Algebra 2 Chapter 9 Page 1
|
|
|
- Irene Porter
- 6 years ago
- Views:
Transcription
1 Section 9.1A Introduction to Rational Functions Work Together How many pounds of peanuts do you think and average person consumed last year? Us the table at the right. What was the average peanut consumption per person in the US in 1993? Year You can use the data in the table to model the average US consumption per person between 1970 and Let 0 represent Input the data into three lists on your calculator. Find a cubic function f () to model the annual consumption of peanuts. US Peanut US Consumption Population (millions of pounds) (millions) Find a quadratic function g() to represent the US population since Write a function h() to model the average peanut consumption in the US since Graph the function on your calculator you wrote to estimate the number of peanuts that were consumed by the average person last year. Wrap Up A rational function occurs when one polynomial is divided by another polynomial. Eample: 3 1 f ( ) ( 3)( + 4) Algebra Chapter 9 Page 1
2 Section 9.1 Multiplying and Dividing Rational Epressions Goals: 1. To simplify rational epressions.. To determine when a rational function is undefined. 3. To simplify comple fractions. Eamples 1. Simplify and determine when the rational epression is undefined: 3y ( y + 7) ( + 5) a. b. y + 7 y ( )( ) ( )( ). For what values of p is p + p 3 p p 15 undefined? 3. Simplify: 4 4 a b a 3 3 a a b 4. Multiply and Simplify: 8 7 y a. b y 16 5a c 4bc 1b 15a b 4 3 c. 3 5y d. 3 15y 6 y 10 y 5y 3yz 3 Algebra Chapter 9 Page
3 5. Divide and Simplify: 10 ps 5ps a. b. 3c d 6c d 3 y 6y 0ab 5a b 3 6. Simplify: k 3 k 4k + 3 a. k k d + 6 d + 3 d + d d + 3d + b. c d + 9 d + d + 4d + 3 d + 5d + 4 d. 7. Simplify the comple fraction: 9 4y a. 3 y 3 b. a a 9b 4 a a + 3b 1 + 5/ + 1 Simplifying Error: Note: You cannot simplify through addition or subtraction. Homework: p all, 13, 17, 5-37, 41 Algebra Chapter 9 Page 3
4 Section 9. Adding and Subtracting Rational Epressions Goals: 1. To find the least common denominator.. To add and subtract rational epressions. A. Find the Least Common Multiple (or LCD) Eamples a bc, 16b c and 0a c. 3 and zy, 3 9 y z, and 4 z and B. Adding and Subtracting Rational and Comple Epressions Eamples 5a b 14a b y 1y a b 1 1 b a b b a Homework p all, 60, Algebra Chapter 9 Page 4
5 Section 9.4 Graphing Rational Functions Goal: 1. To graph rational functions.. To locate asymptotes of a function. I. Definition of Rational Functions A. A function occurs when one is by another. 3 1 B. Eample: f ( ) ( 3)( + 4) II. Asymptotes A. The lines a rational functions. B. The asymptote occurs when the equals. Note One eception in the. C. The asymptote occurs when and the y value a certain. D. Eamples: 1. Determine the equations of any vertical asymptotes and the values of for any holes in the graph of: 4 9 a) f ( ) b) f ( ) Graph and name the asymptotes or any holes in the graphs: a) f ( ) b) f ( ) c) f ( ) 4 d) f ( ) Homework: Worksheet Algebra Chapter 9 Page 5
6 Algebra Worksheet Section 9.4 Name: Algebra Chapter 9 Page 6
7 Algebra Chapter 9 Page 7
8 Section 9.5 Direct, Inverse and Joint Variation Goals: 1. To solve problems involving direct, inverse, and joint variations. A. Direct Variation 1. As ( ), y ( ).. Wording 3. General Equation: y k where k is the constant of variation. 4. This is similar to the equation y m where m is the slope. 5. Eample: a) If y varies directly as and y 15 when 5, find y when 3. Method to solve variation problems: b) If y varies directly as and y 1 when 3, find y when 7. B. Joint Variation 1. Wording. General Equation: y kz where k is the constant of variation. 3. Eample: a) The volume of a cone varies jointly as the square of the radius of the base and the height. Find the equation of joint variation if V 85, r 4, and h 17. b) Suppose y varies jointly as and z. Find y when 3 and z, if y 11 when 5 and z. Algebra Chapter 9 Page 8
