1.1 Checkpoint GCF Checkpoint GCF 2 1. Circle the smaller number in each pair. Name the GCF of the following:
|
|
- Homer Goodwin
- 5 years ago
- Views:
Transcription
1 39
2 0
3 . Checkpoint GCF Name the GCF of the following: y + 5ab y 5y + 7 y y 8 y + y.. Checkpoint GCF. Circle the smaller number in each pair. 5, 0 8, 0,,,, ,,, If you have a hard time comparing numbers, you might want to think of the number line. The smaller number is always to the left. Place the numbers, on the 0 5 number line below. - 0
4 3. Complete the following. WHAT DID THE PET OWNER SAY TO HER OVERWEIGHT PARROT? Match the epression with its factor to be factored out. To answer the riddle, write the letter of the correct answers on the appropriate lines below Y P M. 5 + A. 5 + B E L G N O. L. L. D F. 5 O
5 3.. Checkpoint GCF 3 Factor the following. Then check by using the TABLE feature of your calculator AND the corresponding graphs / / + 9/ 9/ + 9/ 3/ / 3/ + 9/ 3/. Checkpoint Binomial GCF Factor out the GCF of each of the following: a) 8( + ) ( + ) b) ( + 8) + 3 ( + 8) 3 c) ( 3)( 9) + ( 3)( 9)
6 . Checkpoint Binomial GCF Factor out the term with the lowest power: a) 9( + 6) + 8 ( + 6) 7 8 b) 5( ) + 9 ( ) 3 0 c) 0 ( + ) 5 ( + ) 5. Checkpoint Binomial GCF 3 Factor out the term with the lower power: a) 9 7 5( + ) + ( + ) b) 3( ) + ( ) c) ( + 5) + ( + 5). Checkpoint Binomial GCF Factor out the GCF: a) 3 (7 8) + 9 (7 8) b) 5 ( + ) + 75 ( + ) 3 c) 6 (3 5) + 5 (3 5)
7 5.3 Checkpoint Absolute Value Make a number line to show possible values of for each of the following situations. Then write your solution as an interval.. < > 8.3 Checkpoint Absolute Value Mark your possible positions on the number line for each of the equations or inequalities below. Then write your solution using interval notation, where appropriate.. 3 =. = =. + 3 = 5. 3 < < > =. 3 < Think about an algebraic way to solve the above and discuss it with your partner.
8 6. Checkpoint Eponential Functions. Write an eponential function with an initial value of $50,000 and a growth rate of 8%.. Write an eponential function with an initial value of $,000 and a growth rate of %. 3. How much money would you have after years if you invested $3,000 in a Certificate of Deposit (CD) earning 5.5% interest compounded every year?. How much money would you have after 0 years if you invested $,000 in a mutual fund earning 8% interest compounded every year? 5. Eplain why in the formula A( t ) = C t the constant C represents the beginning amount of your quantity, given that the variable t represents time. 6. Are the following eponential functions? Yes or no and why. For those that are eponential functions, identify the initial amount and the growth rate. a) y = 0( ) n e) y = ( ) n b) y = 5n f) 5 y = n = g) y = 5n + c) y ( n ).5 d) y =.(.0) n h) y = ( ) 0 n 7. For each of the following growth rates, name the growth factor. a) 5% d) 00% b) 7.5% e) 00% c) % f) 50% 8. For each of the following growth factors, name the growth rate. a).06 d) 5.00 b).5 e).00 c).50 f) 3.5
9 7. Checkpoint Eponential Functions. Determine the amount of money you would have in 0 years if you invested $3,000 in an account that gives 6.5% interest compounded: a) annually b) semi-annually c) quarterly d) monthly e) daily. Determine the amount of money you would have in 0 years if you invested $ 3,000 in an account that compounds interest monthly if the interest rate was: a).5 % b) % c) 5.5 % d) 8 % e) 0.5 % 3. Suppose that you need $5,000 in 3 years and found an account that will give you 8 % interest compounded quarterly. How much would you need to invest now so that you will have that $5,000 in three years?. A one-page letter is folded into thirds to go into an envelope. If it were possible to repeat this kind of tri-fold 0 times, how many miles thick would the letter be? (A stack of 50 pieces of stationery is one inch thick: mile = 580 feet.)* 5. The population of a small town increases by a growth factor of.5 over a two-year period. a) By what percent does the town increase in size during the two-year period? b) If the town grows by the same percent each year, what is its annual percent growth rate? * NOTE: Problems # and #5 are adapted from Connally, Hughes-Hallett, Gleason et al. Functions Modeling Change. A Preparation for Calculus. New York: John Wiley & Sons, 000, p..
