1. Determine the domain and range of the parabola. Also, say if the parabola opens upward or downward. y

Size: px
Start display at page:

Download "1. Determine the domain and range of the parabola. Also, say if the parabola opens upward or downward. y"

Transcription

1 1. Determine the domain and range of the parabola. Also, sa if the parabola opens upward or downward. A. The domain is D = [3, ) and the range is R = R.The parabola opens upward. B. The domain is D = (, 3] and the range is R = R. The parabola opens downward. C. The domain is D = R and the range is R = [3, ). The parabola opens downward. D. The domain is D = R and the range is R = (, 3]. The parabola opens downward. E. The domain is D = R and the range is R = [3, ). The parabola opens upward. F. The domain is D = [3, ) and the range is R = R.The parabola opens downward.. Use the shape of the graph to match it with the function that defines this graph. A. f() = + 1 B. f() = C. f() = + 1 D. f() = 3 + 1

2

3 3. Find the verte of the parabola f() = + 5. A. The verte is ( 7, 0). B. The verte is ( 3, ). C. The verte is ( 9, 1). D. The verte is ( 7, 7). E. The verte is ( 1, 3). F. The verte is ( 1, ). G. The verte is ( 5, 1). H. The verte is ( 9, 8).. Find the -intercept, -intercepts, and verte of the parabola f() = + 6. A. The -intercept is (0, 6). The -intercepts are ( 13 1, 9 B. The -intercept is (0, 11). The -intercepts are ( 13 19, 9 C. The -intercept is (0, 11). The -intercepts are ( 3 19, 9 D. The -intercept is (0, 6). The -intercepts are ( 13 19, 89 E. The -intercept is (0, 6). The -intercepts are ( 3, 0) and (, 0). The verte is ( 1, 9 F. The -intercept is (0, 11). The -intercepts are ( 3 19, 89 G. The -intercept is (0, 11). The -intercepts are ( 13, 0) and (, 0). The verte is ( 1, 89 H. The -intercept is (0, 11). The -intercepts are ( 13 1, 89

4 5. Use the shape of the graph to match it with the function that defines this graph. A. f() = 3 B. f() = 3 C. f() = 3 3 D. f() = 3 6. Bill Bob owns a coal mine. One da he noticed, contrar to his epectations, that selling more coal doesn t necessaril mean more profit (since producing and selling more coal incurs greater labor and equipment costs). Looking at data from the last ear, Bill Bob (with the help of some mathematicall inclined friends of course) created a function P () = which gives the profit in dollars when tons of coal are produced and sold. Graph this function and use it to help Bill Bob determine the following: a. his overhead costs (Hint: Evaluate P (0).) b. the break-even values (Hint: When does P () = 0?) Round our answers to the nearest hundredth. c. his maimum profit that can be made and the number of tons to sell to create this profit. A. The overhead costs are $5000. The break even points are.5 tons and 55.5 tons. The maimum profit of $65000 is reached when 30 tons of coal are produced and sold. B. The overhead costs are $1000. The break even points are.5 tons and 55.5 tons. The maimum profit is $65000 is reached when 30 tons of coal are produced and sold. C. The overhead costs are $1000. The break even points are.5 tons and 55.5 tons. The maimum profit is $68000 is reached when 30 tons of coal are produced and sold. D. The overhead costs are $5000. The break even points are 5.5 tons and 56.5 tons. The maimum profit is $65000 is reached when 31 tons of coal are produced and sold. E. The overhead costs are $5000. The break even points are.5 tons and 55.5 tons. The maimum profit is $66000 is reached when 30 tons of coal are produced and sold. F. The overhead costs are $1000. The break even points are 7.5 tons and 58.5 tons. The maimum profit is $6000 is reached when 33 tons of coal are produced and sold.

5

6 7. Find the -intercept, -intercepts, and range of the parabola graphed below. A. The -intercept is (0, 3). The -intercepts are ( 1, 0) and (, 0). The range is R = (, 9]. B. The -intercept is (0, 3). The -intercepts are ( 1, 0) and (3, 0). The range is R = [, ). C. The -intercept is (0, 3). The -intercepts are ( 1, 0) and (, 0). The range is R = [ 9, ). D. The -intercept is (0, 8). The -intercepts are ( 6, 0) and (3, 0). The range is R = (, ]. E. The -intercept is (0, 3). The -intercepts are ( 6, 0) and (, 0). The range is R = [ 9, ). F. The -intercept is (0, 8). The -intercepts are ( 1, 0) and (, 0). The range is R = (, 9]. G. The -intercept is (0, 8). The -intercepts are ( 6, 0) and (3, 0). The range is R = [ 9, ). H. The -intercept is (0, 8). The -intercepts are ( 6, 0) and (3, 0). The range is R = (, ]. 8. Find the -intercept, -intercepts, and verte of the parabola f() = A. The -intercept is (0, 7). The -intercepts are ( 3, 0) and (, 0). The verte is ( 7 6, 9 B. The -intercept is (0, 6). The -intercepts are ( 1 3, 0) and (, 0). The verte is ( 1 6, 9 C. The -intercept is (0, 7). The -intercepts are ( 3, 0) and (, 0). The verte is ( 7 6, 9 D. The -intercept is (0, 6). The -intercepts are ( 3, 0) and (1, 0). The verte is ( 1 6, 5 E. The -intercept is (0, 7). The -intercepts are ( 1 3, 0) and (, 0). The verte is ( 7 6, 5 F. The -intercept is (0, 7). The -intercepts are ( 1 3, 0) and (1, 0). The verte is ( 7 6, 9 G. The -intercept is (0, 6). The -intercepts are ( 1 3, 0) and (1, 0). The verte is ( 1 6, 9 H. The -intercept is (0, 6). The -intercepts are ( 1 3, 0) and (, 0). The verte is ( 7 6, 5

