Practice UNIT 2 ACTIVITY 2.2 ACTIVITY 2.1
|
|
- Vernon Warren
- 5 years ago
- Views:
Transcription
1 ACTIVITY.. Use the regression capabilities of our graphing calculator to create a model to represent the data in the table ACTIVITY. Determine the -intercept and end behavior of each function. 7. = = Use what ou know about end behavior and zeros to graph. 9. f () = ( - )( - 6)( + )( + 7). Graph the function ou found in Question and list the important features of the graph.. List the important features of the graph below. Approimate non-integral values f () = ( - ) ( + )( - ) College Board. All rights reserved.. Without using a calculator, find the end behavior and - and -intercepts of f () = ( + )( - )( + )( - 9)( + ).. Without using a calculator, find the end behavior, maimum possible zeros, and maimum possible turning points of f () = Use a graphing calculator to find the zeros, turning points, -intercepts and end behavior of f () = Determine all the rational zeros of f () = Sketch a possible graph of f () = Determine the possible number of positive and negative real zeros of h() = Graph f () = Unit Functions and Their Graphs
2 ACTIVITY. Find a polnomial with real coefficients of lowest degree with the given zeros.. Degree, zeros = -,, 6. Degree, zeros = -, -, -, 0, Find the zeros of the following polnomials and write them as a product of comple factors. 7. f () = + 8. f () = - Rewrite the polnomial functions as a product of comple factors. 9. f () = f () = Find the zeros of each function.. f () = f () = Find all the zeros of f () = + - +, given + i is a zero. Solve each inequalit and write the solution interval > 0 ACTIVITY. 6. Anita is four times as old as her daughter Nia. Nine ears from now, Anita will be two and a half times as old as Nia. a. What is Anita s age? b. Let R() represent the ratio of Anita s age in ears to Nia s age in ears and let represent the number of ears from now, either past or future. Write R as a function of. c. If ou were to graph the ratio of their ages in ears, where = 0 represents the present, at what value of would the graph appear to become vertical? What does this mean in terms of their ages? Use a graphing calculator and R() = Determine where the function is unbounded. 8. Find the equation of the vertical asmptote. 9. Find the equation of the horizontal asmptote. 00 College Board. All rights reserved. SpringBoard Mathematics with Meaning TM Precalculus
3 00 College Board. All rights reserved. ACTIVITY. Sketch a graph of each function or pair of functions. 0. f () = and g () = -.. f () = +.. f () = -.. f () = Find the horizontal asmptote. a. f () = b. g() = Find the horizontal asmptote. a. f () = b. g () = Find the - and -intercepts. a. f () = b. g () = Sketch a graph of each function without using a graphing calculator. a. f () = b. g () = Sketch a graph of the following. a. f () = b. g () = Find the equation of the slant asmptote. a. f () = + + b. g () = ACTIVITY.6 Determine the balance in each account for an initial investment of $8, ears at % interest, compounded annuall. ears at % interest, compounded annuall. 0 ears at.% interest, compounded quarterl. ears at % interest, compounded continuousl. 0 ears at.% interest, compounded continuousl The Tameri tree was introduced to a region in 006 and has been growing eponentiall.. The initial population was 0 trees and the population is increasing at an annual rate of %. Create a continuous eponential function that represents the number of Tameri in the region in a given ear since the first population was measured. 6. In what ear will the population of trees reach 00? 7. A new car was purchased in 00 for $0,000. It depreciates at a rate of 9%. Create a continuous eponential function that represents the value of the car after t ears of ownership. 8. When will the car have a value of $0,000? Unit Functions and Their Graphs
4 ACTIVITY.7 9. Evaluate lo g 6 ( ) 0. Which of the following can be used to find log 8? a. ln 8 b. log 8 ln log 8 c. ln d. ln 8 ln 8. Epand ln z.. Epand ln.. Write ln ( - ) - ln ( + ) + ln as a logarithm of a single quantit. Solve.. 00 e - = e = 7 6. log = 6 7. ln = Solve. Check our solutions. 8. log + log( + ) = ACTIVITY.8 Use the graph of f () for Questions 9 6. Sketch each graph below. 9. = f () 60. = f ( - ) 6. = -f () 6. = f () - Determine if the following functions are odd, even or neither. 6. f () = 6. f () = e - 6. f () = Find the sum, difference, product and quotient and composition of the functions in each question below. State the domain. 66. f () = - 7, g () = f () =, g () = - 00 College Board. All rights reserved. SpringBoard Mathematics with Meaning TM Precalculus