10 8. Checkpoint Eponential Functions: Decay. Write an eponential function with an initial value of 50,000 and a decay rate of 3%.. Write an eponential function with an initial value of,000 and a decay rate of 5%. 3. How many people would live in a town after 5 years if 30,000 people lived there originally and 0% skipped town every year?. How many people would live in a town after 8 years if 0,000 people lived there originally and % skipped town every year? 5. Eplain why in the formula A( t ) = C () t that the constant C represents the beginning amount of your quantity, given that the variable t represents time. 6. The amount (in milligrams) of a drug in the body t hours after taking a pill is given by A( t ) = 5(0.85) t. a) What is the initial dose given? b) What percent of the drug leaves the body each hour? c) What is the amount of the drug left after 0 hours? d) After how many hours will there be less than milligram left in the body?* *NOTE: Problem #6 is from Connally, Hughes-Hallett, Gleason et al. Functions Modeling Change. A Preparation for Calculus. New York: John Wiley & Sons, 000, p... Checkpoint Eponential Decay : Factors and Rates. Identify each of the following as a growth or decay eponential function. Identify the growth or decay factor, rate, and the initial value. a) y = 0 (.0) n e) y = ( ) n b) n y = 5 3 f) y = ( 5) n 5 8 n c) y =.5( ) n g) y = ( ) d) y =.( 0.) n h) y = ( ) 6 n. Create a real world scenario that could be modeled by each of the above eponential models.
11 9.3 Checkpoint: Graphs of Eponential Functions Write a function rule for each of the graphs below.. 6 (,) (,5) (-,)
12 50. 6 (-,3) Below are the graphs of y = and y = 0 near the origin. Identify which graph goes with each function in quadrants I and II. 6. Plot a graph of y = and y = 3 a. For what values of is > 3? on the grid below. b. For what values of is < 3?
13 5.3 Checkpoint : Graphs of Eponential Functions. Without using your graphing calculator, match each of the following graphs with its function rule. A) B) C) D)
14 5 E) F) i) y = 3 3 iv) y = 3 ii) y = 3 v) y = iii) y = 3 vi) y = 3. Are the graphs of the following functions concave up or concave down? Eplain a) y = b) y =. Checkpoint: Continuous Compounding. How much money is an account after 8 years if you deposit $500 in an account giving 5.5% interest compounded continuously?. How much money is an account after years if you deposit $500 in an account giving.5% interest compounded continuously? 3. How much money is an account after 0 years if you deposit $000 in an account giving 6.5% interest compounded continuously?. How much money would you need to invest now in an account that gives % interest compounded continuously if you want to have $5000 in this account in 5 years?
15 53 5. It can be shown that e = , where the approimation 3 3 improves as more terms are included. a. Use your calculator to find the sum of the five terms above b. Find the sum of the first seven terms c. Compare your sums with the calculator s displayed value for e (which you can find be entering e ) and state the number of correct digits in te five and seven term sum. d. How many terms of the sum are needed in order to give a nine decimal digit approimation equal to the calculator s displayed value for e? * *NOTE: Problem #5 from Connally, Hughes-Hallett, Gleason et al. Functions Modeling Change. A Preparation for Calculus. New York: John Wiley & Sons, 000, p Checkpoint Eponential Equations Solve and check.. 3 =. 9 = 7. + = 5. = = Checkpoint: Introduction to Logarithms Without using your calculator, name the WHOLE NUMBER PART (the number to the left of the decimal) of the common logarithm of the following numbers ,56,
16 5 3. Checkpoint Logarithms Find the indicated logarithms.. log(0000). log(0.0) 3. log(0.00). log(00000) 5. log (8) 6. log (6) 7. log 8. log 6 9. log 3 (7) 0. log 5 (5). log 5 5. log (6) 3. log ( 6 ). log() 5. log () 6. log 3 () 7. log 5 () 8. log 5 (5-3 ) 9. log 5 (5 0 ) 0. log(0.3 ). log 9 (3). log 5 (5) 3. log 5 (5). log 9 (7) 5. log log log(00) log (8) log(000) log (6) 30.
17 Checkpoint: The Natural Log Function. Epress each equation in eponential form. a) ln 5 = y b) ln = 0 c) ln( 3) = d) ln( + 5) = 3. Epress each equation in logarithmic form. a) e =0 b) e 5 = t c) e = 0 d) e = y 3. Evaluate each of the following without the use of your calculator. 5 a) ln b) lne c) ln e d) ln e 3. Checkpoint: Graphs of logarithmic functions. Identify the characteristics that graphs of all logarithmic functions of the form y = log b share.. Write a function rule for each of the graphs below. a. 5 3 (5,)
18 5 56 b. 3 (3,) c (0,-) Below are the graphs of y = log and y = ln near the origin. Identify which graph goes with which function rule in quadrants I and IV..