Math Analysis Midterm Review. Directions: This assignment is due at the beginning of class on Friday, January 9th

Math Analysis Midterm Review. Directions: This assignment is due at the beginning of class on Friday, January 9th Math Analysis Midterm Review Name Directions: This assignment is due at the beginning of class on Friday, January 9th This homework is intended to help you prepare for the midterm exam. The questions are

More information

MATH COLLEGE ALGEBRA/BUSN - PRACTICE EXAM #2 - SUMMER DR. DAVID BRIDGE

MATH COLLEGE ALGEBRA/BUSN - PRACTICE EXAM #2 - SUMMER DR. DAVID BRIDGE MATH 13 - COLLEGE ALGEBRA/BUSN - PRACTICE EXAM # - SUMMER 007 - DR. DAVID BRIDGE MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Graph the piecewise

More information

f x f x f x f x x 5 3 y-intercept: y-intercept: y-intercept: y-intercept: y-intercept of a linear function written in function notation

f x f x f x f x x 5 3 y-intercept: y-intercept: y-intercept: y-intercept: y-intercept of a linear function written in function notation Questions/ Main Ideas: Algebra Notes TOPIC: Function Translations and y-intercepts Name: Period: Date: What is the y-intercept of a graph? The four s given below are written in notation. For each one,

More information

2. Find the domain for the following functions. Write you answer in interval notation. 4

2. Find the domain for the following functions. Write you answer in interval notation. 4 Review Quiestions for Eam 4- Math 134 (1. 10.1 10. 10.3 10.4 10.5) NOTE: This review in and of itself does NOT prepare you for the test. You should be doing this review in addition to studying all your

More information

123 PART 1: Solutions to Odd-Numbered Exercises and Practice Tests

123 PART 1: Solutions to Odd-Numbered Exercises and Practice Tests 3 PART : Solutions to Odd-Numbered Eercises and Practice Tests Section.7 Graphs of Rational Functions You should be able to graphf() - q()" (a) Find the - and -intercepts. (b) Find an vertical or horizontal

More information

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Math 1332 Test 2 Review Name SHORT ANSWER. Write the word or phrase that best completes each stateme or answers the question. Plot the poi in the rectangular coordinate sstem. 1) (-, -3) 6 4 2-6 -4-2 2

More information

Name: Common Core Algebra L R Final Exam 2015 CLONE 3 Teacher:

Name: Common Core Algebra L R Final Exam 2015 CLONE 3 Teacher: 1) Which graph represents a linear function? 2) Which relation is a function? A) B) A) {(2, 3), (3, 9), (4, 7), (5, 7)} B) {(0, -2), (3, 10), (-2, -4), (3, 4)} C) {(2, 7), (2, -3), (1, 1), (3, -1)} D)

More information

Math 1101 Exam 1 Practice Problems

Math 1101 Exam 1 Practice Problems Math 1101 Eam 1 Practice Problems These problems are not intended to cover all possible test topics. Rather, the should serve as an activit in preparing for our test, but other stud is required to full

More information

TEST # 1 REVIEW MATH MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

TEST # 1 REVIEW MATH MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. TEST # REVIEW MATH Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Give the domain and range of the relation. ) {(-8, -), (, ), (9, 8), (-, ),

More information

Common Core Algebra L clone 4 review R Final Exam

Common Core Algebra L clone 4 review R Final Exam 1) Which graph represents an exponential function? A) B) 2) Which relation is a function? A) {(12, 13), (14, 19), (11, 17), (14, 17)} B) {(20, -2), (24, 10), (-21, -5), (22, 4)} C) {(34, 8), (32, -3),

More information

Semester Exam Review

Semester Exam Review Semester Exam Review Name Date Block MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. For the given equation, find the values of a, b, and c, determine

More information

8.2 Exercises. Section 8.2 Exponential Functions 783

8.2 Exercises. Section 8.2 Exponential Functions 783 Section 8.2 Eponential Functions 783 8.2 Eercises 1. The current population of Fortuna is 10,000 heart souls. It is known that the population is growing at a rate of 4% per ear. Assuming this rate remains

More information

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. CHAPTER FORM A Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Determine whether the given ordered pair is a solution of the given equation.