5 00 College Board. All rights reserved. Use the graph from Activit.8 on the previous page. 68. Sketch the graph of = f () 69. Which of these is the graph of = f ( )? a. b. c. d. ACTIVITY.9 The swim coach decides to put chlorine in the swimming pool to control the algae concentration. These are the readings after the chlorine is introduced. Da Algae Concentration (ppm) Make a scatter plot of the data. 7. What do ou notice about the scatter plot? 7. Perform a least squares regression for the data. a. Give the equation of the regression line and graph the regression line on the scatter plot. b. What is the correlation coefficient for the data? c. What does this coefficient indicate about the data? 7. What tpe of transformation can be used on the data to make the scatter plot appear more linear? 7. Transform the data and complete the table below. Da Algae Concentration (ppm) ln() a. Calculate the linear regression for the transformed data. b. Find the correlation coefficient. c. compare the correlation coefficient to the previous result. What does this indicate about the transformed data? 7. When can the coach epect the algae concentration to be less than ppm? Eplain our answer. Unit Functions and Their Graphs
3.1 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 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 informationMATH 121 Precalculus Practice problems for Exam 1
MATH 11 Precalculus Practice problems for Eam 1 1. Analze the function and then sketch its graph. Find - and -intercepts of the graph. Determine the behavior of the graph near -intercepts. Find the vertical
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 informationHonors Algebra 2: Semester 1 Review
Name Block Date Honors Algebra : Semester 1 Review NON-CALCULATOR 6-5 1. Given the functions f ( ) 5 11 1, g( ) 6 ( f h)( ) b) ( g f )( ), and h ( ) 4, find each function. g c) (g h)( ) d) ( ) f -1, 4-7,
More informationPractice A ( 1, 3 ( 0, 1. Match the function with its graph. 3 x. Explain how the graph of g can be obtained from the graph of f. 5 x.
8. Practice A For use with pages 65 7 Match the function with its graph.. f. f.. f 5. f 6. f f Lesson 8. A. B. C. (, 6) (0, ) (, ) (0, ) ( 0, ) (, ) D. E. F. (0, ) (, 6) ( 0, ) (, ) (, ) (0, ) Eplain how
More informationf 0 ab a b: base f
Precalculus Notes: Unit Eponential and Logarithmic Functions Sllaus Ojective: 9. The student will sketch the graph of a eponential, logistic, or logarithmic function. 9. The student will evaluate eponential
More informationThe semester B examination for Algebra 2 will consist of two parts. Part 1 will be selected response. Part 2 will be short answer. n times per year: 1
ALGEBRA B Semester Eam Review The semester B eamination for Algebra will consist of two parts. Part 1 will be selected response. Part will be short answer. Students ma use a calculator. If a calculator
More informationTest # 33 QUESTIONS MATH131 091700 COLLEGE ALGEBRA Name atfm131bli www.alvarezmathhelp.com website MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
More informationPre-Calculus B Semester 1 Review Packet December 2015
Pre-Calculus B Semester Review Packet December 05 Name DISCLAIMER The memor on all calculators will be cleared the da of the final. If ou have programs on our calculator that ou would like to keep, please
More informationTest #4 33 QUESTIONS MATH1314 09281700 COLLEGE ALGEBRA Name atfm1314bli28 www.alvarezmathhelp.com website SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
More informationf 2a.) f 4a.) increasing:
MSA Pre-Calculus Midterm Eam Review December 06. Evaluate the function at each specified value of the independent variable and simplify. f ( ) f ( ) c. ( b ) f ) ). Evaluate the function at each specified
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 informationLogarithms. Bacteria like Staph aureus are very common.
UNIT 10 Eponentials and Logarithms Bacteria like Staph aureus are ver common. Copright 009, K1 Inc. All rights reserved. This material ma not be reproduced in whole or in part, including illustrations,
More informationName Period Date. Practice FINAL EXAM Intro to Calculus (50 points) Show all work on separate sheet of paper for full credit!
