations NC Objectives Covered:. Define and compute with comple numbers. Operate with algebraic epressions (polnomial, rational, comple fractions)
More informationLesson Master 91B. REPRESENTATIONS Objective G. Questions on SPUR Objectives. 1. Let f(x) = 1. a. What are the coordinates of the vertex?
Back to Lesson 99B REPRESENTATIONS Objective G. Let f() =. a. What are the coordinates of the verte? b. Is the verte a minimum or a maimum? c. Complete the table of values below. 3 0 3 f() d. Graph the
More informationGrade 11 Mathematics Page 1 of 6 Final Exam Review (updated 2013)
Grade Mathematics Page of Final Eam Review (updated 0) REVIEW CHAPTER Algebraic Tools for Operating With Functions. Simplify ( 9 ) (7 ).. Epand and simplify. ( ) ( ) ( ) ( 0 )( ). Simplify each of the
More information2. Use your graphing calculator to graph each of the functions below over the interval 2, 2
MSLC Math 0 Final Eam Review Disclaimer: This should NOT be used as your only guide for what to study. if 0. Use the piecewise defined function f( ) to answer the following: if a. Compute f(0), f(), f(),
More informationLesson 10.1 Solving Quadratic Equations
Lesson 10.1 Solving Quadratic Equations 1. Sketch the graph of a quadratic equation with each set of conditions. a. One intercept and all nonnegative yvalues b. The verte in the third quadrant and no
More informationHomework 1 Due: Name. List the intercepts of the graph. 1) List the intercepts for the graph of the equation. 2) y2 = x + 1 2) 3) x2 + y  9 = 0 3)
Berkele Cit College Homework 1 Due: Precalculus w/ Analtic Geometr  Math 2  Chapters 12 (half) Name List the intercepts of the graph. 1) 1)     Objective: (1.2) Find Intercepts from a Graph List
More informationSHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Chapter Practice Dicsclaimer: The actual eam is different. On the actual eam ou must show the correct reasoning to receive credit for the question. SHORT ANSWER. Write the word or phrase that best completes
More informationMath 101 chapter six practice exam MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Math 1 chapter si practice eam MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Which equation matches the given calculatorgenerated graph and description?
More informationMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Eam Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) A ceramics workshop makes serving bowls, platters, and bread baskets to sell at its Winter
More informationLesson 9.1 Using the Distance Formula
Lesson. Using the Distance Formula. Find the eact distance between each pair of points. a. (0, 0) and (, ) b. (0, 0) and (7, ) c. (, 8) and (, ) d. (, ) and (, 7) e. (, 7) and (8, ) f. (8, ) and (, 0)
More informationEXPONENTIAL FUNCTIONS REVIEW PACKET FOR UNIT TEST TOPICS OF STUDY: MEMORIZE: General Form of an Exponential Function y = a b xh + k
EXPONENTIAL FUNCTIONS REVIEW PACKET FOR UNIT TEST TOPICS OF STUDY: o Recognizing Eponential Functions from Equations, Graphs, and Tables o Graphing Eponential Functions Using a Table of Values o Identifying
More informationMath 110 Final Exam Review Revised December 2015
Math 110 Final Exam Review Revised December 2015 Factor out the GCF from each polynomial. 1) 60x  15 2) 7x 8 y + 42x 6 3) x 9 y 5  x 9 y 4 + x 7 y 2  x 6 y 2 Factor each fourterm polynomial by grouping.
More information2 variables. is the same value as the solution of. 1 variable. You can use similar reasoning to solve quadratic equations. Work with a partner.
9. b Graphing Essential Question How can ou use a graph to solve a quadratic equation in one variable? Based on what ou learned about the intercepts of a graph in Section., it follows that the intercept
More information17 Exponential Functions
Eponential Functions Concepts: Eponential Functions Graphing Eponential Functions Eponential Growth and Eponential Deca The Irrational Number e and Continuousl Compounded Interest (Section. &.A). Sketch
More information= x. Algebra II Notes Quadratic Functions Unit Graphing Quadratic Functions. Math Background
Algebra II Notes Quadratic Functions Unit 3.1 3. Graphing Quadratic Functions Math Background Previousl, ou Identified and graphed linear functions Applied transformations to parent functions Graphed quadratic
More informationLaw of Sines, Law of Cosines, Heron s Formula:
PreAP Math Analsis nd Semester Review Law of Sines, Law of Cosines, Heron s Formula:. Determine how man solutions the triangle has and eplain our reasoning. (FIND YOUR FLOW CHART) a. A = 4, a = 4 ards,
More information1) Now there are 4 bacteria in a dish. Every day we have two more bacteria than on the preceding day.