More information

Week 19 Algebra 2 Assignment:

Week 19 Algebra 2 Assignment: Week 9 Algebra Assignment: Day : pp. 66-67 #- odd, omit #, 7 Day : pp. 66-67 #- even, omit #8 Day : pp. 7-7 #- odd Day 4: pp. 7-7 #-4 even Day : pp. 77-79 #- odd, 7 Notes on Assignment: Pages 66-67: General

More information

PRINTABLE VERSION. Practice Final Exam

PRINTABLE VERSION. Practice Final Exam Page 1 of 25 PRINTABLE VERSION Practice Final Exam Question 1 The following table of values gives a company's annual profits in millions of dollars. Rescale the data so that the year 2003 corresponds to

More information

MATHS PAPER 1 QUESTIONS

MATHS PAPER 1 QUESTIONS MATHS PAPER 1 QUESTIONS QUESTION 1 1.1 Solve for in the following, correct to two decimal places where necessary. 1.1.1 7 30 1.1. ( ) 5 0 1.1.3 4 7 0 1. 1..1 Solve simultaneously for and y if 6 y 0 and

More information

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. MAC Summer C 6 Worksheet (.,.,.) Table Names MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Sketch the graph of the function and determine whether

More information

Test # 3 Review Math MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Test # 3 Review Math MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Test # Review Math Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Identif the functionʹs etreme values in the given domain, and sa where the

More information

(4, 2) (2, 0) Vertical shift two units downward (2, 4) (0, 2) (1, 2) ( 1, 0) Horizontal shrink each x-value is multiplied by 1 2

(4, 2) (2, 0) Vertical shift two units downward (2, 4) (0, 2) (1, 2) ( 1, 0) Horizontal shrink each x-value is multiplied by 1 2 Section. Rational Functions 9. i i i i 9i. i i i. i 7i i i i i. 9 i9 i i. g f. g f. g f, ), ), ), ), ), ), ), ), ), ), ), ) Horizontal shift two units to the right Vertical shift two units downward Vertical

More information

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. MAC 1 Module Test 1 Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. State whether the graph is or is not that of a function. 1) 1 1 1 1 3 7 9

More information

2.8 Absolute Value Functions

2.8 Absolute Value Functions 2.8 Absolute Value Functions Algebra III Mr. Niedert Algebra III 2.8 Absolute Value Functions Mr. Niedert 1 / 8 Today s Learning Target(s) 1 I can graph absolute value functions and apply them to real-life

More information

MATH 100 DR. MCLOUGHLIN'S HANDY DANDY SYSTEMATIC GRAPHING GUIDE PART II

MATH 100 DR. MCLOUGHLIN'S HANDY DANDY SYSTEMATIC GRAPHING GUIDE PART II Dr. McLoughlin s Handy Dandy Graphing Guide Part II, page MATH 00 DR. MCLOUGHLIN'S HANDY DANDY SYSTEMATIC GRAPHING GUIDE PART II Here we discuss basic graphing techniques of functions from Part I. y =

More information

elementary and intermediate Algebra Warm-up Name atfm0303mk2810yes

elementary and intermediate Algebra Warm-up Name atfm0303mk2810yes MATH000 online PLACEMENT TEST 1 QUESTIONS 11-0-13 Fall 013 elementar and intermediate Algebra Warm-up Name atfm0303mkes www.alvarezmathhelp.com website PROGRAMS ALVAREZLAB (SAVE AND EXTRACT TO YOUR COMPUTER)

More information

P(z) =.0.2X2 + 22x - 400

P(z) =.0.2X2 + 22x - 400 Survey ofcalcu1us I (Math 121 Exam 3 November 13, 2002 Part I. Multiple Choice. (2 points each) P(z) =.0.2X2 + 22x - 400 1. Find the marginal profit at a production level of 50 clocks. numerical answer,

More information

Solve the problem. 1) The price p and the quantity x sold of a certain product obey the demand equation: p = - 1 x + 300, 0 x 800.

Solve the problem. 1) The price p and the quantity x sold of a certain product obey the demand equation: p = - 1 x + 300, 0 x 800. Sample Test 3 Name In the real test ou will have questions and the following rules: You have 0 minutes to complete the test below. The usage of books or notes, or communication with other students is not

More information

Chapter 6 Diagnostic Test

Chapter 6 Diagnostic Test Chapter 6 Diagnostic Test STUDENT BOOK PAGES 310 364 1. Consider the quadratic relation y = x 2 6x + 3. a) Use partial factoring to locate two points with the same y-coordinate on the graph. b) Determine

More information

Chapter 6: Quadratic Functions & Their Algebra

Chapter 6: Quadratic Functions & Their Algebra Chapter 6: Quadratic Functions & Their Algebra Topics: 1. Quadratic Function Review. Factoring: With Greatest Common Factor & Difference of Two Squares 3. Factoring: Trinomials 4. Complete Factoring 5.

