Mesa College Math SAMPLES
|
|
- Britney Higgins
- 5 years ago
- Views:
Transcription
1 Mesa College Math 6 - SAMPLES Directions: NO CALCULATOR. Write neatly, show your work and steps. Label your work so it s easy to ollow. Answers without appropriate work will receive NO credit. For inal answers, be sure to simpliy all radicals and ractions. #. Find the domain o each unction. Epress your answer in interval notation. 4 a) ( ) 4 5 b) g( ) 4 5 c) h( ) 0 8 #. Find ( a + h) ( a). Completely simpliy your result, where: h a) ( ) b) ( ) 5 c) ( ) #. Find ( g)( ), and speciy the domain o g using interval notation, where: a) ( ) + and g( ) b) ( ) and g( ) 4 + c) ( ) g( ) + #4. Find all such that ( ) 0. Write your answer using interval notation, where: 4a) 4 ( ) b) 4 ( ) c) ( ) 9 #5. Find the equations o all vertical and horizontal asymptotes or : 5a) ( ) + + 5b) g( ) 4 5c) h( ) #6. Epress as a single logarithm. Assume all values are properly deined #7. Solve: 6a) b log + 4log y 6log y 6b) log log b y + b b + 7b) ( ) log log log (4 ). 7a) 7d) log log ( 6) log log ( + ) 7c) e) 7 9( ) log 5 7) ( ) log 5 7g) 0.4 e 7h) log 5
2 #8. Suppose A 4, B 5, and C 0. Find the ollowing: 8a) AB 8b) A - C 8c) CB 8d) BC 8e) A - #9. Use augmented matrices and Gaussian elimination to solve: 9a) + y z + y z y + z 0 9b) y + z 9 + y 4 5y + 5z 7 9c) + y 5y z z 7 #0. Maimize P y, given the constraints 0 60, 0 y 45, and 5 + 6y 40. Sketch the graph o the constraint inequalities. Label the critical vertices on the graph. #. An accountant prepares ta returns or individuals and or small businesses. On average, each individual return requires hours o her time, and hour o computer time. Each business requires 4 hours o her time and hours o computer time. Because o other business considerations, her time is limited to 40 hours, and the computer time is limited to 00 hours. I she earns a proit o $80 per each individual return, and a proit o $50 on each business return, how many returns o each type should she prepare to maimize her proit? #. SOLVE each over the comple number system. a) c) 5 6 b) d) #. Sketch the graph o each polynomial unction labeling the zeros and the y-intercepts or each. a) y b) 4 y + #4. Let F() be a polynomial unction with rational coeicients. Solve each, over the comple numbers, i necessary, using the given hints. 4a) , where 5 is a root. 4b) , where is a root #5a) Write a third degree polynomial equation with rational coeicients, that has 5 and as its roots #5b) Write a ourth degree polynomial equation with integer coeicients that has i (where i ) and - as roots, where - is a double root. (also called: - has a multiplicity o two.)
3 #6. The below graph represents part o a unction y (). Sketch each: 6a) y (+) 6b) y () 6c) y ( ) 6d) y ( ) 6e) the relection o () over the y-ais 6) the relection o () over the -ais #7. Suppose () is a continuous, one-to-one unction, ind: 7a) ( ), i () 5, and () is an even unction 7b) ( ), i () 5, and () is an odd unction #8. Sketch the graph o each piece-wise unction. Label the coordinates o each verte and/or each point o discontinuity. 8a), i < y, i 8b), i < y +, i, i > #9. Resolve each into its partial ractions. + 9a) 7 5 9b) ( )( + ) #0. A new drug is injected into a patient. The number o milligrams remaining in the patient s bloodstream t hours is modeled by: D( t) 60 0.t e. (a) How many milligrams were initially injected? (b) How many milligrams o the drug remain ater 5 hours? (c) When will there be one-orth o the initial dosage in the patient s bloodstream? #. Students in a math class took a inal eam. As part o a study, they were tested each month thereater to determine how much they remembered. The ollowing ormula was derived: S( t) log( t + ), t 0. Where S(t) represents the score (as a percent), and t represents months. (a) What was the average initial score on the eam? (b) What was the average score ater 9 months?