9 C. Inverse Variation 1. As ( ), y ( ). Wording k 3. General Equation: y where k is the constant of variation. 4. Eamples a) If y varies inversely as and y when 6, find y when 7. b) If temperature is constant, gas volume varies inversely with its pressure. If an airfilled balloon has a volume of.6 dm when pressure is 10 kpascals, what is the 3 3 pressure if the volume is 3. dm? D. Combined Variations The force is directly related to the product of the masses of two objects and inversely related to the square of the distance between them. Homework p all, 5, 6, 11, 16, 1,, 44, 47, all Algebra Chapter 9 Page 9
10 Section 9.6 Solving Rational Equations and Inequalities Goals: 1. To solve rational equations and inequalities Eamples: p p + 1 p 7 + p p + 1 p 1 p + 1 ( )( ) Tim and Ashley mow lawns together. Tim working alone could complete the job in 4.5 hours, and Ashley could complete it alone in 3.7 hours. How long does it take to complete the job when they work together? Note: Work Rate How much of the can be in a given of. W + W + W W 1 3 Total Algebra Chapter 9 Page 10
11 6. Libby and Nate clean together. Nate working alone could complete the job in 3 hours, and Libby could complete it alone in 5 hours. How long does it take to complete the job when they work together? 7. A car travels 300 km in the same time that a freight train travels 00 km. The speed of the car is 0 km/h faster than the train. Find the speed of the train. Note: Distance 8. Solve: 1 3s + 9s < 3 9. Solve: < 5 5 Homework Day 1: p all, 17-1 odds, 47, 51 Day : p all, 4-7 all, 31, 41, 4 Algebra Chapter 9 Page 11
Honors Algebra 2 Chapter 9 Page 1
Introduction to Rational Functions Work Together How many pounds of peanuts do you think and average person consumed last year? Us the table at the right. What was the average peanut consumption per person
Reteach Variation Functions
8-1 Variation Functions The variable y varies directly as the variable if y k for some constant k. To solve direct variation problems: k is called the constant of variation. Use the known and y values
8-5. A rational inequality is an inequality that contains one or more rational expressions. x x 6. 3 by using a graph and a table.
A rational inequality is an inequality that contains one or more rational expressions. x x 3 by using a graph and a table. Use a graph. On a graphing calculator, Y1 = x and Y = 3. x The graph of Y1 is
Advanced Algebra 2 - Assignment Sheet Chapter 1
Advanced Algebra - Assignment Sheet Chapter #: Real Numbers & Number Operations (.) p. 7 0: 5- odd, 9-55 odd, 69-8 odd. #: Algebraic Expressions & Models (.) p. 4 7: 5-6, 7-55 odd, 59, 6-67, 69-7 odd,
Fundamental Theorem of Algebra (NEW): A polynomial function of degree n > 0 has n complex zeros. Some of these zeros may be repeated.
.5 and.6 Comple Numbers, Comple Zeros and the Fundamental Theorem of Algebra Pre Calculus.5 COMPLEX NUMBERS 1. Understand that - 1 is an imaginary number denoted by the letter i.. Evaluate the square root
Algebra Concepts Equation Solving Flow Chart Page 1 of 6. How Do I Solve This Equation?
Algebra Concepts Equation Solving Flow Chart Page of 6 How Do I Solve This Equation? First, simplify both sides of the equation as much as possible by: combining like terms, removing parentheses using
Day 3: Section P-6 Rational Expressions; Section P-7 Equations. Rational Expressions
1 Day : Section P-6 Rational Epressions; Section P-7 Equations Rational Epressions A rational epression (Fractions) is the quotient of two polynomials. The set of real numbers for which an algebraic epression
7.1 Rational Expressions and Their Simplification
7.1 Rational Epressions and Their Simplification Learning Objectives: 1. Find numbers for which a rational epression is undefined.. Simplify rational epressions. Eamples of rational epressions: 3 and 1