More information

Polynomial and Rational Functions

Polynomial and Rational Functions Chapter 4 Polnomial and Rational Functions 4.3 Rational Functions I 1. In R() = 4 3, the denominator, q( ) = 3, has a zero at 3. Thus, the domain of R() is all real numbers ecept 3.. In R() = 5 3 +, the

More information

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) Answer: No Correct Answer Was Provided. Provide an appropriate response. ) If a relation eists

More information

QUADRATIC. Parent Graph: How to Tell it's a Quadratic: Helpful Hints for Calculator Usage: Domain of Parent Graph:, Range of Parent Graph: 0,

QUADRATIC. Parent Graph: How to Tell it's a Quadratic: Helpful Hints for Calculator Usage: Domain of Parent Graph:, Range of Parent Graph: 0, Parent Graph: How to Tell it's a Quadratic: If the equation's largest exponent is 2 If the graph is a parabola ("U"-Shaped) Opening up or down. QUADRATIC f x = x 2 Domain of Parent Graph:, Range of Parent

More information

MLC at Boise State Polynomials Activity 3 Week #5

MLC at Boise State Polynomials Activity 3 Week #5 Polynomials Activity 3 Week #5 This activity will be discuss maximums, minimums and zeros of a quadratic function and its application to business, specifically maximizing profit, minimizing cost and break-even

More information

Linear function and equations Linear function, simple interest, cost, revenue, profit, break-even

Linear function and equations Linear function, simple interest, cost, revenue, profit, break-even Exercises 4 Linear function and equations Linear function, simple interest, cost, revenue, profit, break-even Objectives - be able to think of a relation between two quantities as a function. - be able

More information

Linear Relationships UNIT 3 Warm-Up A. Finding Percents Mentally Find 10% of each of the following numbers. (Move the decimal 1 place to the left.

Linear Relationships UNIT 3 Warm-Up A. Finding Percents Mentally Find 10% of each of the following numbers. (Move the decimal 1 place to the left. Linear Relationships UNIT 3 Warm-Up A Find 10% of each of the following numbers. (Move the decimal 1 place to the left.) 1) 600 2) 50 3) 36 4) 574 5) 26.5 6) 900 7) 270 8)13.8 9) 246 10) 0.36 11) Record

More information

GRAPHS IN ECONOMICS. Appendix. Key Concepts. A Positive Relationship

GRAPHS IN ECONOMICS. Appendix. Key Concepts. A Positive Relationship Appendi GRAPHS IN ECONOMICS Ke Concepts Graphing Data Graphs represent quantit as a distance on a line. On a graph, the horizontal scale line is the -ais, the vertical scale line is the -ais, and the intersection

More information

Week #7 - Maxima and Minima, Concavity, Applications Section 4.4

Week #7 - Maxima and Minima, Concavity, Applications Section 4.4 Week #7 - Maxima and Minima, Concavity, Applications Section 4.4 From Calculus, Single Variable by Hughes-Hallett, Gleason, McCallum et. al. Copyright 2005 by John Wiley & Sons, Inc. This material is used

More information

Name Period. Linear Correlation

Name Period. Linear Correlation Linear Regression Models Directions: Use the information below to solve the problems in this packet. Packets are due at the end of the period and students who do not finish will be required to come in

More information

Practice Exam #2 Math 1160

Practice Exam #2 Math 1160 Practice Eam # Math 60 The material on this eam does not cover all of the possile topics that could e on the real eam. This practice eam is meant as supplement to the normal studying routines efore eams.

More information

Pre-Calculus Midterm Exam REVIEW January 2013

Pre-Calculus Midterm Exam REVIEW January 2013 Pre-Calculus Midterm Eam REVIEW Januar 0 Name: Date: Teacher: Period: Your midterm eamination will consist of: 0 multiple-choice questions (including true/false & matching) these will be completed on the

More information

Exponential Growth and Decay

Exponential Growth and Decay Exponential Growth and Decay Identifying Exponential Growth vs Decay A. Exponential Equation: f(x) = Ca x 1. C: COEFFICIENT 2. a: BASE 3. X: EXPONENT B. Exponential Growth 1. When the base is greater than

More information

1) Please EXPLAIN below your error in problem #1. What will you do to correct this error in the future?

1) Please EXPLAIN below your error in problem #1. What will you do to correct this error in the future? Individualized Quiz Remedial Help Name: ALL QUESTIONS REQUIRING YOU TO WRITE IN ENGLISH MUST BE ANSWERED IN COMPLETE SENTENCES. If you answered question #1 incorrectly please answer the following. 1) Please

More information

Quadratic Modeling Elementary Education 10 Business 10 Profits

Quadratic Modeling Elementary Education 10 Business 10 Profits Quadratic Modeling Elementary Education 10 Business 10 Profits This week we are asking elementary education majors to complete the same activity as business majors. Our first goal is to give elementary

More information

Instructor: Elhoussine Ghardi Course: calcmanagementspring2018

Instructor: Elhoussine Ghardi Course: calcmanagementspring2018 Student: Date: Instructor: Elhoussine Ghardi Course: calcmanagementspring018 Assignment: HW3spring018 1. Differentiate the following function. f (x) = f(x) = 7 4x + 9 e x. f(x) = 6 ln x + 5x 7 3. Differentiate

More information

1) State whether the following are functions and give an explanation for your reason. Give the domain and range for each relation.