Name Period Date Practice FINAL EXAM Intro to Calculus (0 points) Show all work on separate sheet of paper for full credit! ) Evaluate the algebraic epression for the given value or values of the variable(s).
More informationN x. You should know how to decompose a rational function into partial fractions.
Section.7 Partial Fractions Section.7 Partial Fractions N You should know how to decompose a rational function into partial fractions. D (a) If the fraction is improper, divide to obtain N D p N D (a)
More informationMath 111 Final Exam Review KEY
Math Final Eam Review KEY. Use the graph of = f in Figure to answer the following. Approimate where necessar. a Evaluate f. f = 0 b Evaluate f0. f0 = 6 c Solve f = 0. =, =, =,or = 3 d Solve f = 7..5, 0.5,
More informationSec 5.1 Exponential & Logarithmic Functions (Exponential Models)
Sec 5.1 Eponential & Logarithmic Functions (Eponential Models) 1. The population of the cit Suwanee, GA has consistentl grown b 4% for the last several ears. In the ear 000, the population was 9,500 people.
More informationThe formulas below will be provided in the examination booklet. Compound Interest: r n. Continuously: n times per year: 1
HONORS ALGEBRA B Semester Eam Review The semester B eamination for Honors Algebra will consist of two parts. Part will be selected response on which a calculator will not be allowe Part will be short answer
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 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 informationREVIEW. log e. log. 3 k. x 4. log ( x+ 3) log x= ,if x 2 y. . h
Math REVIEW Part I: Problems Simplif (without the use of calculators) ln log 000 e 0 k = k = k 7 log ( ) 8 lo g (log ) Solve the following equations/inequalities Check when necessar 8 =0 9 0 + = log (
More informationMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Final Eam Review MAC 1 Spring 0 Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve and check the linear equation. 1) (- + ) - = -( - 7) {-
More informationEAST LOS ANGELES COLLEGE
EAST LOS ANGELES COLLEGE NAME: MATHEMATICS FINAL EXAM SAMPLE INSTRUCTOR: ANNE SISWANTO; TIME: 10 MINUTES --------------------------------------------------------------------------------------------------------------------------
More informationMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Final Eam Review MAC 1 Fall 011 Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve and check the linear equation. 1) (- + ) - = -( - 7) A)
More informationMath 111 Final Exam Review
Math 111 Final Eam Review With the eception of rounding irrational logarithmic epressions and problems that specif that a calculator should be used, ou should be prepared to do the entire problem without
More informationMAT 116 Final Exam Review
MAT 116 Final Eam Review 1. Determine the equation for the line described, writing the answer in slope-intercept form. The line is parallel to = 8 and passes through ( 1,9). The line is perpendicular to
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 NON-CALCULATOR DIRECTIONS: The problems
More informationLearning Goals. College of Charleston Department of Mathematics Math 101: College Algebra Final Exam Review Problems 1
College of Charleston Department of Mathematics Math 0: College Algebra Final Eam Review Problems Learning Goals (AL-) Arithmetic of Real and Comple Numbers: I can classif numbers as natural, integer,
More informationFirst Semester Final Review NON-Graphing Calculator
Algebra First Semester Final Review NON-Graphing Calculator Name:. 1. Find the slope of the line passing through the points ( 5, ) and ( 3, 7).. Find the slope-intercept equation of the line passing through
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 016-017 1. Model the following situation with a linear equation in slope-intercept form. 4 The gas tank in a truck holds 15 gallons. The truck uses gallon per mile. 7.
More informationChapter 8 Notes SN AA U2C8
Chapter 8 Notes SN AA U2C8 Name Period Section 8-: Eploring Eponential Models Section 8-2: Properties of Eponential Functions In Chapter 7, we used properties of eponents to determine roots and some of
More informationChapter 4 Page 1 of 16. Lecture Guide. Math College Algebra Chapter 4. to accompany. College Algebra by Julie Miller
Chapter 4 Page 1 of 16 Lecture Guide Math 105 - College Algebra Chapter 4 to accompan College Algebra b Julie Miller Corresponding Lecture Videos can be found at Prepared b Stephen Toner & Nichole DuBal
More informationab is shifted horizontally by h units. ab is shifted vertically by k units.