19 57 3. Checkpoint: Graphs of logarithmic functions. For each number below, evaluate 0. Then take the common log of your answer. 0 log For each number below, evaluate log. Then use your answer as an eponent with a base of 0. log 0 log
20 58 3. Given the graph below of y = b, sketch in the graph of y = log b. 0 8 y = Checkpoint: Domains of Logarithmic Functions Find the domain of each of the following functions.. y = log( + ). y = ln( + ) 3. y = log( 6). y = ln( 00) 5. y = log( )
21 Checkpoint Logarithmic Equations Solve and check.. log8 =. log 5 = 5 3. log = log ( + 5) =. log (9 0) = Checkpoint.A: Graphs of Simple Rational Functions Write each of the following symbolic epressions in words:. As, f ( ) 5. As, f ( ) 3 3. As, f ( ) 7. As, f ( ) 7 5. As, f ( ) + 6. As 3, f ( ) 7. As, f ( ) 8. As, f ( ) 9. As, f ( ) 0. As, f ( ) Now make a sketch of each of the above. For each epression, you will only have one piece of the graph of f, but there may be more than one possible way of sketching it. Checkpoint.B: Graphs of Reciprocal Functions Identify the horizontal and vertical asymptotes for each of the following functions. Use proper symbols to verify your choices. The find the and y intercepts if they eist.. f ( ) 3. h( ) 5. g( ) =. g( ) = 3 5 =. f ( ) = 6 = 6. h( ) =
22 60 Checkpoint.A: Make a table of values for ( f ( )), as like in the tet. Then do the same for and determine the horizontal asymptote for each of the functions represented below.. f ( ) = f ( ) =. f ( ) = + 6. f ( ) = 3 5. f ( ) 6. f ( ) = + = f ( ) = 8 8. f ( ) = f ( ) f ( ) = + 9 = Now make a conjecture (guess) about the horizontal asymptote of a reciprocal function of the c form f ( ) = + k. Eplain your reasoning. n Checkpoint.B: Determine the horizontal asymptote of the graph of each of the functions, f, below. Verify your answer. 3. f ( ) = 6 3. f ( ) = f ( ) 5. f ( ) = 5 8. f ( ) = ( ) = 9 = + f 3 7. f ( ) 0 8. ( ) = + 6 = + f f ( ) ( ) = + 8 = f
23 6 Checkpoint.C: Determine the vertical asymptote(s) of the graph of each functions indicated below.. f ( ). g( ) = = y = + 5. m( ) = n( ) = 3 6. y = h( ) = 7 9. f ( ) = y = 7 3. g( ) = g( ) = g( ) = + 5. y = 5 5. y = Checkpoint.3A: Combine terms in each of the function rules for f and epress the function as a ratio of polynomials:. f ( ) = f ( ) = f ( ). f ( ) = 9 = + 5. f ( ) = 3 7. f ( ) = f ( ) = + ( + 7) ( ) 8. f ( ) = + ( + ) 3 ( 3) 3
24 6 Checkpoint.3B: Name the horizontal asymptote of the graph of each of the functions g represented below. Then find the -intercept(s) and the y-intercept g( ) = g( ) = 3 6. g( ) = g( ) = g( ) = 5 6. g( ) = g( ) = g( ) =
MA 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 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 informationSummer MA Lesson 20 Section 2.7 (part 2), Section 4.1
Summer MA 500 Lesson 0 Section.7 (part ), Section 4. Definition of the Inverse of a Function: Let f and g be two functions such that f ( g ( )) for every in the domain of g and g( f( )) for every in the
More informationFinal Exam Review Sheet Algebra for Calculus Fall Find each of the following:
Final Eam Review Sheet Algebra for Calculus Fall 007 Find the distance between each pair of points A) (,7) and (,) B), and, 5 5 Find the midpoint of the segment with endpoints (,) and (,) Find each of
More informationCOLLEGE ALGEBRA. Practice Problems Exponential and Logarithm Functions. Paul Dawkins
COLLEGE ALGEBRA Practice Problems Eponential and Logarithm Functions Paul Dawkins Table of Contents Preface... ii Eponential and Logarithm Functions... Introduction... Eponential Functions... Logarithm
More informationExponential and Logarithmic Functions
Exponential and Logarithmic Functions Learning Targets 1. I can evaluate, analyze, and graph exponential functions. 2. I can solve problems involving exponential growth & decay. 3. I can evaluate expressions
More informationChapter 8 Prerequisite Skills
Chapter 8 Prerequisite Skills BLM 8. How are 9 and 7 the same? How are they different?. Between which two consecutive whole numbers does the value of each root fall? Which number is it closer to? a) 8
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 informationCHAPTER 6. Exponential Functions
CHAPTER 6 Eponential Functions 6.1 EXPLORING THE CHARACTERISTICS OF EXPONENTIAL FUNCTIONS Chapter 6 EXPONENTIAL FUNCTIONS An eponential function is a function that has an in the eponent. Standard form:
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 information1.1 Prep Exercise: Greatest Common Factor. Finding the GCF. x andx 3. = x x x x x. x = x x x. greatest factor common to all expressions?
