# Precalculus Fall Final Exam REVIEW Evaluate the function at the specified value(s) of the independent variable and simplify.

Save this PDF as:

Size: px
Start display at page:

Download "Precalculus Fall Final Exam REVIEW Evaluate the function at the specified value(s) of the independent variable and simplify."

## Transcription

1 Precalculus Fall Final Eam EVIEW 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. Evaluate the function at the specified value(s) of the independent variable and simplif. 5 gbg ; gbn g. A publishing compan estimates that the average cost (in dollars) for one cop of a new scenic calendar it plans to produce can be approimated b the function Cbg where is the number of calendars printed. Find the average cost per calendar when the compan prints 0 calendars. 4. Find the domain of the function. f Use a graphing utilit to find an relative minimum or maimum values of the function. f Describe the transformation that occurs in the function. b g b g g 5 7. If f 5 and g 4, find (a) g f 8. Find an equation that represents as a function of. b gb g and (b) b f ggbg. [A] [B] 7 [C] 8 [D] b g that represents as a function of. mb 1 g, b8 1g, b8 1g, b1 8gr [C] mb 1, g, b, 8g, b 1, 1gr mb 1 g, b 1g, b1 1gr [D] l 1,, 8, 1q 9. Find a set of ordered pairs, [A],,,, [B],,, b g b g b g b g. Construct a model of the relation m 6,,, 1, 6, 1, 7, 6r. Determine whether the relation is a function.

2 Precalculus Fall Final Eam EVIEW Evaluate the function at the specified value(s) of the independent variable and simplif. f ; f 9 b g 1. Find the domain of the function. 5 hbg 6 1. Find f g c h b gb g and b f ggb g 4 for f 5 and g If fbg and gbg 5, find b f ggbg. 15. Find the inverse of the function. f 5, 8, 8, 5, 8, 9 b g mb g b g b gr 16. The table shows Christine s best javelin throws each ear. Use a graphing utilit to determine an equation for the line of best fit for the data. Use 0 for Year Distance (m) Find the equation of a quadratic function whose graph opens upward. [A] f b g b g 8 11 [C] fbg 9b 5 9g [B] f 8 9 [D] f Find the graph of the quadratic function. f [A] [B]

3 Precalculus Fall Final Eam EVIEW [C] [D] 19. Sketch the graph of the quadratic function and list an -intercepts. f 0. Write the equation of the quadratic function in standard form and find the verte of the graph. f Upco Manufacturing estimates that its profit P in hundreds of dollars is P 6 1 where is the number of units produced in thousands. How man units must be produced to obtain the maimum profit?. Find the equation of the function graphed below. [A] f [B] f [C] f [D] f. Find a polnomial function that has zeros at 1,, and 1 and matches the graph below.

4 Precalculus Fall Final Eam EVIEW [A] f [B] f [C] f [D] f 4. Factor 8 given that is one of its factors. 5. Find the standard form of the given comple number. 1i 4i 6. Find all the zeros of the function. 4 f Determine the domain of the function. f b g b 1 g 8 6 b gb g 8. Find the horizontal asmptotes, if an, of the graph of f Find the vertical asmptote(s), if an, for f The population of an endangered animal species is given b b g b g t f where 70 is the number of animals currentl in the population and t is the time in ears. The population is decreasing at an annual rate of 17%. What is the estimated number of animals in this population in 5 ears? 1. Sketch the graph of the function. f 1

5 Precalculus Fall Final Eam EVIEW Sketch the graph of the logarithmic function. f log 6 b g b g. Use the properties of logarithms to epand the epression. (Assume all variables are positive.) 6 log 8 4. Solve the eponential equation algebraicall e Find the value of. b g 5. log b g 6. log log Find the value of. 7. 5ln An automobile manufacturer is introducing a new fuel-efficient model and estimates the demand for the car as N = 57,000 lnb6t 7g where N is the estimated number of cars to be sold and t is the number of ears after the car is introduced. When will the demand be 15,000 cars? 9. Find a graph that models an eponential growth function. [A] [B]