2. Which of the following expressions represents the product of four less than three times x and two more than x?
Algebra Topics COMPASS Review You will be allowed to use a calculator on the COMPASS test. Acceptable calculators are: basic calculators, scientific calculators, and graphing calculators up through the
Reteach Multiplying and Dividing Rational Expressions
8-2 Multiplying and Dividing Rational Expressions Examples of rational expressions: 3 x, x 1, and x 3 x 2 2 x 2 Undefined at x 0 Undefined at x 0 Undefined at x 2 When simplifying a rational expression:
Lesson #9 Simplifying Rational Expressions
Lesson #9 Simplifying Rational Epressions A.A.6 Perform arithmetic operations with rational epressions and rename to lowest terms Factor the following epressions: A. 7 4 B. y C. y 49y Simplify: 5 5 = 4
Precalculus Chapter 7 Page 1
Section 7.1 Polynomial Functions 1. To evaluate polynomial functions.. To identify general shapes of the graphs of polynomial functions. I. Terminology A. Polynomials in one variable B. Examples: Determine
Math 154 :: Elementary Algebra
Math 4 :: Elementary Algebra Section. Additive Property of Equality Section. Multiplicative Property of Equality Section.3 Linear Equations in One-Variable Section.4 Linear Equations in One-Variable with
Section 5.1 Model Inverse and Joint Variation
108 Section 5.1 Model Inverse and Joint Variation Remember a Direct Variation Equation y k has a y-intercept of (0, 0). Different Types of Variation Relationship Equation a) y varies directly with. y k
A2T. Rational Expressions/Equations. Name: Teacher: Pd:
AT Packet #1: Rational Epressions/Equations Name: Teacher: Pd: Table of Contents o Day 1: SWBAT: Review Operations with Polynomials Pgs: 1-3 HW: Pages -3 in Packet o Day : SWBAT: Factor using the Greatest
INTRODUCTION TO RATIONAL EXPRESSIONS EXAMPLE:
INTRODUCTION TO RATIONAL EXPRESSIONS EXAMPLE: You decide to open a small business making gluten-free cakes. Your start-up costs were $, 000. In addition, it costs $ 0 to produce each cake. What is the
Review of Rational Expressions and Equations
Page 1 of 14 Review of Rational Epressions and Equations A rational epression is an epression containing fractions where the numerator and/or denominator may contain algebraic terms 1 Simplify 6 14 Identification/Analysis
Mini-Lecture 6.1 Rational Functions and Multiplying and Dividing Rational Expressions
Learning Objectives: Mini-Lecture 6. Rational Functions and Multiplying and Dividing Rational Epressions. Find the domain of a rational function.. Simplify rational epressions.. Multiply rational epressions.
Definition 8.1 Two inequalities are equivalent if they have the same solution set. Add or Subtract the same value on both sides of the inequality.
8 Inequalities Concepts: Equivalent Inequalities Linear and Nonlinear Inequalities Absolute Value Inequalities (Sections.6 and.) 8. Equivalent Inequalities Definition 8. Two inequalities are equivalent
CHAPTER 5 RATIONAL FUNCTIONS
CHAPTER 5 RATIONAL FUNCTIONS Big IDEAS: ) Graphing rational functions ) Performing operations with rational epressions 3) Solving rational equations Section: 5- Model Inverse and Joint Variation Essential
Algebra. Robert Taggart
Algebra Robert Taggart Table of Contents To the Student.............................................. v Unit 1: Algebra Basics Lesson 1: Negative and Positive Numbers....................... Lesson 2: Operations
9.1 Adding and Subtracting Rational Expressions
9.1 Adding and Subtracting Rational Epressions Essential Question: How can you add and subtract rational epressions? Resource Locker Eplore Identifying Ecluded Values Given a rational epression, identify
IOWA End-of-Course Assessment Programs. Released Items ALGEBRA II. Copyright 2010 by The University of Iowa.
IOWA End-of-Course Assessment Programs Released Items Copyright 2010 by The University of Iowa. ALGEBRA II 1 Which cubic equation has roots of 2, 1, and 3? A 3 6 = 0 INCORRECT: The student wrote a cubic
(1) Assignment # 1 Absolute Value. (2) Assignment # 2 Compound Absolute Values. (3) Assignment # 3 Exponents. (4) Assignment # 4 Simplifying Radicals
Alg_0 Packet # The beginning of our Quest () Assignment # Absolute Value () Assignment # Compound Absolute Values () Assignment # Eponents () Assignment # Simplifying Radicals (5) Assignment # 5 Fractional
Adding and Subtracting Rational Expressions
Adding and Subtracting Rational Epressions As a review, adding and subtracting fractions requires the fractions to have the same denominator. If they already have the same denominator, combine the numerators
HAlgebra 2: Unit 7: Chapter 9 Spring Day Date Lesson Assignment. Section 9.1: Direct, Inverse, & Joint Variation Classwork: Packet p.