4 ANSWERS to Math 6 Challenge Eam SAMPLES Disclaimer: A ew o these answers may (will) be wrong! There s a myriad o reasons why: I m stooped, my ingers are at, I m dysleic, I m tired, the summer sun has baked my brain. Please, me your suggested solution(s), I ll double check it, and get back to you. Thanks. Larry Foster: laoster@sdccd.edu NOTE: I have NOT yet included the GRAPHS someday. *********************************************************************************************** a) Domain ) ( ) b) Domain ( 5, ) ( 5, 8 c) Domain ( ) 4,, a) -a + h b) 4a 5 + h c) a + ah 5, a) b) g +, domain (, ) (,0) (0, ) g +, domain ( (, ), ) (, ) c) g +, domain ( (, ), ) (, ) 4a) ( ) > 0, when [, ] 4b) ( ) > 0, when [, ] [, ) 4c) ( ) > 0, when [, ] (, ) 5a) ( ),, vertical Asymptote: none, horizontal Asymptote: y 0, + Point o Discontinuity (aka: hole ): (0, ) 5b) 5c) + g( ),, vert: 4, horiz: 4 + y, (, ) 5 + h( ), 0, vert: ±, horiz: 0 ( + )( ) y, ( 0, ) 6a) log( y) 6b) 7a) { }, 0 rejects 7b) { }, 7 6 rejects 7c) { 5 } 7d) { }, -9 rejects 7e) { 8} 7) { } 7g) ln 0.04 this is best possible w/o calculator 7h) { 5 } 8a) 9 9 8b) 0 6 8c) 0 7 8d) not deined 8e) 4
5 { } { } { } 9) ater a LOT o work: 9a) (,, ) 9b) (,, ) 9c) ( 4,,) Remember: the parenthesis inside o the solution set is mandatory! 0) See below or sketch. corners: (0,0), (0,45), (60,0), 0,45), (60,0) The ma value o P occurs when 60 and y 0. ) Let # o individual returns, y # o business returns Objective unction: P y Constraints: 0 y 0 + 4y 40 + y 00 corners: (0,0), (0, 50), (40,0), 80,0) Ma proit (40,0 ) she should prepare 40 individual returns, and 0 business returns. a) { ±, ± i} b) {,} c) { 8, } 8 d) { } i,, ± # See below or sketches. Using a combination o: Rational Root theorem, synthetic division, actoring, and quadratic ormula: a) y ( + )( )( ) zeros:,,, y-intercept: ( ) 0, + check out it s etreme behavior b) y ( ) ( + ), zeros: 0, -, (multiplicity o ), y-int: (0,0) #4 see hints rom # 4a) ( 5)( + )( + 4) 0 { 5,,4} 4b) ( )( )( + + ) 0 {,, ± i} 5a) remember with rational coeicients, each irrational and comple root must include its conjugate. ( 5)( + 5)( ) b) 4 ( i)( + i)( + )( + ) #6 graphs later. Each corner o the shape should be modiied as indicated below. Then, connect the dots. 6a) shit entire graph let units. (subtract rom -values, keep y-values the same) 6b) (divide -values by, keep y-values the same) 6c) swap all y that is: (-,4) (4,-) (0,) (,0) (,) (,)
6 (5,0) (0,5) 6d) shit entire graph down units: (keep -value the same, subtract rom y-values) 6e) (change all -values to their opposite, keep y-value the same) 6) (keep -value same, change y-values to their opposite) 7a) ( ) 5 7b) ( ) 5 #8 see below or sketches (someday) 9a) 7 + ( + ) ( 5) 5 0 9b) + + ( + ) + o course you don t need this last raction 0a) 60 mg 0b) 60e - mg, or 60 e mg 0c) ln( 4) hours, or 0. ln(4) 0. hours. a) The initial average score was 77.4% b) Ater 9 months, the resulting average score was 57.4%
Objectives. By the time the student is finished with this section of the workbook, he/she should be able
FUNCTIONS Quadratic Functions......8 Absolute Value Functions.....48 Translations o Functions..57 Radical Functions...61 Eponential Functions...7 Logarithmic Functions......8 Cubic Functions......91 Piece-Wise
More informationRATIONAL FUNCTIONS. Finding Asymptotes..347 The Domain Finding Intercepts Graphing Rational Functions
RATIONAL FUNCTIONS Finding Asymptotes..347 The Domain....350 Finding Intercepts.....35 Graphing Rational Functions... 35 345 Objectives The ollowing is a list o objectives or this section o the workbook.