1) State whether the following are functions and give an explanation for your reason. Give the domain and range for each relation. MCF M Calc Questions:,,, 7, 8, 9,,,, QUADRATIC FUNCTIONS ) State whether the following are functions and give an eplanation for your reason. Give the domain and range for each relation. a) - 7 b) y c)

More information

Quadratic Functions. As review, we will look at the definition of a quadratic function. A quadratic function is a function f of the form

Quadratic Functions. As review, we will look at the definition of a quadratic function. A quadratic function is a function f of the form Quadratic Functions To this point, we have had some experience with quadratic equations. We know that the graph of a quadratic equation gives us a parabola. In this section, we will see how quadratic equations

More information

Test # 1 Review Math MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Test # 1 Review Math MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Test # 1 Review Math 135 Name (Sections 1.3,.,3.7,..1,.3,11.1,11.,11.3,and 11.) _ MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Factor out the greatest

More information

Financial Applications Involving Exponential Functions

Financial Applications Involving Exponential Functions Section 6.5: Financial Applications Involving Exponential Functions When you invest money, your money earns interest, which means that after a period of time you will have more money than you started with.

More information

2) y = 4 x ) y = ( 1 2)x + 1

2) y = 4 x ) y = ( 1 2)x + 1 UCHS Algebra n sl0c1z5c nkguwt^aa USjovfztowjapr^eA jl[l_cn.k U kajldl[ Tr_iNgmhPtIsY _rvejszerrdvnewd[. 9.3 HW Assignment Sketch the graph of each function. Name Date 1) = 3 + - 1 ) = - 1 + 0 - - - -

More information

Math1090 Midterm 2 Review Sections , Solve the system of linear equations using Gauss-Jordan elimination.

Math1090 Midterm 2 Review Sections , Solve the system of linear equations using Gauss-Jordan elimination. Math1090 Midterm 2 Review Sections 2.1-2.5, 3.1-3.3 1. Solve the system of linear equations using Gauss-Jordan elimination. 5x+20y 15z = 155 (a) 2x 7y+13z=85 3x+14y +6z= 43 x+z= 2 (b) x= 6 y+z=11 x y+

More information

Review Problems for Mid-Term 1 (MAT1250/Cal Poly Pomona Fall 2018) ( x + 1) 36 [Hint: Find x] x + x x. x 1. = + g.

Review Problems for Mid-Term 1 (MAT1250/Cal Poly Pomona Fall 2018) ( x + 1) 36 [Hint: Find x] x + x x. x 1. = + g. Prof: M. Nasab Review Problems for Mid-Term (MAT50/Cal Pol Pomona Fall 08). Factor completel 5 +. Find all real zeroes of 8 4 + [Hint: Find ]. Find all real zeroes of ( + ) 6 [Hint: Find ] 4. Add and reduce

More information

Name: Class: Date: in general form.

Name: Class: Date: in general form. Write the equation in general form. Mathematical Applications for the Management Life and Social Sciences 11th Edition Harshbarger TEST BANK Full clear download at: https://testbankreal.com/download/mathematical-applications-management-life-socialsciences-11th-edition-harshbarger-test-bank/

More information

2-6 Rates, Ratios, and Proportions

2-6 Rates, Ratios, and Proportions 2-6 Rates, Ratios, and Proportions Warm Up Lesson Presentation Lesson Quiz Bell Quiz 2-6(a) Solve each equation. Check your answer. 1. 6x = 36 2. 3. 5m = 18 4. Multiply. 7 5. 8 8 10 pts possible Questions

More information

2-6 Rates, Ratios, and Proportions. Warm Up Lesson Presentation Lesson Quiz Holt Algebra 1

2-6 Rates, Ratios, and Proportions. Warm Up Lesson Presentation Lesson Quiz Holt Algebra 1 2-6 Rates, Ratios, and Proportions Warm Up Lesson Presentation Lesson Quiz 2-6 1 Questions on 2-5 2-6 2 Objectives Write and use ratios, rates, and unit rates. Write and solve proportions. 2-6 3 Vocabulary

More information

Optimization. Example of an appropriate method. Maximum possible income before the new constraint. Income: 8x y

Optimization. Example of an appropriate method. Maximum possible income before the new constraint. Income: 8x y Optimization 1 Eample of an appropriate method Maimum possible income before the new constraint Verte Income: 8 + 9.50 P (16, 0) 8 (16) + 9.50 (0) = $128 Q (16, 20) 8 (16) + 9.50 (20) = $318 R (20, 20)

More information

Key Terms: exponential function, exponential equation, compound interest, future value, present value, compound amount, continuous compounding.