6 64. Prep Eercise: Greatest Common Factor Finding the GCF Greatest common factor. Think about those three words. Greatest. Common. Factor. What is the greatest factor common to all epressions? Eample.
More informationMath M111: Lecture Notes For Chapter 10
Math M: Lecture Notes For Chapter 0 Sections 0.: Inverse Function Inverse function (interchange and y): Find the equation of the inverses for: y = + 5 ; y = + 4 3 Function (from section 3.5): (Vertical
More informationevery hour 8760 A every minute 525,000 A continuously n A
In the previous lesson we introduced Eponential Functions and their graphs, and covered an application of Eponential Functions (Compound Interest). We saw that when interest is compounded n times per year
More informationTwo-Year Algebra 2 A Semester Exam Review
Semester Eam Review Two-Year 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 informationName Date Period. Pre-Calculus Midterm Review Packet (Chapters 1, 2, 3)
Name Date Period Sections and Scoring Pre-Calculus Midterm Review Packet (Chapters,, ) Your midterm eam will test your knowledge of the topics we have studied in the first half of the school year There
More informationIntermediate Algebra Chapter 12 Review
Intermediate Algebra Chapter 1 Review Set up a Table of Coordinates and graph the given functions. Find the y-intercept. Label at least three points on the graph. Your graph must have the correct shape.
More informationMath 103 Final Exam Review Problems Rockville Campus Fall 2006
Math Final Eam Review Problems Rockville Campus Fall. Define a. relation b. function. For each graph below, eplain why it is or is not a function. a. b. c. d.. Given + y = a. Find the -intercept. b. Find
More information8-1 Exploring Exponential Models
8- Eploring Eponential Models Eponential Function A function with the general form, where is a real number, a 0, b > 0 and b. Eample: y = 4() Growth Factor When b >, b is the growth factor Eample: y =
More informationAlgebra II Non-Calculator Spring Semester Exam Review
Algebra II Non-Calculator Spring Semester Eam Review Name: Date: Block: Simplify the epression. Leave only positive eponents.. ( a ). ( p s ). mn 9cd cd. mn. ( w )( w ). 7. 7 7 Write the answer in scientific
More information2.) Find an equation for the line on the point (3, 2) and perpendicular to the line 6x - 3y = 1.
College Algebra Test File Summer 007 Eam #1 1.) Find an equation for the line that goes through the points (-5, -4) and (1, 4)..) Find an equation for the line on the point (3, ) and perpendicular to the
More informationReview for Final Exam Show your work. Answer in exact form (no rounded decimals) unless otherwise instructed.
Review for Final Eam Show your work. Answer in eact form (no rounded decimals) unless otherwise instructed. 1. Consider the function below. 8 if f ( ) 8 if 6 a. Sketch a graph of f on the grid provided.
More informationwhere is a constant other than ( and ) and
Section 12.1: EXPONENTIAL FUNCTIONS When you are done with your homework you should be able to Evaluate eponential functions Graph eponential functions Evaluate functions with base e Use compound interest
More informationMATH 135 Sample Review for the Final Exam
MATH 5 Sample Review for the Final Eam This review is a collection of sample questions used by instructors of this course at Missouri State University. It contains a sampling of problems representing the
More informationExponential Growth and Decay Functions (Exponent of t) Read 6.1 Examples 1-3
CC Algebra II HW #42 Name Period Row Date Section 6.1 1. Vocabulary In the eponential growth model Eponential Growth and Decay Functions (Eponent of t) Read 6.1 Eamples 1-3 y = 2.4(1.5), identify the initial
More informationC. HECKMAN TEST 1A SOLUTIONS 170
C. HECKMAN TEST 1A SOLUTIONS 170 1) Thornley s Bank of Atlanta offers savings accounts which earn 4.5% per year. You have $00, which you want to invest. a) [10 points] If the bank compounds the interest
More informationPlease show all work and simplify and box answers. Non-graphing scientific calculators are allowed.
Math Precalculus Algebra FINAL PRACTICE PROBLEMS Name Please show all work and simplify and bo answers. Non-graphing scientific calculators are allowed. Solve for w. 3 1) m yw tw ) a) Find the equation
More informationExponential Growth. b.) What will the population be in 3 years?
0 Eponential Growth y = a b a b Suppose your school has 4512 students this year. The student population is growing 2.5% each year. a.) Write an equation to model the student population. b.) What will the
More information6-1 LESSON MASTER. Name. Skills Objective A In 1 4, evaluate without a calculator In 5 and 6, rewrite each using a radical sign.
6-1 Skills Objective A In 1 4, evaluate without a calculator. 1. 2. 64 1 3 3 3. -343 4. 36 1 2 4 16 In 5 and 6, rewrite each using a radical sign. 5. ( 2 ) 1 4 m 1 6 In 7 10, rewrite without a radical
More informationCHAPTER 2: Polynomial and Rational Functions
(Exercises for Chapter 2: Polynomial and Rational Functions) E.2.1 CHAPTER 2: Polynomial and Rational Functions (A) means refer to Part A, (B) means refer to Part B, etc. (Calculator) means use a calculator.