More informationMath-3 Lesson 1-4. Review: Cube, Cube Root, and Exponential Functions
Math- Lesson -4 Review: Cube, Cube Root, and Eponential Functions Quiz - Graph (no calculator):. y. y ( ) 4. y What is a power? vocabulary Power: An epression ormed by repeated Multiplication o the same
More informationSyllabus Objective: 2.9 The student will sketch the graph of a polynomial, radical, or rational function.
Precalculus Notes: Unit Polynomial Functions Syllabus Objective:.9 The student will sketch the graph o a polynomial, radical, or rational unction. Polynomial Function: a unction that can be written in
More informationPolynomials, Linear Factors, and Zeros. Factor theorem, multiple zero, multiplicity, relative maximum, relative minimum
Polynomials, Linear Factors, and Zeros To analyze the actored orm o a polynomial. To write a polynomial unction rom its zeros. Describe the relationship among solutions, zeros, - intercept, and actors.
More informationMath-3 Lesson 8-5. Unit 4 review: a) Compositions of functions. b) Linear combinations of functions. c) Inverse Functions. d) Quadratic Inequalities
Math- Lesson 8-5 Unit 4 review: a) Compositions o unctions b) Linear combinations o unctions c) Inverse Functions d) Quadratic Inequalities e) Rational Inequalities 1. Is the ollowing relation a unction
More informationCurve Sketching. The process of curve sketching can be performed in the following steps:
Curve Sketching So ar you have learned how to ind st and nd derivatives o unctions and use these derivatives to determine where a unction is:. Increasing/decreasing. Relative extrema 3. Concavity 4. Points
More informationLesson 7.1 Polynomial Degree and Finite Differences
Lesson 7.1 Polynomial Degree and Finite Differences 1. Identify the degree of each polynomial. a. 1 b. 0.2 1. 2 3.2 3 c. 20 16 2 20 2. Determine which of the epressions are polynomials. For each polynomial,
More information( x) f = where P and Q are polynomials.
9.8 Graphing Rational Functions Lets begin with a deinition. Deinition: Rational Function A rational unction is a unction o the orm ( ) ( ) ( ) P where P and Q are polynomials. Q An eample o a simple rational
More informationMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. B) 6x + 4
Math1420 Review Comprehesive Final Assessment Test Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Add or subtract as indicated. x + 5 1) x2
More informationQuestions From Old Exams
MATH 0 OLD EXAM QUESTIONS FOR EXAM 3 ON CHAPTERS 3 AND 4 PAGE Questions From Old Eams. Write the equation of a quadratic function whose graph has the following characteristics: It opens down; it is stretched
More informationMATH 1314 College Algebra Scott Travis Fall 2014 Review for Exam #2
MATH 1314 College Algebra Scott Travis Fall 2014 Review for Exam #2 There are eight sections from Chapters 4 and 5 included in the exam: 4.1, 4.3, 5.1 to 5.6. This review should help you prepare. For each
More informationFinal Exam C Name i D) 2. Solve the equation by factoring. 4) x2 = x + 72 A) {1, 72} B) {-8, 9} C) {-8, -9} D) {8, 9} 9 ± i
Final Exam C Name First, write the value(s) that make the denominator(s) zero. Then solve the equation. 7 ) x + + 3 x - = 6 (x + )(x - ) ) A) No restrictions; {} B) x -, ; C) x -; {} D) x -, ; {2} Add
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 informationMath Analysis Chapter 2 Notes: Polynomial and Rational Functions
Math Analysis Chapter Notes: Polynomial and Rational Functions Day 13: Section -1 Comple Numbers; Sections - Quadratic Functions -1: Comple Numbers After completing section -1 you should be able to do
More informationName. SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
REVIEW Eam #3 : 3.2-3.6, 4.1-4.5, 5.1 Name SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Use the Leading Coefficient Test to determine the end behavior
More information11 /2 12 /2 13 /6 14 /14 15 /8 16 /8 17 /25 18 /2 19 /4 20 /8
MAC 1147 Exam #1a Answer Key Name: Answer Key ID# Summer 2012 HONOR CODE: On my honor, I have neither given nor received any aid on this examination. Signature: Instructions: Do all scratch work on the