6 Precalculus Fall Final Eam EVIEW [C] [D] 40. Earl in the 1900s, an airplane manufacturer was able to increase the time its planes could sta aloft b constantl refining its techniques. Use a graphing utilit to find an eponential equation that best models the data. Assume is the number of ears after 19 and is the time aloft in hours. Years after Time aloft (h) Solve the sstem b the method of substitution. 8 S T 4. Solve the sstem b elimination S T 6 4. Use back-substitution to solve the sstem of linear equations. 7 7 z 5 S T 9 z 5 z Solve the sstem of linear equations using Gaussian elimination. 7 z 6 S T 5 5 z 1 z 45. Determine the order of the matri.

7 Precalculus Fall Final Eam EVIEW Find a matri that is equal to the matri below. [A] [B] [C] [D] Evaluate the epression. 4A 7B A , B Find the inverse of the matri (if it eists) Find the determinant of the matri Find the product, if possible. AB, if A 0 4 1, 1 0 B

### MULTIPLE 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)

### Law 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,

### Chapters 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

### C)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.

### MATH 115: Final Exam Review. Can you find the distance between two points and the midpoint of a line segment? (1.1)

MATH : Final Eam Review Can ou find the distance between two points and the midpoint of a line segment? (.) () Consider the points A (,) and ( 6, ) B. (a) Find the distance between A and B. (b) Find the

### 6. 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

### M122 College Algebra Review for Final Exam

M1 College Algebra Review for Final Eam Revised Fall 017 for College Algebra - Beecher All answers should include our work (this could be a written eplanation of the result, a graph with the relevant feature

### Shape and Structure. Forms of Quadratic Functions. Lesson 2.1 Assignment

Lesson.1 Assignment Name Date Shape and Structure Forms of Quadratic Functions 1. Analze the graph of the quadratic function. a. The standard form of a quadratic function is f() 5 a 1 b 1 c. What possible

### Instructor: 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

### 3.2 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

### MAT 1033C -- Martin-Gay Intermediate Algebra Chapter 8 (8.1, 8.2, 8.5, 8.6) Practice for the Exam

MAT 33C -- Martin-Ga Intermediate Algebra Chapter 8 (8.1 8. 8. 8.6) Practice for the Eam Name Date Da/Time: SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

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

Spring 0 Math 08 Eam Preparation Ch Dressler Name SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Solve the quadratic equation b the square root propert.

### SHORT 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

### PRACTICE FINAL EXAM. 3. Solve: 3x 8 < 7. Write your answer using interval notation. Graph your solution on the number line.

MAC 1105 PRACTICE FINAL EXAM College Algebra *Note: this eam is provided as practice onl. It was based on a book previousl used for this course. You should not onl stud these problems in preparing for

### ( ) ( ) ( )( ) Algebra II Semester 2 Practice Exam A DRAFT. = x. Which expression is equivalent to. 1. Find the solution set of. f g x? B.

Algebra II Semester Practice Eam A. Find the solution set of 5 5 +, 9 9 +, 5 5 +, =.. Let f ( ) = and g( ) =. Which epression is equivalent to f g? ( ) ( ) + ( ) 9 9 +, 5. If h( ) = 0 and j( ) h( ) + j

Math 00 Final Review Questions In problems 6, perform the indicated operations and simplif if necessar.. 8 6 8. 7 6. ( i) ( 4 i) 4. (8 i). ( 9 i)( 7 i) 6. ( i)( i) In problems 7-, solve the following applications.