Key Terms: exponential function, exponential equation, compound interest, future value, present value, compound amount, continuous compounding. 4.2 Exponential Functions Exponents and Properties Exponential Functions Exponential Equations Compound Interest The Number e and Continuous Compounding Exponential Models Section 4.3 Logarithmic Functions

More information

Graph A Graph B Graph C Graph D. t g(t) h(t) k(t) f(t) Graph

Graph A Graph B Graph C Graph D. t g(t) h(t) k(t) f(t) Graph MATH 119 Chapter 1 Test (Sample B ) NAME: 1) Each of the function in the following table is increasing or decreasing in different way. Which of the graphs below best fits each function Graph A Graph B

More information

9.6 Notes Part I Exponential Growth and Decay

9.6 Notes Part I Exponential Growth and Decay 9.6 Notes Part I Exponential Growth and Decay I. Exponential Growth y C(1 r) t Time Final Amount Initial Amount Rate of Change Ex 1: The original value of a painting is $9000 and the value increases by

More information

Use Scantron 882E to transfer the answers. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Use Scantron 882E to transfer the answers. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. HW Date: Name Use Scantron 88E to transfer the answers. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. The graph shows sales in thousands of dollars

More information

Suggested Solutions to Assignment 3

Suggested Solutions to Assignment 3 ECON 1010C Principles of Macroeconomics Instructor: Sharif F. Khan Department of Economics Atkinson College York University Summer 2005 Suggested Solutions to Assignment 3 Part A Multiple-Choice Questions

More information

3.1 Solutions to Exercises

3.1 Solutions to Exercises .1 Solutions to Exercises 1. (a) f(x) will approach + as x approaches. (b) f(x) will still approach + as x approaches -, because any negative integer x will become positive if it is raised to an even exponent,

More information

Study Guide - Part 1

Study Guide - Part 1 Math 116 Spring 2015 Study Guide - Part 1 1. Find the slope of a line that goes through the points (1, 5) and ( 3, 13). The slope is (A) Less than -1 (B) Between -1 and 1 (C) Between 1 and 3 (D) More than

More information

TCM Final Review Packet Name Per.

TCM Final Review Packet Name Per. TCM Final Review Packet Name Per. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Translate the statement into a formula. 1) The total distance traveled,

More information

Possibilities, Preferences, and Choices

Possibilities, Preferences, and Choices 9 Possibilities, Preferences, and Choices Learning Objectives Household s budget line and show how it changes when prices or income change Use indifference curves to map preferences and explain the principle

More information

14.1 Fitting Exponential Functions to Data

14.1 Fitting Exponential Functions to Data Name Class Date 14.1 Fitting Eponential Functions to Data Essential Question: What are ways to model data using an eponential function of the form f() = ab? Resource Locker Eplore Identifying Eponential

More information

Pre-Algebra Blizzard Bag Number 3

Pre-Algebra Blizzard Bag Number 3 Name: Class: Date: ID: A Pre-Algebra Blizzard Bag Number 3 Multiple Choice Identify the choice that best completes the statement or answers the question. Express each ratio as a fraction in simplest form..

More information

Piecewise-Defined Functions

Piecewise-Defined Functions The Right Stuff: Appropriate Mathematics for All Students Promoting materials that engage students in meaningful activities, promote the effective use of technology to support the mathematics, further

More information

3.1 Solutions to Exercises

3.1 Solutions to Exercises .1 Solutions to Exercises 1. (a) f(x) will approach + as x approaches. (b) f(x) will still approach + as x approaches -, because any negative integer x will become positive if it is raised to an even exponent,

More information

CHAPTER 5 THE COST OF MONEY (INTEREST RATES)

CHAPTER 5 THE COST OF MONEY (INTEREST RATES) CHAPTER 5 THE COST OF MONEY (INTEREST RATES) 1 Learning Outcomes LO.1 Describe the cost of money and factors that affect the cost of money. LO.2 Describe how interest rates are determined. LO.3 Describe

More information

FUNCTIONS. Revenue functions and Demand functions

FUNCTIONS. Revenue functions and Demand functions Revenue functions and Demand functions FUNCTIONS The Revenue functions are related to Demand functions. ie. We can get the Revenue function from multiplying the demand function by quantity (x). i.e. Revenue

More information

BARUCH COLLEGE MATH 2003 SPRING 2006 MANUAL FOR THE UNIFORM FINAL EXAMINATION

BARUCH COLLEGE MATH 2003 SPRING 2006 MANUAL FOR THE UNIFORM FINAL EXAMINATION BARUCH COLLEGE MATH 003 SPRING 006 MANUAL FOR THE UNIFORM FINAL EXAMINATION The final examination for Math 003 will consist of two parts. Part I: Part II: This part will consist of 5 questions similar

More information

Falling Cat 2. Falling Cat 3. Falling Cats 5. Falling Cat 4. Acceleration due to Gravity Consider a cat falling from a branch

Falling Cat 2. Falling Cat 3. Falling Cats 5. Falling Cat 4. Acceleration due to Gravity Consider a cat falling from a branch Calculus for the Life Sciences Lecture Notes Velocit and Tangent Joseph M. Mahaff, jmahaff@mail.sdsu.edu Department of Mathematics and Statistics Dnamical Sstems Group Computational Sciences Research Center