More informationFinal Exam A Name. 20 i C) Solve the equation by factoring. 4) x2 = x + 30 A) {-5, 6} B) {5, 6} C) {1, 30} D) {-5, -6} -9 ± i 3 14
Final Exam A Name First, write the value(s) that make the denominator(s) zero. Then solve the equation. 1 1) x + 3 + 5 x - 3 = 30 (x + 3)(x - 3) 1) A) x -3, 3; B) x -3, 3; {4} C) No restrictions; {3} D)
More information3 6 x a. 12 b. 63 c. 27 d. 0. 6, find
Advanced Algebra Topics COMPASS Review revised Summer 0 You will be allowed to use a calculator on the COMPASS test Acceptable calculators are basic calculators, scientific calculators, and approved models
More informationAlgebra Summer Review Packet
Name: Algebra Summer Review Packet About Algebra 1: Algebra 1 teaches students to think, reason, and communicate mathematically. Students use variables to determine solutions to real world problems. Skills
More information1/100 Range: 1/10 1/ 2. 1) Constant: choose a value for the constant that can be graphed on the coordinate grid below.
Name 1) Constant: choose a value or the constant that can be graphed on the coordinate grid below a y Toolkit Functions Lab Worksheet thru inverse trig ) Identity: y ) Reciprocal: 1 ( ) y / 1/ 1/1 1/ 1
More information1. Find the domain of the following functions. Write your answer using interval notation. (9 pts.)
MATH- Sample Eam Spring 7. Find the domain of the following functions. Write your answer using interval notation. (9 pts.) a. 9 f ( ) b. g ( ) 9 8 8. Write the equation of the circle in standard form given
More informationMath 2412 Activity 2(Due by EOC Feb. 27) Find the quadratic function that satisfies the given conditions. Show your work!
Math 4 Activity (Due by EOC Feb 7) Find the quadratic function that satisfies the given conditions Show your work! The graph has a verte at 5, and it passes through the point, 0 7 The graph passes through
More informationMath 1051, Robertson, Exam 3 on Chapters 3 & 4 on Friday 12 November 2010 KEY page 1
Math, Robertson, Eam on Chapters & on Friday November 0 KEY page. You earned points out of. Ans: f 6 Write the equation of a quadratic function whose graph has the following characteristics: It opens down;
More informationAP Calculus AB Summer Assignment
AP Calculus AB Summer Assignment As Advanced placement students, our irst assignment or the 07-08 school ear is to come to class the ver irst da in top mathematical orm. Calculus is a world o change. While
More informationM30-1: Polynomial, Radical and Rational Functions, Graphs and Equations Exam /20
Class: Date: ID: A M30-1: Polynomial, Radical and Rational Functions, Graphs and Equations Exam /20 Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Which
More informationMath 2412 Activity 1(Due by EOC Sep. 17)
Math 4 Activity (Due by EOC Sep. 7) Determine whether each relation is a unction.(indicate why or why not.) Find the domain and range o each relation.. 4,5, 6,7, 8,8. 5,6, 5,7, 6,6, 6,7 Determine whether
More informationMath 95 Practice Final Exam
Part 1: No Calculator Evaluating Functions and Determining their Domain and Range The domain of a function is the set of all possible inputs, which are typically x-values. The range of a function is the
More information1 Chapter 1: Graphs, Functions, and Models
1 Chapter 1: Graphs, Functions, and Models 1.1 Introduction to Graphing 1.1.1 Know how to graph an equation Eample 1. Create a table of values and graph the equation y = 1. f() 6 1 0 1 f() 3 0 1 0 3 4
More informationUNIT 3. Rational Functions Limits at Infinity (Horizontal and Slant Asymptotes) Infinite Limits (Vertical Asymptotes) Graphing Rational Functions
UNIT 3 Rational Functions Limits at Infinity (Horizontal and Slant Asymptotes) Infinite Limits (Vertical Asymptotes) Graphing Rational Functions Recall From Unit Rational Functions f() is a rational function
More informationMath 030 Review for Final Exam Revised Fall 2010 RH/ DM 1
Math 00 Review for Final Eam Revised Fall 010 RH/ DM 1 1. Solve the equations: (-1) (7) (-) (-1) () 1 1 1 1 f. 1 g. h. 1 11 i. 9. Solve the following equations for the given variable: 1 Solve for. D ab
More informationIntermediate Algebra 100A Final Exam Review Fall 2007