Math 093 and 117A Linear Functions and Eponential Functions Pages 1, 2, and 3 are due the class after eam 1 Your Name If you need help go to the Math Science Center in MT 02 For each of problems 14, do
More information25) x x + 30 x2 + 15x ) x Graph the equation. 30) y =  x  1
PreAP Algebra Final Eam Review Solve. ) A stone is dropped from a tower that is feet high. The formula h =  t describes the stoneʹs height above the ground, h, in feet, t seconds after it was dropped.
More informationAlgebra 2, Spring Semester Review
Class: Date: Algebra, Spring Semester Review 1. (1 point) Graph the relation and its inverse. Use open circles to graph the points of the inverse. x 0 4 9 10 y 3 7 1 a. c. b. d. 1 . (1 point) Is relation
More informationLog Test Review  Graphing Problems
Algebra Honors  Mr. AllenBlack d^0id7i wkpuftza SSqoffLtrw`aerZef CLOLACq.m H LAwlrl` _raidgqhvtssb reisaenrdvqekdr. Log Test Review  Graphing Problems ) = 3 Name ID: ) = ( Date Period       
More informationExponential and Logarithmic Functions
7 Eponential and Logarithmic Functions In this chapter ou will stud two tpes of nonalgebraic functions eponential functions and logarithmic functions. Eponential and logarithmic functions are widel used
More informationLesson 5.1 Exponential Functions
Lesson.1 Eponential Functions 1. Evaluate each function at the given value. Round to four decimal places if necessar. a. r (t) 2(1 0.0) t, t 8 b. j() 9.(1 0.09), 10 2. Record the net three terms for each
More informationBRONX COMMUNITY COLLEGE of the City University of New York DEPARTMENT OF MATHEMATICS & COMPUTER SCIENCE. MTH06 Review Sheet y 6 2x + 5 y.
BRONX COMMUNITY COLLEGE of the Cit Universit of New York DEPARTMENT OF MATHEMATICS & COMPUTER SCIENCE MTH06 Review Sheet. Perform the indicated operations and simplif: n n 0 n +n ( 9 )( ) + + 6 + 9ab a+b
More informationChapter 3. Exponential and Logarithmic Functions. Selected Applications
Chapter 3 Eponential and Logarithmic Functions 3. Eponential Functions and Their Graphs 3.2 Logarithmic Functions and Their Graphs 3.3 Properties of Logarithms 3.4 Solving Eponential and Logarithmic Equations
More informationSECTION 3.1: Quadratic Functions
SECTION 3.: Quadratic Functions Objectives Graph and Analyze Quadratic Functions in Standard and Verte Form Identify the Verte, Ais of Symmetry, and Intercepts of a Quadratic Function Find the Maimum or
More informationM112 Short Course In Calculus V. J. Motto Spring 2013 Applications of Derivatives Worksheet
M11 Short Course In Calculus V. J. Motto Spring 01 Applications of Derivatives Worksheet 1. A tomato is thrown from the top of a tomato cart its distance from the ground in feet is modeled by the equation
More information( ) ( ) x. The exponential function f(x) with base b is denoted by x
Page of 7 Eponential and Logarithmic Functions Eponential Functions and Their Graphs: Section Objectives: Students will know how to recognize, graph, and evaluate eponential functions. The eponential function
More information8.4. If we let x denote the number of gallons pumped, then the price y in dollars can $ $1.70 $ $1.70 $ $1.70 $ $1.
8.4 An Introduction to Functions: Linear Functions, Applications, and Models We often describe one quantit in terms of another; for eample, the growth of a plant is related to the amount of light it receives,
More informationAnswer Explanations. The SAT Subject Tests. Mathematics Level 1 & 2 TO PRACTICE QUESTIONS FROM THE SAT SUBJECT TESTS STUDENT GUIDE
The SAT Subject Tests Answer Eplanations TO PRACTICE QUESTIONS FROM THE SAT SUBJECT TESTS STUDENT GUIDE Mathematics Level & Visit sat.org/stpractice to get more practice and stud tips for the Subject Test
More information1. Find all relations which are functions. 2. Find all one to one functions.
1 PRACTICE PROBLEMS FOR FINAL (1) Function or not (vertical line test or y = x expression) 1. Find all relations which are functions. (A) x + y = (C) y = x (B) y = x 1 x+ (D) y = x 5 x () One to one function
More information7.4. Characteristics of Logarithmic Functions with Base 10 and Base e. INVESTIGATE the Math
7. Characteristics of Logarithmic Functions with Base 1 and Base e YOU WILL NEED graphing technolog EXPLORE Use benchmarks to estimate the solution to this equation: 1 5 1 logarithmic function A function
More information