More informationMath 103 Intermediate Algebra Final Exam Review Practice Problems
Math 10 Intermediate Algebra Final Eam Review Practice Problems The final eam covers Chapter, Chapter, Sections 4.1 4., Chapter 5, Sections 6.1-6.4, 6.6-6.7, Chapter 7, Chapter 8, and Chapter 9. The list
More informationPRECALCULUS GROUP FINAL FIRST SEMESTER Approximate the following 1-3 using: logb 2 0.6, logb 5 0.7, 2. log. 2. log b
PRECALCULUS GROUP FINAL FIRST SEMESTER 008 Approimate the following 1-3 using: log 0.6, log 5 0.7, and log 7 0. 9 1. log = log log 5 =... 5. log 10 3. log 7 4. Find all zeros algeraically ( any comple
More informationMath 180 Chapter 4 Lecture Notes. Professor Miguel Ornelas
Math 80 Chapter 4 Lecture Notes Professor Miguel Ornelas M. Ornelas Math 80 Lecture Notes Section 4. Section 4. Inverse Functions Definition of One-to-One Function A function f with domain D and range
More informationName: Math Analysis Chapter 3 Notes: Exponential and Logarithmic Functions
Name: Math Analysis Chapter 3 Notes: Eponential and Logarithmic Functions Day : Section 3-1 Eponential Functions 3-1: Eponential Functions After completing section 3-1 you should be able to do the following:
More informationMATH 175: Final Exam Review for Pre-calculus
MATH 75: Final Eam Review for Pre-calculus In order to prepare for the final eam, you need too be able to work problems involving the following topics:. Can you graph rational functions by hand after algebraically
More informationExample 1: What do you know about the graph of the function
Section 1.5 Analyzing of Functions In this section, we ll look briefly at four types of functions: polynomial functions, rational functions, eponential functions and logarithmic functions. Eample 1: What
More informationExponential and Logarithmic Functions. 3. Pg #17-57 column; column and (need graph paper)
Algebra 2/Trig Unit 6 Notes Packet Name: Period: # Exponential and Logarithmic Functions 1. Worksheet 2. Worksheet 3. Pg 483-484 #17-57 column; 61-73 column and 76-77 (need graph paper) 4. Pg 483-484 #20-60
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 informationx x x 2. Use your graphing calculator to graph each of the functions below over the interval 2,2
MSLC Math 48 Final Eam Review Disclaimer: This should NOT be used as your only guide for what to study.. Use the piece-wise defined function 4 4 if 0 f( ) to answer the following: if a) Compute f(-), f(-),
More informationMATH 175: Final Exam Review for Pre-calculus
MATH 75: Final Eam Review for Pre-calculus In order to prepare for the final eam, you need to be able to work problems involving the following topics:. Can you find and simplify the composition of two
More informationOne-to-One Functions YouTube Video
Section 9. One-to-One Functions YouTue Video A function in which each element in the range corresponds to one and only one element in the domain. Determine if the following are One-to-one functions:,,
More informationExponential and Logarithmic Functions
Öğr. Gör. Volkan ÖĞER FBA 1021 Calculus 1/ 40 Exponential and Logarithmic Functions Exponential Functions The functions of the form f(x) = b x, for constant b, are important in mathematics, business, economics,
More informationGeometry Placement Exam Review Revised 2017 Maine East High School
Geometry Placement Exam Review Revised 017 Maine East High School The actual placement exam has 91 questions. The placement exam is free response students must solve questions and write answer in space
More informationAP Calculus AB - Mrs. Mora. Summer packet 2010
AP Calculus AB - Mrs. Mora Summer packet 010 These eercises represent some of the more fundamental concepts needed upon entering AP Calculus AB This "packet is epected to be completed and brought to class
More informationReview of Functions A relation is a function if each input has exactly output. The graph of a function passes the vertical line test.