1 Basic Concepts 1. Sets and Other Basic Concepts Words/Concepts to Know: roster form, set builder notation, union, intersection, real numbers, natural numbers, whole numbers, integers, rational numbers,
More informationTopic: Expressions & Operations AII.1
Topic: Epressions & Operations AII.1 AII.1 The student will identify field properties, aioms of equality and inequality, and properties of order that are valid for the set of real numbers and its subsets,
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 informationFunctions: Review of Algebra and Trigonometry
Sec. and. Functions: Review o Algebra and Trigonoetry A. Functions and Relations DEFN Relation: A set o ordered pairs. (,y) (doain, range) DEFN Function: A correspondence ro one set (the doain) to anther
More informationAlgebra II Midterm Exam Review Packet
Algebra II Midterm Eam Review Packet Name: Hour: CHAPTER 1 Midterm Review Evaluate the power. 1.. 5 5. 6. 7 Find the value of each epression given the value of each variable. 5. 10 when 5 10 6. when 6
More informationMATH 111 Departmental Midterm Exam Review Exam date: Tuesday, March 1 st. Exam will cover sections and will be NON-CALCULATOR EXAM.
MATH Departmental Midterm Eam Review Eam date: Tuesday, March st Eam will cover sections -9 + - and will be NON-CALCULATOR EXAM Terms to know: quadratic function, ais of symmetry, verte, minimum/maimum
More informationMath 120, Sample Final Fall 2015
Math 10, Sample Final Fall 015 Disclaimer: This sample final is intended to help students prepare for the final exam The final exam will be similar in structure and type of problems, however the actual
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 informationExam 2 Review F15 O Brien. Exam 2 Review:
Eam Review:.. Directions: Completely rework Eam and then work the following problems with your book notes and homework closed. You may have your graphing calculator and some blank paper. The idea is to
More informationMAT 114 Fall 2015 Print Name: Departmental Final Exam - Version X
MAT 114 Fall 2015 Print Name: Departmental Final Eam - Version X NON-CALCULATOR SECTION EKU ID: Instructor: Calculators are NOT allowed on this part of the final. Show work to support each answer. Full
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 informationFunction Operations. I. Ever since basic math, you have been combining numbers by using addition, subtraction, multiplication, and division.
Function Operations I. Ever since basic math, you have been combining numbers by using addition, subtraction, multiplication, and division. Add: 5 + Subtract: 7 Multiply: (9)(0) Divide: (5) () or 5 II.
More informationPolynomials and Polynomial Functions
Unit 5: Polynomials and Polynomial Functions Evaluating Polynomial Functions Objectives: SWBAT identify polynomial functions SWBAT evaluate polynomial functions. SWBAT find the end behaviors of polynomial
More information3x 2. x ))))) and sketch the graph, labelling everything.
Fall 2006 Practice Math 102 Final Eam 1 1. Sketch the graph of f() =. What is the domain of f? [0, ) Use transformations to sketch the graph of g() = 2. What is the domain of g? 1 1 2. a. Given f() = )))))
More informationICM ~ Unit 4 ~ Day 3. Horizontal Asymptotes, End Behavior
ICM ~ Unit 4 ~ Day 3 Horizontal Asymptotes, End Behavior Warm Up ~ Day 3 1. Find the domain, then convert to fractional/rational eponent. f ( ) 7. Simplify completely: 3( + 5). 3. Find the domain, & y
More informationThe final is cumulative, but with more emphasis on chapters 3 and 4. There will be two parts.
Math 141 Review for Final The final is cumulative, but with more emphasis on chapters 3 and 4. There will be two parts. Part 1 (no calculator) graphing (polynomial, rational, linear, exponential, and logarithmic
More informationPART 1: USING SCIENTIFIC CALCULATORS (41 PTS.) 1) The Vertex Form for the equation of a parabola in the usual xy-plane is given by y = 3 x + 4
MIDTERM SOLUTIONS (CHAPTERS AND 3: POLYNOMIAL, RATIONAL, EXP L, LOG FUNCTIONS) MATH 141 FALL 018 KUNIYUKI 150 POINTS TOTAL: 41 FOR PART 1, AND 109 FOR PART PART 1: USING SCIENTIFIC CALCULATORS (41 PTS.)