Algera II Notes Unit Eight: Eponential and Logarithmic Functions Sllaus Ojective: 8. The student will graph logarithmic and eponential functions including ase e. Eponential Function: a, 0, Graph of an
More informationPolynomial and Rational Functions
Name Date Chapter Polnomial and Rational Functions Section.1 Quadratic Functions Objective: In this lesson ou learned how to sketch and analze graphs of quadratic functions. Important Vocabular Define
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 informationAnswers for the problems can be found at the end of this packet starting on Page 12.
MAC 0 Review for Final Eam The eam will consists of problems similar to the ones below. When preparing, focus on understanding and general procedures (when available) rather than specific question. Answers
More informationa [A] +Algebra 2/Trig Final Exam Review Fall Semester x [E] None of these [C] 512 [A] [B] 1) Simplify: [D] x z [E] None of these 2) Simplify: [A]
) Simplif: z z z 6 6 z 6 z 6 ) Simplif: 9 9 0 ) Simplif: a a a 0 a a ) Simplif: 0 0 ) Simplif: 9 9 6) Evaluate: / 6 6 6 ) Rationalize: ) Rationalize: 6 6 0 6 9) Which of the following are polnomials? None
More information6.4 graphs OF logarithmic FUnCTIOnS
SECTION 6. graphs of logarithmic functions 9 9 learning ObjeCTIveS In this section, ou will: Identif the domain of a logarithmic function. Graph logarithmic functions. 6. graphs OF logarithmic FUnCTIOnS
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 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 informationChapters 8 & 9 Review for Final
Math 203 - 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
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 informationUnit 2 Review. No Calculator Allowed. 1. Find the domain of each function. (1.2)
PreCalculus Unit Review Name: No Calculator Allowed 1. Find the domain of each function. (1.) log7 a) g 9 7 b) hlog7 c) h 97 For questions &, (1.) (a) Find the domain (b) Identif an discontinuities as
More informationPreCalculus Honors: Functions and Their Graphs. Unit Overview. Student Focus. Example. Semester 1, Unit 2: Activity 9. Resources: Online Resources:
Resources: SpringBoard- PreCalculus PreCalculus Honors: Functions and Their Graphs Semester 1, Unit 2: Activity 9 Unit Overview In this unit, students study polynomial and rational functions. They graph
More informationHonors Pre-Calculus. Multiple Choice 1. An expression is given. Evaluate it at the given value
Honors Pre-Calculus Multiple Choice. An epression is given. Evaluate it at the given value, (A) (B) 9 (C) 9 (D) (E). Simplif the epression. (A) + (B) (C) (D) (E) 7. Simplif the epression. (A) (B) (C) (D)
More information3.1 Graphing Quadratic Functions. Quadratic functions are of the form.
3.1 Graphing Quadratic Functions A. Quadratic Functions Completing the Square Quadratic functions are of the form. 3. It is easiest to graph quadratic functions when the are in the form using transformations.
More informationa > 0 parabola opens a < 0 parabola opens
Objective 8 Quadratic Functions The simplest quadratic function is f() = 2. Objective 8b Quadratic Functions in (h, k) form Appling all of Obj 4 (reflections and translations) to the function. f() = a(
More information7-1. Exploring Exponential Models. Vocabulary. Review. Vocabulary Builder. Use Your Vocabulary. 1. Cross out the expressions that are NOT powers.
7-1 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 informationFinal Exam Review Spring a. Is this a quadratic? 2 a. Is this a quadratic? b. EXPLAIN why or why not. b. EXPLAIN why or why not!!
Final Exam Review Spring 01-013 Name Module 4 Fill in the charts below. x x -6 0 Change in 0 0 Change in -3 1 1-1 4 5 0 9 3 10 16 4 17 5 5 5 6 6 36 6 37 1 Is this a quadratic? Is this a quadratic? b. EXPLAIN
More informationName DIRECTIONS: PLEASE COMPLET E ON A SEPARATE SHEET OF PAPER. USE THE ANSWER KEY PROVIDED TO CORRECT YOUR WORK. THIS WILL BE COLLECTED!!!