### Find the distance between the pair of points. 2) (7, -7) and (3, -5) A) 12 3 units B) 2 5 units C) 6 units D) 12 units B) 8 C) 63 2

Sample Departmental Final - Math 9 Write the first five terms of the sequence whose general term is given. 1) a n = n 2 - n 0, 2,, 12, 20 B) 2,, 12, 20, 30 C) 0, 3, 8, 1, 2 D) 1,, 9, 1, 2 Find the distance

### Intermediate Algebra / MAT 135 Spring 2017 Master ( Master Templates)

Test 1 Review #1 Intermediate Algebra / MAT 135 Spring 017 Master ( Master Templates) Student Name/ID: 1. Solve for. = 8 18. Solve for. = + a b 3. Solve for. a b = L 30. Two trains leave stations miles

### Linear and Nonlinear Systems of Equations. The Method of Substitution. Equation 1 Equation 2. Check (2, 1) in Equation 1 and Equation 2: 2x y 5?

3330_070.qd 96 /5/05 Chapter 7 7. 9:39 AM Page 96 Sstems of Equations and Inequalities Linear and Nonlinear Sstems of Equations What ou should learn Use the method of substitution to solve sstems of linear

### Diagnostic Tests Study Guide

California State Universit, Sacramento Department of Mathematics and Statistics Diagnostic Tests Stud Guide Descriptions Stud Guides Sample Tests & Answers Table of Contents: Introduction Elementar Algebra

### 9 (0, 3) and solve equations to earn full credit.

Math 0 Intermediate Algebra II Final Eam Review Page of Instructions: (6, ) Use our own paper for the review questions. For the final eam, show all work on the eam. (-6, ) This is an algebra class do not

### y x+ 2. A rectangular frame for a painting has a perimeter of 82 inches. If the length of the frame is 25 inches, find the width of the frame.

. Simplif the complex fraction x 4 4 x. x 4 x x 4 x x 4 x x 4 x x E) 4 x. A rectangular frame for a painting has a perimeter of 8 inches. If the length of the frame is inches, find the width of the frame.

### PreCalculus Final Exam Review Revised Spring 2014

PreCalculus Final Eam Review Revised Spring 0. f() is a function that generates the ordered pairs (0,0), (,) and (,-). a. If f () is an odd function, what are the coordinates of two other points found

### Name Class Date. Quadratic Functions and Transformations. 4 6 x

- Quadratic Functions and Transformations For Eercises, choose the correct letter.. What is the verte of the function 53()? D (, ) (, ) (, ) (, ). Which is the graph of the function f ()5(3) 5? F 6 6 O

### LESSON #12 - FORMS OF A LINE COMMON CORE ALGEBRA II

LESSON # - FORMS OF A LINE COMMON CORE ALGEBRA II Linear functions come in a variet of forms. The two shown below have been introduced in Common Core Algebra I and Common Core Geometr. TWO COMMON FORMS

### Find the integral. 12) 15)

Find the location of the indicated absolute etremum within the specified domain. ) Minimum of f() = /- /; [0, ] 8) Maimum h() ) Minimum of f() = - + - ; [-, ] ) Minimum of f() = ( + )/; [-, ] ) Maimum

### N x. You should know how to decompose a rational function into partial fractions.

Section 7. Partial Fractions 0. 0 7 0 0 0 0 Solution:, 0 Equation Equation Eq. Eq. 07. nswers will var. Section 7. Partial Fractions N You should know how to decompose a rational function into partial

### ab 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

### 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.

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

### LESSON #11 - FORMS OF A LINE COMMON CORE ALGEBRA II

LESSON # - FORMS OF A LINE COMMON CORE ALGEBRA II Linear functions come in a variet of forms. The two shown below have been introduced in Common Core Algebra I and Common Core Geometr. TWO COMMON FORMS

### Honors Algebra 2 ~ Spring 2014 Name 1 Unit 3: Quadratic Functions and Equations

Honors Algebra ~ Spring Name Unit : Quadratic Functions and Equations NC Objectives Covered:. Define and compute with comple numbers. Operate with algebraic epressions (polnomial, rational, comple fractions)

### Summary, 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

SECTION 3.: Quadratic Functions Objectives Graph and Analyze Quadratic Functions in Standard and Verte Form Identify the Verte, Ais of Symmetry, and Intercepts of a Quadratic Function Find the Maimum or