CA-Fall 011-Jordan College Algebra, 4 th edition, Beecher/Penna/Bittinger, Pearson/Addison Wesley, 01 Chapter 5: Exponential Functions and Logarithmic Functions 1 Section 5.1 Inverse Functions Inverse
More information5.1. EXPONENTIAL FUNCTIONS AND THEIR GRAPHS
5.1. EXPONENTIAL FUNCTIONS AND THEIR GRAPHS 1 What You Should Learn Recognize and evaluate exponential functions with base a. Graph exponential functions and use the One-to-One Property. Recognize, evaluate,
More informationMath 20 Final Review. Factor completely. a x bx a y by. 2x 162. from. 10) Factor out
Math 0 Final Review Factor completely ) 6 ) 6 0 ) a b a y by ) n n ) 0 y 6) y 6 7) 6 8 y 6 yz 8) 9y 0y 9) ( ) ( ) 0) Factor out from 6 0 ) Given P ( ) 6 a) Using the Factor Theorem determine if is a factor
More informationWest Essex Regional School District. AP Calculus AB. Summer Packet
West Esse Regional School District AP Calculus AB Summer Packet 05-06 Calculus AB Calculus AB covers the equivalent of a one semester college calculus course. Our focus will be on differential and integral
More information3.2 Logarithmic Functions and Their Graphs
96 Chapter 3 Eponential and Logarithmic Functions 3.2 Logarithmic Functions and Their Graphs Logarithmic Functions In Section.6, you studied the concept of an inverse function. There, you learned that
More informationCALCULUS I. Practice Problems. Paul Dawkins
CALCULUS I Practice Problems Paul Dawkins Table of Contents Preface... iii Outline... iii Review... Introduction... Review : Functions... Review : Inverse Functions... 6 Review : Trig Functions... 6 Review
More informationGoal: To graph points in the Cartesian plane, identify functions by graphs and equations, use function notation
Section -1 Functions Goal: To graph points in the Cartesian plane, identify functions by graphs and equations, use function notation Definition: A rule that produces eactly one output for one input is
More information* Circle these problems: 23-27, 37, 40-44, 48, No Calculator!
AdvPreCal 1 st Semester Final Eam Review Name 1. Solve using interval notation: 7 8 * Circle these problems: -7, 7, 0-, 8, 6-66 No Calculator!. Solve and graph: 0. Solve using a number line and leave answer
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 informationSample Questions. Please be aware that the worked solutions shown are possible strategies; there may be other strategies that could be used.
Sample Questions Students who achieve the acceptable standard should be able to answer all the following questions, ecept for any part of a question labelled SE. Parts labelled SE are appropriate eamples
More informationAlgebra 2-2nd Semester Exam Review 11
Algebra 2-2nd 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 informationWrite each expression as a sum or difference of logarithms. All variables are positive. 4) log ( ) 843 6) Solve for x: 8 2x+3 = 467
Write each expression as a single logarithm: 10 Name Period 1) 2 log 6 - ½ log 9 + log 5 2) 4 ln 2 - ¾ ln 16 Write each expression as a sum or difference of logarithms. All variables are positive. 3) ln
More informationChapter 2 Exponentials and Logarithms
Chapter Eponentials and Logarithms The eponential function is one of the most important functions in the field of mathematics. It is widely used in a variety of applications such as compounded interest,
More informationHonors Calculus Summer Preparation 2018
Honors Calculus Summer Preparation 08 Name: ARCHBISHOP CURLEY HIGH SCHOOL Honors Calculus Summer Preparation 08 Honors Calculus Summer Work and List of Topical Understandings In order to be a successful
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 informationnotes.notebook April 08, 2014
Chapter 7: Exponential Functions graphs solving equations word problems Graphs (Section 7.1 & 7.2): c is the common ratio (can not be 0,1 or a negative) if c > 1, growth curve (graph will be increasing)
More informationExponential and Logarithmic Functions. Copyright Cengage Learning. All rights reserved.
3 Exponential and Logarithmic Functions Copyright Cengage Learning. All rights reserved. 3.1 Exponential Functions and Their Graphs Copyright Cengage Learning. All rights reserved. What You Should Learn
More informationSummer Mathematics Prep
Summer Mathematics Prep Entering Calculus Chesterfield County Public Schools Department of Mathematics SOLUTIONS Domain and Range Domain: All Real Numbers Range: {y: y } Domain: { : } Range:{ y : y 0}
More information) approaches e
COMMON CORE Learning Standards HSF-IF.C.7e HSF-LE.B.5. USING TOOLS STRATEGICALLY To be proficient in math, ou need to use technological tools to eplore and deepen our understanding of concepts. The Natural
More informationWBHS Algebra 2 - Final Exam
Class: _ Date: _ WBHS Algebra 2 - Final Eam Multiple Choice Identify the choice that best completes the statement or answers the question. Describe the pattern in the sequence. Find the net three terms.
More information1. What is the domain and range of the function? 2. Any asymptotes?
Section 8.1 Eponential Functions Goals: 1. To simplify epressions and solve eponential equations involving real eponents. I. Definition of Eponential Function An function is in the form, where and. II.
More informationSuggested Problems for Math 122
Suggested Problems for Math 22 Note: This file will grow as the semester evolves and more sections are added. CCA = Contemporary College Algebra, SIA = Shaum s Intermediate Algebra SIA(.) Rational Epressions
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 informationMA Practice Questions for the Final Exam 07/10 .! 2! 7. 18! 7.! 30! 12 " 2! 3. A x y B x y C x xy x y D.! 2x! 5 y E.