More informationDirections: Please read questions carefully. It is recommended that you do the Short Answer Section prior to doing the Multiple Choice.
AP Calculus AB SUMMER ASSIGNMENT Multiple Choice Section Directions: Please read questions carefully It is recommended that you do the Short Answer Section prior to doing the Multiple Choice Show all work
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 informationTroy High School AP Calculus Summer Packet
Troy High School AP Calculus Summer Packet As instructors of AP Calculus, we have etremely high epectations of students taking our courses. We epect a certain level of independence to be demonstrated by
More informationFox Lane High School Department of Mathematics
Fo Lane High School Department of Mathematics June 08 Hello Future AP Calculus AB Student! This is the summer assignment for all students taking AP Calculus AB net school year. It contains a set of problems
More informationQuadratic Functions. The graph of the function shifts right 3. The graph of the function shifts left 3.
Quadratic Functions The translation o a unction is simpl the shiting o a unction. In this section, or the most part, we will be graphing various unctions b means o shiting the parent unction. We will go
More informationHONORS PRE-CALCULAUS ACP Summer Math Packet
Name Date Section HONORS PRE-CALCULAUS ACP Summer Math Packet For all incoming Honors Pre-Calculus ACP students, the summer math packet will be on the school website. Students will need to print a cop
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 informationf ( x ) = x Determine the implied domain of the given function. Express your answer in interval notation.
Test Review Section.. Given the following function: f ( ) = + 5 - Determine the implied domain of the given function. Epress your answer in interval notation.. Find the verte of the following quadratic
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 informationCOUNCIL ROCK HIGH SCHOOL MATHEMATICS. A Summer Review of Algebra. Designed for the Student Entering Accelerated/Honors Analysis
COUNCIL ROCK HIGH SCHOOL MATHEMATICS A Summer Review of Algebra Designed for the Student Entering Accelerated/Honors Analysis Please print this packet in its entirety to be completed for evaluation on
More informationFlip-Flop Functions KEY
For each rational unction, list the zeros o the polynomials in the numerator and denominator. Then, using a calculator, sketch the graph in a window o [-5.75, 6] by [-5, 5], and provide an end behavior
More informationAvon High School Name AP Calculus AB Summer Review Packet Score Period
Avon High School Name AP Calculus AB Summer Review Packet Score Period f 4, find:.) If a.) f 4 f 4 b.) Topic A: Functions f c.) f h f h 4 V r r a.) V 4.) If, find: b.) V r V r c.) V r V r.) If f and g
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 information5. Determine the discriminant for each and describe the nature of the roots.
4. Quadratic Equations Notes Day 1 1. Solve by factoring: a. 3 16 1 b. 3 c. 8 0 d. 9 18 0. Quadratic Formula: The roots of a quadratic equation of the form A + B + C = 0 with a 0 are given by the following
More informationPre-Calculus Summer Packet
Pre-Calculus Summer Packet Name ALLEN PARK HIGH SCHOOL Summer Assessment Pre-Calculus Summer Packet For Students Entering Pre-Calculus Summer 05 This summer packet is intended to be completed by the FIRST
More informationPrecalculus Summer Packet
Precalculus Summer Packet These problems are to be completed to the best of your ability by the first day of school You will be given the opportunity to ask questions about problems you found difficult
More informationFunctions and Their Graphs
Functions and Their Graphs 015 College Board. All rights reserved. Unit Overview In this unit you will study polynomial and rational functions, their graphs, and their zeros. You will also learn several
More informationUnit 4: Polynomial and Rational Functions
50 Unit 4: Polynomial and Rational Functions Polynomial Functions A polynomial function y p() is a function of the form p( ) a a a... a a a n n n n n n 0 where an, an,..., a, a, a0 are real constants and
More informationSolutions to the Math 1051 Sample Final Exam (from Spring 2003) Page 1
Solutions to the Math 0 Sample Final Eam (from Spring 00) Page Part : Multiple Choice Questions. Here ou work out the problems and then select the answer that matches our answer. No partial credit is given
More informationMIDTERM REVIEW. Write an algebraic expression to represent the following verbal expressions. 1) Double the difference of a number and 7.