### 2.1 Evaluate and Graph Polynomial

2. Evaluate and Graph Polnomial Functions Georgia Performance Standard(s) MM3Ab, MM3Ac, MM3Ad Your Notes Goal p Evaluate and graph polnomial functions. VOCABULARY Polnomial Polnomial function Degree of

### MTH 112 Practice Test 3 Sections 3.3, 3.4, 3.5, 1.9, 7.4, 7.5, 8.1, 8.2

MTH 112 Practice Test 3 Sections 3.3, 3., 3., 1.9, 7., 7., 8.1, 8.2 Use properties of logarithms to epand the logarithmic epression as much as possible. Where possible, evaluate logarithmic epressions

### What Did You Learn? Key Terms. Key Concepts. 158 Chapter 1 Functions and Their Graphs

333371_010R.qxp 12/27/0 10:37 AM Page 158 158 Chapter 1 Functions and Their Graphs Ke Terms What Did You Learn? equation, p. 77 solution point, p. 77 intercepts, p. 78 slope, p. 88 point-slope form, p.

### FGCU 6th Annual Math Competition 2008 Precalculus - Individual Exam

FGCU 6th Annual Math Competition 008 Precalculus - Individual Eam Find the domain of the rational function. ) f() = + + 9 A) all real numbers B) { -, } C){ -,, -} D) { 0, -9} Solve the equation b epressing

### 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

### 8.4. If we let x denote the number of gallons pumped, then the price y in dollars can \$ \$1.70 \$ \$1.70 \$ \$1.70 \$ \$1.

8.4 An Introduction to Functions: Linear Functions, Applications, and Models We often describe one quantit in terms of another; for eample, the growth of a plant is related to the amount of light it receives,

### Rolle s Theorem and the Mean Value Theorem. Rolle s Theorem

0_00qd //0 0:50 AM Page 7 7 CHAPTER Applications o Dierentiation Section ROLLE S THEOREM French mathematician Michel Rolle irst published the theorem that bears his name in 9 Beore this time, however,

### f 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

### MATH 122A FINAL EXAM STUDY GUIDE (Spring 2014)

MATH A FINAL EXAM STUDY GUIDE (Spring 0) The final eam for spring 0 will have a multiple choice format. This will allow us to offer the final eam as late in the course as possible, giving more in-class

### Copyrighted by Gabriel Tang B.Ed., B.Sc. Page 1.

Chapter : Linear and Quadratic Functions Chapter : Linear and Quadratic Functions -: Points and Lines Sstem of Linear Equations: - two or more linear equations on the same coordinate grid. Solution of

### Exponential 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

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

MAT 10 Test 2 Review (chapters 6,7,11) Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Multipl both sides of each equation b a common denominator

### 5g on a rectangular coordinate system.

Chapter : Functions and Graphs Section.1 A Two-Dimensional Coordinate Sstem and Graphs Cartesian Coordinate Sstems 1. Plot the point C b, 5 on a rectanular coordinate sstem. C C C C. Identif the point

### 7-1. 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)

### 25) x x + 30 x2 + 15x ) x Graph the equation. 30) y = - x - 1

Pre-AP Algebra Final Eam Review Solve. ) A stone is dropped from a tower that is feet high. The formula h = - t describes the stoneʹs height above the ground, h, in feet, t seconds after it was dropped.

### lim 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

### 17. f(x) = x 2 + 5x f(x) = x 2 + x f(x) = x 2 + 3x f(x) = x 2 + 3x f(x) = x 2 16x f(x) = x 2 + 4x 96

Section.3 Zeros of the Quadratic 473.3 Eercises In Eercises 1-8, factor the given quadratic polnomial. 1. 2 + 9 + 14 2. 2 + 6 + 3. 2 + + 9 4. 2 + 4 21. 2 4 6. 2 + 7 8 7. 2 7 + 12 8. 2 + 24 In Eercises