FINAL EXAM REVIEW 0 PRECALCULUS Name DIRECTIONS: PLEASE COMPLET E ON A SEPARATE SHEET OF PAPER. USE THE ANSWER KEY PROVIDED TO CORRECT YOUR WORK. THIS WILL BE COLLECTED!!! State the domain of the rational
More informationMath 111 Final Exam Review KEY
Math 111 Final Eam Review KEY 1. Use the graph of = f in Figure 1 to answer the following. Approimate where necessar. a b Evaluate f 1. f 1 = 0 Evaluate f0. f0 = 6 c Solve f = 0. =, = 1, =, or = 3 Solution
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 informationItems with a symbol next to the item number indicate that a student should be prepared to complete items like these with or without a calculator.
HNRS ALGEBRA B Semester Eam Review The semester B eamination for Honors Algebra will consist of two parts. Part is selected response on which a calculator will NT be allowed. Part is short answer on which
More informationCHAPTER 3 Exponential and Logarithmic Functions
CHAPTER Eponential and Logarithmic Functions Section. Eponential Functions and Their Graphs......... Section. Logarithmic Functions and Their Graphs......... Section. Properties of Logarithms..................
More information2. Tell whether the equation or graph represents an exponential growth or exponential decay function.
Name: Date: Period: ID: 1 Unit 9 Review Eponents & Logarithms NO GRAPHING CALCULATOR 1. Under each function, write es if it is an eponential function. If the answer is no, write an eplanation wh not. a)
More information1.2 Functions and Their Properties PreCalculus
1. Functions and Their Properties PreCalculus 1. FUNCTIONS AND THEIR PROPERTIES Learning Targets for 1. 1. Determine whether a set of numbers or a graph is a function. Find the domain of a function given
More informationThe Natural Base e. ( 1, e 1 ) 220 Chapter 3 Exponential and Logarithmic Functions. Example 6 Evaluating the Natural Exponential Function.
0 Chapter Eponential and Logarithmic Functions (, e) f() = e (, e ) (0, ) (, e ) FIGURE.9 The Natural Base e In man applications, the most convenient choice for a base is the irrational number e.78888....
More informationCHAPTER 3 Exponential and Logarithmic Functions
CHAPTER Eponential and Logarithmic Functions Section. Eponential Functions and Their Graphs You should know that a function of the form f a, where a >, a, is called an eponential function with base a.
More information7Exponential and. Logarithmic Functions
7Eponential and Logarithmic Functions A band of green light occasionall appears above the rising or setting sun. This phenomenon is known as a green flash because it lasts for a ver brief period of time.
More informationCHAPTER 3 Exponential and Logarithmic Functions
CHAPTER Eponential and Logarithmic Functions Section. Eponential Functions and Their Graphs......... Section. Logarithmic Functions and Their Graphs......... Section. Properties of Logarithms..................
More informationis on the graph of y = f 1 (x).
Objective 2 Inverse Functions Illustrate the idea of inverse functions. f() = 2 + f() = Two one-to-one functions are inverses of each other if (f g)() = of g, and (g f)() = for all in the domain of f.
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 2-3 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 informationReview Exercises for Chapter 2
Review Eercises for Chapter 7 Review Eercises for Chapter. (a) Vertical stretch Vertical stretch and a reflection in the -ais Vertical shift two units upward (a) Horizontal shift two units to the left.
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 information9) A) f-1(x) = 8 - x B) f-1(x) = x - 8 C)f-1(x) = x + 8 D) f-1(x) = x 8
Review for Final Eam Name Algebra- Trigonometr MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Factor the polnomial completel. If a polnomial cannot
More informationAlgebra II Notes Unit Six: Polynomials Syllabus Objectives: 6.2 The student will simplify polynomial expressions.