NAME MIDTERM REVIEW DATE Write an algebraic epression to represent the following verbal epressions. 1) Double the difference of a number and 7. ) Find the value of the epression 0. Solve each equation.
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 informationINTRODUCTION TO RATIONAL FUNCTIONS COMMON CORE ALGEBRA II
Name: Date: INTRODUCTION TO RATIONAL FUNCTIONS COMMON CORE ALGEBRA II Rational functions are simply the ratio of polynomial functions. They take on more interesting properties and have more interesting
More informationA. Incorrect! Apply the rational root test to determine if any rational roots exist.
College Algebra - Problem Drill 13: Zeros of Polynomial Functions No. 1 of 10 1. Determine which statement is true given f() = 3 + 4. A. f() is irreducible. B. f() has no real roots. C. There is a root
More information1. Evaluate the function at each specified value of the independent variable and simplify. f 2a.)
Honors Pre-Calculus Midterm Eam Review Name: January 04 Chapter : Functions and Their Graphs. Evaluate the function at each specified value of the independent variable and simplify. f ( ) f () b. f ( )
More informationMATH section 3.4 Curve Sketching Page 1 of 29
MATH section. Curve Sketching Page of 9 The step by step procedure below is for regular rational and polynomial functions. If a function contains radical or trigonometric term, then proceed carefully because
More informationMATH 115: Review for Chapter 5
MATH 5: Review for Chapter 5 Can you find the real zeros of a polynomial function and identify the behavior of the graph of the function at its zeros? For each polynomial function, identify the zeros of
More informationScope and Sequence Mathematics Algebra 2 400
Scope and Sequence Mathematics Algebra 2 400 Description : Students will study real numbers, complex numbers, functions, exponents, logarithms, graphs, variation, systems of equations and inequalities,
More informationAlgebra Review. Unit 7 Polynomials
Algebra Review Below is a list of topics and practice problems you have covered so far this semester. You do not need to work out every question on the review. Skip around and work the types of questions
More informationCOUNCIL ROCK HIGH SCHOOL MATHEMATICS. A Note Guideline of Algebraic Concepts. Designed to assist students in A Summer Review of Algebra
COUNCIL ROCK HIGH SCHOOL MATHEMATICS A Note Guideline of Algebraic Concepts Designed to assist students in A Summer Review of Algebra [A teacher prepared compilation of the 7 Algebraic concepts deemed
More informationC. Finding roots of trinomials: 1st Example: x 2 5x = 14 x 2 5x 14 = 0 (x 7)(x + 2) = 0 Answer: x = 7 or x = -2
AP Calculus Students: Welcome to AP Calculus. Class begins in approimately - months. In this packet, you will find numerous topics that were covered in your Algebra and Pre-Calculus courses. These are
More informationAP Calculus BC Summer Packet Welcome! L Logarithms and Exponential Functions R Rational Expressions and Equations
AP Calculus BC Summer Packet 06 Welcome! This packet includes a sampling of problems that students entering AP Calculus BC should be able to answer. The questions are organized by topic: A Basic Algebra
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 informationACCUPLACER MATH 0311 OR MATH 0120
The University of Teas at El Paso Tutoring and Learning Center ACCUPLACER MATH 0 OR MATH 00 http://www.academics.utep.edu/tlc MATH 0 OR MATH 00 Page Factoring Factoring Eercises 8 Factoring Answer to Eercises
More informationThis problem set is a good representation of some of the key skills you should have when entering this course.