### Pre-Calculus and Trigonometry Capacity Matrix

Pre-Calculus and Capacity Matri Review Polynomials A1.1.4 A1.2.5 Add, subtract, multiply and simplify polynomials and rational epressions Solve polynomial equations and equations involving rational epressions

### Sample Final Exam Problems Solutions Math 107

Sample Final Eam Problems Solutions Math 107 1 (a) We first factor the numerator and the denominator of the function to obtain f() = (3 + 1)( 4) 4( 1) i To locate vertical asymptotes, we eamine all locations

### Mth 95 Module 4 Chapter 8 Spring Review - Solving quadratic equations using the quadratic formula

Mth 95 Module 4 Chapter 8 Spring 04 Review - Solving quadratic equations using the quadratic formula Write the quadratic formula. The NUMBER of REAL and COMPLEX SOLUTIONS to a quadratic equation ( a b

3. Graph Quadratic Functions in Standard Form Georgia Performance Standard(s) MMA3b, MMA3c Goal p Use intervals of increase and decrease to understand average rates of change of quadratic functions. Your

### Math 102 Final Exam Review

. Compute f ( + h) f () h Math 0 Final Eam Review for each of the following functions. Simplify your answers. f () 4 + 5 f ( ) f () + f ( ). Find the domain of each of the following functions. f( ) g (

### Final Exam Review Part 2 #4

Final Eam Review Part # Intermediate Algebra / MAT 135 Fall 01 Master (Prof. Fleischner) Student Name/ID: 1. Solve for, where is a real number. + = 8. Solve for, where is a real number. 9 1 = 3. Solve

### Determine whether the lines through each pair of points are parallel, perpendicular, or neither. 5) (3, -10) and (-17, -2); (-8, 9) and (-4, -1)

MATH 30/GRACEY 3.4-4.1 Name Determine whether the lines through each pair of points are parallel. 1) (2, 4) and (-14, -14); (6, ) and (-2, -4) 2) (, -7) and (2, 7); (8, -6) and (12, 1) Determine whether

### MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 2) A) Not defined B) - 2 5

Stud Guide for TEST I Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the slope of the line passing through the given pair of points. )

### 7Exponential 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.

### dx dx x sec tan d 1 4 tan 2 2 csc d 2 ln 2 x 2 5x 6 C 2 ln 2 ln x ln x 3 x 2 C Now, suppose you had observed that x 3

CHAPTER 8 Integration Techniques, L Hôpital s Rule, and Improper Integrals Section 8. Partial Fractions Understand the concept of a partial fraction decomposition. Use partial fraction decomposition with

### Lesson 9.1 Using the Distance Formula

Lesson. Using the Distance Formula. Find the eact distance between each pair of points. a. (0, 0) and (, ) b. (0, 0) and (7, ) c. (, 8) and (, ) d. (, ) and (, 7) e. (, 7) and (8, ) f. (8, ) and (, 0)

### 13.1 Exponential Growth Functions

Name Class Date 1.1 Eponential Growth Functions Essential Question: How is the graph of g () = a b - h + k where b > 1 related to the graph of f () = b? Resource Locker Eplore 1 Graphing and Analzing f

### Answer Explanations. The SAT Subject Tests. Mathematics Level 1 & 2 TO PRACTICE QUESTIONS FROM THE SAT SUBJECT TESTS STUDENT GUIDE

The SAT Subject Tests Answer Eplanations TO PRACTICE QUESTIONS FROM THE SAT SUBJECT TESTS STUDENT GUIDE Mathematics Level & Visit sat.org/stpractice to get more practice and stud tips for the Subject Test

### PRECALCULUS FINAL EXAM REVIEW

PRECALCULUS FINAL EXAM REVIEW Evaluate the function at the indicated value of. Round our result to three decimal places.. f () 4(5 ); 0.8. f () e ; 0.78 Use the graph of f to describe the transformation

### University of Bergen. Solutions to Exam in MAT111 - Calculus 1

Universit of Bergen The Facult of Mathematics and Natural Sciences English Solutions to Eam in MAT - Calculus Wednesda Ma 0, 07, 09.00-4.00 Eercise. a) Find the real numbers and such that the comple variable