Algebra II Notes Unit Si: Polnomials Sllabus Objectives: 6. The student will simplif polnomial epressions. Review: Properties of Eponents (Allow students to come up with these on their own.) Let a and
More informationLesson Goals. Unit 5 Exponential/Logarithmic Functions Exponential Functions (Unit 5.1) Exponential Functions. Exponential Growth: f (x) = ab x, b > 1
Unit 5 Eponential/Logarithmic Functions Eponential Functions Unit 5.1) William Bill) Finch Mathematics Department Denton High School Lesson Goals When ou have completed this lesson ou will: Recognize and
More information6.2 Indicate whether the function is one-to-one. 16) {(-13, -20), (-10, -20), (13, -8)}
Math 0 Eam Review. Evaluate the epression using the values given in the table. ) (f g)() 7 f() - - - g() - 7 Evaluate the epression using the graphs of = f() and = g(). ) Evaluate (fg)(). 9) H() = - 7
More informationExponential and Logarithmic Functions
Eponential and Logarithmic Functions. Eponential Functions and Their Graphs. Logarithmic Functions and Their Graphs. Properties of Logarithms. Eponential and Logarithmic Equations.5 Eponential and Logarithmic
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 informationMaintaining Mathematical Proficiency
Name Date Chapter 8 Maintaining Mathematical Proficienc Graph the linear equation. 1. = 5. = + 3 3. 1 = + 3. = + Evaluate the epression when =. 5. + 8. + 3 7. 3 8. 5 + 8 9. 8 10. 5 + 3 11. + + 1. 3 + +
More information1. For each of the following, state the domain and range and whether the given relation defines a function. b)
Eam Review Unit 0:. For each of the following, state the domain and range and whether the given relation defines a function. (,),(,),(,),(5,) a) { }. For each of the following, sketch the relation and
More informationChapter 12 and 13 Math 125 Practice set Note: the actual test differs. Given f(x) and g(x), find the indicated composition and
Chapter 1 and 13 Math 1 Practice set Note: the actual test differs. Given f() and g(), find the indicated composition. 1) f() = - ; g() = 3 + Find (f g)(). Determine whether the function is one-to-one.
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 informationCalculus Summer Packet
Calculus Summer Packet Congratulations on reaching this level of mathematics in high school. I know some or all of you are bummed out about having to do a summer math packet; but keep this in mind: we
More informationReady To Go On? Skills Intervention 7-1 Exponential Functions, Growth, and Decay
7A Find these vocabular words in Lesson 7-1 and the Multilingual Glossar. Vocabular Read To Go On? Skills Intervention 7-1 Eponential Functions, Growth, and Deca eponential growth eponential deca asmptote
More informationChapter 8. Exponential and Logarithmic Functions
Chapter 8 Eponential and Logarithmic Functions Lesson 8-1 Eploring Eponential Models Eponential Function The general form of an eponential function is y = ab. Growth Factor When the value of b is greater
More informationAlgebra 1B Assignments Exponential Functions (All graphs must be drawn on graph paper!)
Name Score Algebra 1B Assignments Eponential Functions (All graphs must be drawn on graph paper!) 8-6 Pages 463-465: #1-17 odd, 35, 37-40, 43, 45-47, 50, 51, 54, 55-61 odd 8-7 Pages 470-473: #1-11 odd,
More informationPre-Calculus First Semester Review
NON CALCULATOR Pre-Calculus First Semester Review Unit 1: 1 37 Unit : 1 18, 38 49 Unit 3: 19,, 5 6 [1.] Find the domain. Epress the answer in interval notation. 1. f( ) log ( 5) = +. 3 f( ) = 7 + 4 [1.]
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 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 informationSample Questions. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Sample Questions MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Determine whether the equation is linear or nonlinear. 1) - = A) linear nonlinear
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 informationAdvanced Algebra 2 Final Review Packet KG Page 1 of Find the slope of the line passing through (3, -1) and (6, 4).
Advanced Algebra Final Review Packet KG 0 Page of 8. Evaluate (7 ) 0 when and. 7 7. Solve the equation.. Solve the equation.. Solve the equation. 6. An awards dinner costs $ plus $ for each person making
More informationUnit 8: Exponential & Logarithmic Functions
Date Period Unit 8: Eponential & Logarithmic Functions DAY TOPIC ASSIGNMENT 1 8.1 Eponential Growth Pg 47 48 #1 15 odd; 6, 54, 55 8.1 Eponential Decay Pg 47 48 #16 all; 5 1 odd; 5, 7 4 all; 45 5 all 4
More information1. Simplify each expression and write all answers without negative exponents. for variable L.