Math 4 Review of Previous Material: This problem set is a good representation of some of the key skills you should have when entering this course. Based on the course work leading up to Math 4, you should
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 informationPre-Calculus Summer Math Packet 2018 Multiple Choice
Pre-Calculus Summer Math Packet 208 Multiple Choice Page A Complete all work on separate loose-leaf or graph paper. Solve problems without using a calculator. Write the answers to multiple choice questions
More informationGraphs of Basic Polynomial Functions
Section 1 2A: Graphs of Basic Polynomial Functions The are nine Basic Functions that we learn to graph in this chapter. The pages that follow this page will show how several values can be put into the
More informationProcedure for Graphing Polynomial Functions
Procedure for Graphing Polynomial Functions P(x) = a nx n + a n-1x n-1 + + a 1x + a 0 To graph P(x): As an example, we will examine the following polynomial function: P(x) = 2x 3 3x 2 23x + 12 1. Determine
More informationSchool Year
AP Calculus AB Assignment 06 07 School Year In order to ensure that our AP Calculus classes meet the standards required by the College Board, it is strongly recommended that all calculus students complete
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 informationComplete your Parent Function Packet!!!!
PARENT FUNCTIONS Pre-Ap Algebra 2 Complete your Parent Function Packet!!!! There are two slides per Parent Function. The Parent Functions are numbered in the bottom right corner of each slide. The Function
More informationAP Calculus AB Summer Assignment
Name: AP Calculus AB Summer Assignment Due Date: The beginning of class on the last class day of the first week of school. The purpose of this assignment is to have you practice the mathematical skills
More informationGraphing Rational Functions KEY. (x 4) (x + 2) Factor denominator. y = 0 x = 4, x = -2
6 ( 6) Factor numerator 1) f ( ) 8 ( 4) ( + ) Factor denominator n() is of degree: 1 -intercepts: d() is of degree: 6 y 0 4, - Plot the -intercepts. Draw the asymptotes with dotted lines. Then perform
More informationMath RE - Calculus I Functions Page 1 of 10. Topics of Functions used in Calculus
Math 0-03-RE - Calculus I Functions Page of 0 Definition of a function f() : Topics of Functions used in Calculus A function = f() is a relation between variables and such that for ever value onl one value.
More informationWheeler High School. The packets are due to your instructor on your first day of class.
Wheeler High School To: Honors Calculus and AP Calculus AB Students From: Mrs. Barry, Mrs. Massey, Mrs. Walls, and Mr. Furstein - Calculus Instructors Re: Summer work Honors Calculus and AP Calculus AB
More informationNAME DATE PERIOD. Power and Radical Functions. New Vocabulary Fill in the blank with the correct term. positive integer.
2-1 Power and Radical Functions What You ll Learn Scan Lesson 2-1. Predict two things that you expect to learn based on the headings and Key Concept box. 1. 2. Lesson 2-1 Active Vocabulary extraneous solution
More informationSummer AP Assignment Coversheet Falls Church High School
Summer AP Assignment Coversheet Falls Church High School Course: AP Calculus AB Teacher Name/s: Veronica Moldoveanu, Ethan Batterman Assignment Title: AP Calculus AB Summer Packet Assignment Summary/Purpose:
More informationPre-Calculus: Functions and Their Properties (Solving equations algebraically and graphically, matching graphs, tables, and equations, and
Pre-Calculus: 1.1 1.2 Functions and Their Properties (Solving equations algebraically and graphically, matching graphs, tables, and equations, and finding the domain, range, VA, HA, etc.). Name: Date:
More informationx 20 f ( x ) = x Determine the implied domain of the given function. Express your answer in interval notation.
Test 2 Review 1. Given the following relation: 5 2 + = -6 - y Step 1. Rewrite the relation as a function of. Step 2. Using the answer from step 1, evaluate the function at = -1. Step. Using the answer
More informationH-Pre-Calculus Targets Chapter I can write quadratic functions in standard form and use the results to sketch graphs of the function.
H-Pre-Calculus Targets Chapter Section. Sketch and analyze graphs of quadratic functions.. I can write quadratic functions in standard form and use the results to sketch graphs of the function. Identify
More informationClifton High School Mathematics Summer Workbook
Clifton High School Mathematics Summer Workbook Algebra II-H: 9 th grade Completion of this summer work is required on the first day of the school year. Date Received: Date Completed: Student Signature:
More informationModule 1: Whole Numbers Module 2: Fractions Module 3: Decimals and Percent Module 4: Real Numbers and Introduction to Algebra
Course Title: College Preparatory Mathematics I Prerequisite: Placement with a score below 20 on ACT, below 450 on SAT, or assessing into Basic Applied Mathematics or Basic Algebra using Accuplacer, ASSET
More information