### Algebra 2 Unit 1 Practice

Algebra Unit Practice LESSON - Use this information for Items. Aaron has \$ to rent a bike in the cit. It costs \$ per hour to rent a bike. The additional fee for a helmet is \$ for the entire ride.. Write

### Algebra 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

### Printed Name: Section #: Instructor:

Printed Name: Section #: Instructor: Please do not ask questions during this eam. If you consider a question to be ambiguous, state your assumptions in the margin and do the best you can to provide the

### Name: Period: SM Starter on Reading Quadratic Graph. This graph and equation represent the path of an object being thrown.

SM Name: Period: 7.5 Starter on Reading Quadratic Graph This graph and equation represent the path of an object being thrown. 1. What is the -ais measuring?. What is the y-ais measuring? 3. What are the

### Algebra 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

### Applied Algebra II Semester 2 Practice Exam A DRAFT. 6. Let f ( x) = 2x A. 47 B. 92 C. 139 D. 407

Applied Algebra II Semester Practice Eam A. Find the solution set of { + 0, 0} { + i 0, i 0} { + i, i } { +, } + = 9.. Let f ( ) = and ( ) 0 g =. Which epression is equivalent to f g? ( ) ( ). What is

### Section 2.5: Graphs of Functions

Section.5: Graphs of Functions Objectives Upon completion of this lesson, ou will be able to: Sketch the graph of a piecewise function containing an of the librar functions. o Polnomial functions of degree

### Partial Fractions. dx dx x sec tan d 1 4 tan 2. 2 csc d. csc cot C. 2x 5. 2 ln. 2 x 2 5x 6 C. 2 ln. 2 ln x

460_080.qd //04 :08 PM Page CHAPTER 8 Integration Techniques, L Hôpital s Rule, and Improper Integrals Section 8. Partial Fractions Understand the concept of a partial fraction decomposition. Use partial

### 2.) 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

### Exponential 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

### Functions. Introduction CHAPTER OUTLINE

Functions,00 P,000 00 0 970 97 980 98 990 99 000 00 00 Figure Standard and Poor s Inde with dividends reinvested (credit "bull": modification of work b Praitno Hadinata; credit "graph": modification of

### 2014 TEXAS STAAR TEST END OF COURSE ALGEBRA I

0 TEXAS STAAR TEST END OF COURSE ALGEBRA I Total Possible Score: 5 Needed Correct to Pass: 0 Advanced Performance: Time Limit: Hours This file contains the State of Teas Assessments of Academic Readiness

### Tangent Line Approximations. y f c f c x c. y f c f c x c. Find the tangent line approximation of. f x 1 sin x

SECTION 9 Differentials 5 Section 9 EXPLORATION Tangent Line Approimation Use a graphing utilit to graph f In the same viewing window, graph the tangent line to the graph of f at the point, Zoom in twice

### ( ) ( ) 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

### Chapter 9. Rational Functions

Chapter 9 Rational Functions Lesson 9-4 Rational Epressions Rational Epression A rational epression is in simplest form when its numerator and denominator are polnomials that have no common divisors. Eample

### Test 1 Review #5. Intermediate Algebra / MAT 135 Fall 2016 Master (Prof. Fleischner)

Test 1 Review #5 Intermediate Algebra / MAT 135 Fall 016 Master (Prof. Fleischner) Student Name/ID: 1. Solve for n. d = m + 9n. Solve for b. r = 5 b + a 3. Solve for C. A = 7 8 B + C ALEKS Test 1 Review

### Logarithmic Functions and Their Graphs

Section 3. Logarithmic Functions and Their Graphs Look at the graph of f(x) = x Does this graph pass the Horizontal Line Test? es What does this mean? that its inverse is a function Find the inverse of