More information

MATH 1015 Final Exam Review Rev 02/2018

MATH 1015 Final Exam Review Rev 02/2018 MATH 1 Final Exam Review Rev 0/018 ============================================================================== 1)Find the domain and range for the function. 1) 3 1-7 - - - -3 - -1 1 3 7 - -3 - - - -7

More information

Factoring Quadratics: ax 2 + bx + c

Factoring Quadratics: ax 2 + bx + c 4.4 Factoring Quadratics: a 2 + b + c GOAL Factor quadratic epressions of the form a 2 + b + c, where a. LEARN ABOUT the Math Kellie was asked to determine the -intercepts of y = 2 + + 6 algebraically.

More information

MA 109 College Algebra EXAM 3 - REVIEW

MA 109 College Algebra EXAM 3 - REVIEW MA 9 College Algebra EXAM - REVIEW Name: Sec.:. In the picture below, the graph of = f(x) is the solid graph, and the graph of = g(x) is the dashed graph. Find a formula for g(x). 9 7 - -9 - -7 - - - -

More information

Math 111 Midterm II February 20th, 2007

Math 111 Midterm II February 20th, 2007 NAME: Student ID #: QUIZ SECTION: Math 111 Midterm II February 0th, 007 Problem 1 15 Problem 14 Problem 3 15 Problem 4 6 Total: 50 Your exam should contain 5 pages in total and 4 problems Please check

More information

NCC Pre Calculus Partnership Program Final Examination, 2009

NCC Pre Calculus Partnership Program Final Examination, 2009 NCC Pre Calculus Partnership Program Final Examination, 2009 2009 Final Part I: Answer all 25 questions in this part. Each question is worth 2 points. Leave all answers in EXACT form, i.e., in terms of

More information

Math 122 Calculus for Business Admin. and Social Sciences

Math 122 Calculus for Business Admin. and Social Sciences Math 122 Calculus for Business Admin. and Social Sciences Instructor: Ann Clifton Name: Exam #1 A July 3, 2018 Do not turn this page until told to do so. You will have a total of 1 hour 40 minutes to complete

More information

Lattice Valuation of Options. Outline

Lattice Valuation of Options. Outline Lattice Valuation of Options Richard de Neufville Professor of Engineering Systems and of Civil and Environmental Engineering MIT Massachusetts Institute of Technology Lattice Valuation Slide 1 of 35 Outline

More information

Unit 7 Exponential Functions. Name: Period:

Unit 7 Exponential Functions. Name: Period: Unit 7 Exponential Functions Name: Period: 1 AIM: YWBAT evaluate and graph exponential functions. Do Now: Your soccer team wants to practice a drill for a certain amount of time each day. Which plan will

More information

Mathematics 5 SN OPTIMIZATION. Jonathan makes $8 per hour when cleaning the premises and $9.50 per hour when working in the kitchen. x + y 40.

Mathematics 5 SN OPTIMIZATION. Jonathan makes $8 per hour when cleaning the premises and $9.50 per hour when working in the kitchen. x + y 40. Mathematics 5 SN OPTIMIZATION 1 Jonathan works at a golf club during his summer vacation. He sometimes cleans the premises and sometimes works in the kitchen at the club's restaurant. Jonathan makes $8

More information

FINANCE 100 Corporate Finance

FINANCE 100 Corporate Finance FINNCE 100 Corporate Finance Professor Roberts Solutions to Sample Quiz # NME: SECTION: Question Maimum Student Score Question 1 50 Question 50 TOTL 100 Instructions: You may bring one 8.511 inch sheet

More information

Name: Class: Date: A2R 3.4 Problem Set - Major Characteristics of Polynomial Graphs

Name: Class: Date: A2R 3.4 Problem Set - Major Characteristics of Polynomial Graphs Name: Class: Date: A2R 3.4 Problem Set - Major Characteristics of Polynomial Graphs Use the coordinate plane to sketch a graph with the given characteristics. If the graph is not possible to sketch, explain

More information

Lesson 4 - The Power of Exponential Growth and Decay

Lesson 4 - The Power of Exponential Growth and Decay - The Power of Exponential Growth and Decay Learning Targets: I can recognize situations in which a quantity grows or decays by a constant percent rate. I can write an exponential function to model a real

More information

Math 110 Sample Final. 8) x = x 4

Math 110 Sample Final. 8) x = x 4 Math 0 Sample Final Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve. ) Find the area.. miles.3 miles A) sq mi B). sq mi C). sq mi 0. sq

More information

EXAMPLE 2 COMMON CORE

EXAMPLE 2 COMMON CORE REFLECT. Why can it be helpful to solve a linear equation for y? Graphing a Linear Function Using the Slope and y-intercept You can graph the linear function f() = m + b using only the slope m and y-intercept