MATH 0: PRACTICE FINAL Spring, 007 Chapter # :. Simplif each epression and write all answers without negative eponents. ( ab ) Ans. b 9 7a 6 Ans.. Solve each equation. 5( ) = 5 5 Ans. man solutions + 7
More informationExponential and Logarithmic Functions
Chapter 6 Eponential and Logarithmic Functions 6.3 Logarithmic Functions. 9 = 3 is equivalent to = log 3 9. 6 = 4 is equivalent to = log 4 6 3. a =.6 is equivalent to = log a.6 4. a 3 =. is equivalent
More informationHCC-SE MATH DEPT. 1 Revised Fall 2008
FINAL EXAM REVIEW ITEMS Math : College Algebra Find the -intercepts and an -intercepts. ) f() = + 7-0 ) = Name ) Select the equation that describes the graph. Solve the equation and epress the solution
More information7-1 Practice. Graphing Exponential Functions. Graph each function. State the domain and range. 1. y = 1.5(2) x 2. y = 4(3) x 3. y = 3(0.
7-1 Practice Graphing Eponential Functions Graph each function. State the domain and range. 1. = 1.5(2) 2. = 4(3) 3. = 3(0.5) 4. = 5 ( 1 2) - 8 5. = - 2 ( 1 4) - 3 6. = 1 2 (3) + 4-5 7. BILGY The initial
More informationLecture Notes Basic Functions and their Properties page 1
Lecture Notes Basic Functions and their Properties page De nition: A function f is (or injective) if for all a and b in its domain, if a = b, then f (a) = f (b). Alternative de nition: A function f is
More informationSHORT ANSWER. Write the word or phrase that best completes each statement or answers the question
Midterm Review 0 Precalculu Name SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question ) A graph of a function g is shown below. Find g(0). (-, ) (-, 0) - -
More informationAdvanced Calculus BC Summer Work Due: 1 st Day of School
Dear Calculus BC student, I hope that ou re all enjoing our first few das of summer! Here s something that will make it a little more fun! Enclosed ou will find a packet of review questions that ou should
More informationis on the graph of y = f 1 (x).
Objective 2 Inverse Functions Illustrate the idea of inverse functions. f() = 2 + f() = Two one-to-one functions are inverses of each other if (f g)() = of g, and (g f)() = for all in the domain of f.
More information4.5 Practice B. 4.5 Practice A. Name Date. Possible zeros: Possible zeros: 5. Justify. your answer. your answer. In Exercises 1 6, solve the equation.
Practice A Practice B In Eercises, solve the equation.. q q 0q 0. k + k + 9k 0.. p p. 8u u n + n 9n 8 0 In Eercises 7 0, find the zeros of the function. Then sketch a graph of the function. 7. f + 8. g
More informationPolynomial Functions. INVESTMENTS Many grandparents invest in the stock market for
4-1 BJECTIVES Determine roots of polnomial equations. Appl the Fundamental Theorem of Algebra. Polnomial Functions INVESTMENTS Man grandparents invest in the stock market for their grandchildren s college
More informationPRE-CALCULUS: by Finney,Demana,Watts and Kennedy Chapter 3: Exponential, Logistic, and Logarithmic Functions 3.1: Exponential and Logistic Functions
PRE-CALCULUS: Finne,Demana,Watts and Kenned Chapter 3: Eponential, Logistic, and Logarithmic Functions 3.1: Eponential and Logistic Functions Which of the following are eponential functions? For those
More information( ) ( ) ( ) ( ) MATHEMATICS Precalculus Martin Huard Fall 2007 Semester Review. 1. Simplify each expression. 4a b c. x y. 18x. x 2x.
MATHEMATICS 0-009-0 Precalculus Martin Huard Fall 007. Simplif each epression. a) 8 8 g) ( ) ( j) m) a b c a b 8 8 8 n f) t t ) h) + + + + k) + + + n) + + + + + ( ) i) + n 8 + 9 z + l) 8 o) ( + ) ( + )
More informationAP Calculus AB Summer Assignment Mrs. Berkson
AP Calculus AB Summer Assignment Mrs. Berkson The purpose of the summer assignment is to prepare ou with the necessar Pre- Calculus skills required for AP Calculus AB. Net ear we will be starting off the
More information5A Exponential functions
Chapter 5 5 Eponential and logarithmic functions bjectives To graph eponential and logarithmic functions and transformations of these functions. To introduce Euler s number e. To revise the inde and logarithm
More information