### 17 Exponential Functions

Eponential Functions Concepts: Eponential Functions Graphing Eponential Functions Eponential Growth and Eponential Deca The Irrational Number e and Continuousl Compounded Interest (Section. &.A). Sketch

### Name: Period: QVMS GTA FALL FINAL EXAM REVIEW PRE-AP ALGEBRA 1

Name: Period: QVMS GTA FALL FINAL EXAM REVIEW PRE-AP ALGEBRA ) When simplifing an epression, ou perform operations inside grouping smbols first. a. alwas b. sometimes c. never ) The opposite of a negative

### Exponential 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

### 3. A boat that costs \$4000 decreases in value by 17% per year. How much will the boat be worth after 6 years?

Algebra Stud Guide 1. Write a recursive formula for the sequence.,, 50, 50,.... Given that u = 3, u = 1, and u = 5u + u where n 3, what is the fifth term of the sequence? [A] 57 [B] 63 [C] 307 [D] 1649

### Two-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

### Fitting Integrands to Basic Rules. x x 2 9 dx. Solution a. Use the Arctangent Rule and let u x and a dx arctan x 3 C. 2 du u.

58 CHAPTER 8 Integration Techniques, L Hôpital s Rule, and Improper Integrals Section 8 Basic Integration Rules Review proceres for fitting an integrand to one of the basic integration rules Fitting Integrands

### KEY IDEAS. Chapter 1 Function Transformations. 1.1 Horizontal and Vertical Translations Pre-Calculus 12 Student Workbook MHR 1

Chapter Function Transformations. Horizontal and Vertical Translations A translation can move the graph of a function up or down (vertical translation) and right or left (horizontal translation). A translation

### Calculus w/applications Prerequisite Packet Paint Branch High School Math Department

Updated 6/014 The problems in this packet are designed to help you review topics from previous math courses that are important to your success in Calculus with Applications. It is important that you take

### Math125 Exam 5 (Final) Review Name. Do the following as indicated. 17) log 17x = 1.2 (Round answer to four decimal places.)

Math12 Eam (Final) Review Name Do the following as indicated. For the given functions f and g, find the requested function. 1) f() = - 6; g() = 92 Find (f - g)(). 2) f() = 33 + 1; g() = 2-2 Find (f g)().

### N5 R1.1 Linear Equations - Revision

N5 R Linear Equations - Revision This revision pack covers the skills at Unit Assessment and eam level for Linear Equations so ou can evaluate our learning of this outcome. It is important that ou prepare

### Functions. 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

### SAMPLE. Chapter 1: Basic Skills. Chapter 2: Systems of Linear Equations. Chapter 3: Analytic Geometry. Chapter 4: Polynomials

Overview... 3 Chapter : Basic Skills. Order of Operations... 6. lgebraic Epressions... 9.3 Equations.... Simple Linear Equations... 5 Chapter : Sstems of Linear Equations. Graphing Sstems of Linear Equations....

### 4 B. 4 D. 4 F. 3. How can you use the graph of a quadratic equation to determine the number of real solutions of the equation?

3.1 Solving Quadratic Equations COMMON CORE Learning Standards HSA-SSE.A. HSA-REI.B.b HSF-IF.C.8a Essential Question Essential Question How can ou use the graph of a quadratic equation to determine the

### Chapter 5: Systems of Equations

Chapter : Sstems of Equations Section.: Sstems in Two Variables... 0 Section. Eercises... 9 Section.: Sstems in Three Variables... Section. Eercises... Section.: Linear Inequalities... Section.: Eercises.

### Algebra y funciones [219 marks]

Algebra y funciones [9 marks] Let f() = 3 ln and g() = ln5 3. a. Epress g() in the form f() + lna, where a Z +. attempt to apply rules of logarithms e.g. ln a b = b lna, lnab = lna + lnb correct application

### Section 0.4 Inverse functions and logarithms

Section 0.4 Inverse functions and logarithms (5/3/07) Overview: Some applications require not onl a function that converts a numer into a numer, ut also its inverse, which converts ack into. In this section