More information

B) 2x3-5x D) 2x3 + 5x

B) 2x3-5x D) 2x3 + 5x Pre Calculus Final Review 2010 (April) Name Divide f(x) by d(x), and write a summary statement in the form indicated. 1) f x = x - 4; d x = x + 7 (Write answer in polynomial form) 1) A) f x = x + 7 x2-7x

More information

There are three parts to this document on separate pages

There are three parts to this document on separate pages There are three parts to this document on separate pages I. The description of the case II. Hints for the steps you need to take (don t look at this until you try to figure out what you need to do for

More information

Best Reply Behavior. Michael Peters. December 27, 2013

Best Reply Behavior. Michael Peters. December 27, 2013 Best Reply Behavior Michael Peters December 27, 2013 1 Introduction So far, we have concentrated on individual optimization. This unified way of thinking about individual behavior makes it possible to

More information

1) Find the amount of increase or decrease. To do that we will use the following equation:

1) Find the amount of increase or decrease. To do that we will use the following equation: 7.4 Percent Increase or ecrease To do the percent increase or decrease problems we will need to break the problem into two parts. 1) Find the amount of increase or decrease. To do that we will use the

More information

Answers to Problem Set 4. Homework 4 Economics 301

Answers to Problem Set 4. Homework 4 Economics 301 Answers to Problem Set 4 Homework 4 Economics 301 Dividend Problem: For the questions below, assume that the asset in question is a bond with a two year maturity which will pay $100 at the end of the first

More information

x-intercepts, asymptotes, and end behavior together

x-intercepts, asymptotes, and end behavior together MA 2231 Lecture 27 - Sketching Rational Function Graphs Wednesday, April 11, 2018 Objectives: Explore middle behavior around x-intercepts, and the general shapes for rational functions. x-intercepts, asymptotes,

More information

1. f(x) = x2 + x 12 x 2 4 Let s run through the steps.

1. f(x) = x2 + x 12 x 2 4 Let s run through the steps. Math 121 (Lesieutre); 4.3; September 6, 2017 The steps for graphing a rational function: 1. Factor the numerator and denominator, and write the function in lowest terms. 2. Set the numerator equal to zero

More information

Review for Test 3: Linear Functions

Review for Test 3: Linear Functions Name: Date: Period: Review for Test 3: Linear Functions Slope Formula: y 2 y 1 x 2 x 1 1. Graph the line that passes through the given points. Then identify the slope, whichever intercept is asked for,

More information

Chapter 4 Factoring and Quadratic Equations

Chapter 4 Factoring and Quadratic Equations Chapter 4 Factoring and Quadratic Equations Lesson 1: Factoring by GCF, DOTS, and Case I Lesson : Factoring by Grouping & Case II Lesson 3: Factoring by Sum and Difference of Perfect Cubes Lesson 4: Solving

More information

Business Mathematics 2017 Spring

Business Mathematics 2017 Spring Business Mathematics 2017 Spring 1 Simple Interest In all problems involving days, a 360-day year is assumed. When annual rates are requested as an answer, compute 100% to three decimal places. 1.1. If

More information

Section 1.1 Notes. May 29, 2018

Section 1.1 Notes. May 29, 2018 Section 1.1 Notes May 29, 2018 Mathematical Models Goal: Recall the following facts about lines: 1) Equation: 2) Slope: 3) x-intercept: 4) y-intercept: Definition 1. Let D and R be two collections of objects.

More information

6.1 Exponential Growth and Decay Functions Warm up

6.1 Exponential Growth and Decay Functions Warm up 6.1 Exponential Growth and Decay Functions Warm up Simplify the expression. 1. 2. 3. 4. 5. 6. 7. Your Lester's bill is $14. How much do you owe your server if you tip 15%? 8. Your Lester's bill is $P.

More information

Math 142 Week-in-Review #1 (Sections A.8, 1.0, 1.1 topics, 1.2 topics, and 1.3)

Math 142 Week-in-Review #1 (Sections A.8, 1.0, 1.1 topics, 1.2 topics, and 1.3) Math 142 WIR, copyright Angie Allen, Spring 2016 1 Math 142 Week-in-Review #1 (Sections A.8, 1.0, 1.1 topics, 1.2 topics, and 1.3) 1. Classify each of the following as a power function, rational function,

More information

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. MGF 1107 Practice Final Dr. Schnackenberg MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Graph the equation. Select integers for x, -3 x 3. 1) y

More information

A city, Maple Valley s population is growing by 124 people per year. If there were 25,125 people in 2014, what is the population in 2015? 2016?

A city, Maple Valley s population is growing by 124 people per year. If there were 25,125 people in 2014, what is the population in 2015? 2016? Section 6.1: Exponential Functions 1. India is the second most populous country in the world with a population of about 1.25 billion people in 2013. The population is growing at a rate of about 1.2% each

More information

Appendix E. Fueling Up. Application Practice

Appendix E. Fueling Up. Application Practice Appendix E Fueling Up Motorists often complain about rising gas prices. Some motorists purchase fuel efficient vehicles and participate in trip reduction plans, such as carpooling and using alternative

More information