MA 00 Practice Questions for the Final Eam 07/0 ) Simplify:! y " [! (y " )].!! 7. 8! 7.! 0! "! A y B y C y y D.!! y E. None of these ) Which number is irrational? A.! B..4848... C. 7 D.. E.! ) The slope
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 informationAP Calculus BC Summer Assignment School Year
AP Calculus BC Summer Assignment School Year 018-019 Objective of the summer assignment: i. To build on students readiness in foundational skills and knowledge ii. To review prerequisites topics for the
More informationMath 112 Fall 2015 Midterm 2 Review Problems Page 1. has a maximum or minimum and then determine the maximum or minimum value.
Math Fall 05 Midterm Review Problems Page f 84 00 has a maimum or minimum and then determine the maimum or minimum value.. Determine whether Ma = 00 Min = 00 Min = 8 Ma = 5 (E) Ma = 84. Consider the function
More informationName Date. Logarithms and Logarithmic Functions For use with Exploration 3.3
3.3 Logarithms and Logarithmic Functions For use with Eploration 3.3 Essential Question What are some of the characteristics of the graph of a logarithmic function? Every eponential function of the form
More informationChapter 11 Logarithms
Chapter 11 Logarithms Lesson 1: Introduction to Logs Lesson 2: Graphs of Logs Lesson 3: The Natural Log Lesson 4: Log Laws Lesson 5: Equations of Logs using Log Laws Lesson 6: Exponential Equations using
More informationMath 120 Handouts. Functions Worksheet I (will be provided in class) Point Slope Equation of the Line 3. Functions Worksheet III 15
Math 0 Handouts HW # (will be provided to class) Lines: Concepts from Previous Classes (emailed to the class) Parabola Plots # (will be provided in class) Functions Worksheet I (will be provided in class)
More informationIntermediate Algebra Section 9.3 Logarithmic Functions
Intermediate Algebra Section 9.3 Logarithmic Functions We have studied inverse functions, learning when they eist and how to find them. If we look at the graph of the eponential function, f ( ) = a, where
More informationUnit #3 Rules of Differentiation Homework Packet
Unit #3 Rules of Differentiation Homework Packet In the table below, a function is given. Show the algebraic analysis that leads to the derivative of the function. Find the derivative by the specified
More informationDo we have any graphs that behave in this manner that we have already studied?
Boise State, 4 Eponential functions: week 3 Elementary Education As we have seen, eponential functions describe events that grow (or decline) at a constant percent rate, such as placing capitol in a savings
More informationMath 117, Spring 2003, Math for Business and Economics Final Examination
Math 117, Spring 2003, Math for Business and Economics Final Eamination Instructions: Try all of the problems and show all of your work. Answers given with little or no indication of how they were obtained
More informationMath 1160 Final Review (Sponsored by The Learning Center) cos xcsc tan. 2 x. . Make the trigonometric substitution into
Math 60 Final Review (Sponsored by The Learning Center). Simplify cot csc csc. Prove the following identities: cos csc csc sin. Let 7sin simplify.. Prove: tan y csc y cos y sec y cos y cos sin y cos csc
More informationINTERNET MAT 117 Review Problems. (1) Let us consider the circle with equation. (b) Find the center and the radius of the circle given above.
INTERNET MAT 117 Review Problems (1) Let us consider the circle with equation x 2 + y 2 + 2x + 3y + 3 4 = 0. (a) Find the standard form of the equation of the circle given above. (b) Find the center and
More informationAlgebra 2 & Trigonometry Honors Midterm Review 2016
Algebra & Trigonometry Honors Midterm Review 016 Solving Equations 1) Find all values of x that satisfy the equation, 5x 1 = x + 3 ) Solve the following by completing the square. Express your answer in
More information1. Graph each of the given equations, state the domain and range, and specify all intercepts and symmetry. a) y 3x
MATH 94 Final Exam Review. Graph each of the given equations, state the domain and range, and specify all intercepts and symmetry. a) y x b) y x 4 c) y x 4. Determine whether or not each of the following
More information4 Exponential and Logarithmic Functions
4 Exponential and Logarithmic Functions 4.1 Exponential Functions Definition 4.1 If a > 0 and a 1, then the exponential function with base a is given by fx) = a x. Examples: fx) = x, gx) = 10 x, hx) =
More informationMath 120 Handouts. Functions Worksheet I (will be provided in class) Point Slope Equation of the Line 5. Functions Worksheet III 17
Math 0 Handouts HW # (will be provided to class) Lines: Concepts from Previous Classes (emailed to the class) Parabola Plots # (will be provided in class) Functions Worksheet I (will be provided in class)
More informationComposition of and the Transformation of Functions
1 3 Specific Outcome Demonstrate an understanding of operations on, and compositions of, functions. Demonstrate an understanding of the effects of horizontal and vertical translations on the graphs of
More informationMath 11A Graphing Exponents and Logs CLASSWORK Day 1 Logarithms Applications
Log Apps Packet Revised: 3/26/2012 Math 11A Graphing Eponents and Logs CLASSWORK Day 1 Logarithms Applications Eponential Function: Eponential Growth: Asymptote: Eponential Decay: Parent function for Eponential
More informationOBJECTIVE 4 EXPONENTIAL FORM SHAPE OF 5/19/2016. An exponential function is a function of the form. where b > 0 and b 1. Exponential & Log Functions
OBJECTIVE 4 Eponential & Log Functions EXPONENTIAL FORM An eponential function is a function of the form where > 0 and. f ( ) SHAPE OF > increasing 0 < < decreasing PROPERTIES OF THE BASIC EXPONENTIAL
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 piece-wise defined function f( ) to answer the following: if a. Compute f(0), f(), f(-),
More informationSection 5.1 Determine if a function is a polynomial function. State the degree of a polynomial function.
Test Instructions Objectives Section 5.1 Section 5.1 Determine if a function is a polynomial function. State the degree of a polynomial function. Form a polynomial whose zeros and degree are given. Graph
More informationName Date. Show all work! Exact answers only unless the problem asks for an approximation.
Advanced Calculus & AP Calculus AB Summer Assignment Name Date Show all work! Eact answers only unless the problem asks for an approimation. These are important topics from previous courses that you must
More information2018 Pre-Cal Spring Semester Review Name: Per:
08 Pre-Cal Spring Semester Review Name: Per: For # 4, find the domain of each function. USE INTERVAL NOTATION!!. 4 f ( ) 5. f ( ) 6 5. f( ) 5 4. f( ) 4 For #5-6, find the domain and range of each graph.
More informationAdvanced Algebra Scope and Sequence First Semester. Second Semester
Last update: April 03 Advanced Algebra Scope and Sequence 03-4 First Semester Unit Name Unit : Review of Basic Concepts and Polynomials Unit : Rational and Radical Epressions Sections in Book 0308 SLOs
More informationUnit 10 Prerequisites for Next Year (Calculus)
Unit 0 Prerequisites for Net Year (Calculus) The following Study Guide is the required INDEPENDENT review for you to work through for your final unit. You WILL have a test that covers this material after
More informationName Advanced Math Functions & Statistics. Non- Graphing Calculator Section A. B. C.
1. Compare and contrast the following graphs. Non- Graphing Calculator Section A. B. C. 2. For R, S, and T as defined below, which of the following products is undefined? A. RT B. TR C. TS D. ST E. RS
More informationL E S S O N M A S T E R. Name. Vocabulary. 1. In the expression b n, b is called the?.
Vocabulary 7- See pages 7-7 for objectives.. In the epression b n, b is called the?.. The identity function f has the equation f()?.. If g(), is g an eample of a power function? Why or why not?. In a game
More informationMock Final Exam Name. Solve and check the linear equation. 1) (-8x + 8) + 1 = -7(x + 3) A) {- 30} B) {- 6} C) {30} D) {- 28}
Mock Final Exam Name Solve and check the linear equation. 1) (-8x + 8) + 1 = -7(x + 3) 1) A) {- 30} B) {- 6} C) {30} D) {- 28} First, write the value(s) that make the denominator(s) zero. Then solve the
More informationx 1 2 i 1 5 2i 11 9x 9 3x 3 1 y 2 3y 4 y 2 1 Poudre School District s College Algebra Course Review
. Perform the indicated operations and simplify the result. Leave the answer in factored form. 9x 9 x a. b. 9x 9 x x. Solve: x 7x x 0. a. x., b. x 0,., x,0,. x.,0,. Find the quotient and the remainder
More informationEXPONENTS AND LOGS (CHAPTER 10)
EXPONENTS AND LOGS (CHAPTER 0) POINT SLOPE FORMULA The point slope formula is: y y m( ) where, y are the coordinates of a point on the line and m is the slope of the line. ) Write the equation of a line
More informationMath 0210 Common Final Review Questions (2 5 i)(2 5 i )
Math 0 Common Final Review Questions In problems 1 6, perform the indicated operations and simplif if necessar. 1. ( 8)(4) ( )(9) 4 7 4 6( ). 18 6 8. ( i) ( 1 4 i ) 4. (8 i ). ( 9 i)( 7 i) 6. ( i)( i )
More informationCalculator Inactive Write your answers in the spaces provided. Present clear, concise solutions
11/3/09 Chapter 8 Exponential & Logarithmic Functions Page 1 of 8 Calculator Inactive Write your answers in the spaces provided. Present clear, concise solutions 1. Convert 3 x 2 8 into log form: (1M)
More informationAccuplacer College Level Math Study Guide
Testing Center Student Success Center Accuplacer Study Guide The following sample questions are similar to the format and content of questions on the Accuplacer College Level Math test. Reviewing these
More information