HAlgebra : Unit 7: Chapter Spring 0 Name RATIONAL FUNCTIONS. NC Objectives:.0 Operate with algebraic epressions (polynomial, rational, comple fractions) to solve problems..0 Model and solve problems using
CHAPTER 8A- RATIONAL FUNCTIONS AND RADICAL FUNCTIONS Section Multiplying and Dividing Rational Expressions
Name Objectives: Period CHAPTER 8A- RATIONAL FUNCTIONS AND RADICAL FUNCTIONS Section 8.3 - Multiplying and Dividing Rational Expressions Multiply and divide rational expressions. Simplify rational expressions,
9.1 Adding and Subtracting Rational Expressions
Name Class Date 9.1 Adding and Subtracting Rational Epressions Essential Question: How can you add and subtract rational epressions? Resource Locker Eplore Identifying Ecluded Values Given a rational epression,
10.7 Polynomial and Rational Inequalities
10.7 Polynomial and Rational Inequalities In this section we want to turn our attention to solving polynomial and rational inequalities. That is, we want to solve inequalities like 5 4 0. In order to do
Intermediate 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,
Name. Unit 1 Worksheets Math 150 College Algebra and Trig
Name Unit 1 Worksheets Math 10 College Algebra and Trig Revised: Fall 009 Worksheet 1: Integral Eponents Simplify each epression. Write all answers in eponential form. 1. (8 ). ( y). (a b ). y 6. (7 8
Solving Equations. Solving Equations - decimal coefficients and constants. 2) Solve for x: 3(3x 6) = 3(x -2) 1) Solve for x: 5 x 2 28 x
Level C Review Packet This packet briefly reviews the topics covered on the Level A Math Skills Assessment. If you need additional study resources and/or assistance with any of the topics below, please
Department of Mathematics, University of Wisconsin-Madison Math 114 Worksheet Sections (4.1),
Department of Mathematics, University of Wisconsin-Madison Math 114 Worksheet Sections (4.1), 4.-4.6 1. Find the polynomial function with zeros: -1 (multiplicity ) and 1 (multiplicity ) whose graph passes
INTRODUCTION 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
Math 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
Problem 1 Oh Snap... Look at the Denominator on that Rational
Problem Oh Snap... Look at the Denominator on that Rational Previously, you learned that dividing polynomials was just like dividing integers. Well, performing operations on rational epressions involving
LESSON 8.3 EQUATIONS WITH FRACTIONS
LESSON 8. EQUATIONS WITH FRACTIONS LESSON 8. EQUATIONS WITH FRACTIONS OVERVIEW Here is what you'll learn in this lesson: Solving Equations a. Solving equations with rational epressions b. Solving for an
7.3 Adding and Subtracting Rational Expressions
7.3 Adding and Subtracting Rational Epressions LEARNING OBJECTIVES. Add and subtract rational epressions with common denominators. 2. Add and subtract rational epressions with unlike denominators. 3. Add
Algebra Final Exam Review Packet
Algebra 1 00 Final Eam Review Packet UNIT 1 EXPONENTS / RADICALS Eponents Degree of a monomial: Add the degrees of all the in the monomial together. o Eample - Find the degree of 5 7 yz Degree of a polynomial:
Vocabulary: I. Inverse Variation: Two variables x and y show inverse variation if they are related as. follows: where a 0
8.1: Model Inverse and Joint Variation I. Inverse Variation: Two variables x and y show inverse variation if they are related as follows: where a 0 * In this equation y is said to vary inversely with x.
Rational Equations. You can use a rational function to model the intensity of sound.
UNIT Rational Equations You can use a rational function to model the intensit of sound. Copright 009, K Inc. All rights reserved. This material ma not be reproduced in whole or in part, including illustrations,
Chapter 7 Rational Expressions, Equations, and Functions
Chapter 7 Rational Expressions, Equations, and Functions Section 7.1: Simplifying, Multiplying, and Dividing Rational Expressions and Functions Section 7.2: Adding and Subtracting Rational Expressions
Multiplying and Dividing Rational Expressions y y v 2 3 v 2-13v x z 25 x. n - 6 n 2-6n. 6x + 2 x 2. w y a 3 w.
8- Multiplying and Dividing Rational Epressions Simplify each epression.. 9 a b 7 a b c. ( m n ) -8 m 5 n. 0 y + 5y 5 y - 5y. k - k - 5 k - 9 5. 5 - v v - v - 0. + - - 7. - u y 5 z 5 5 u y 8. a + y y +
Chapter 9 Rational Expressions and Equations Lesson 9-1 Multiplying and Dividing Rational Expressions Pages
Chapter 9 Rational Epressions and Equations Lesson 9- Multipling and Dividing Rational Epressions Pages 76 78. Sample answer: 3. Never; solving the equation using cross products leads to 5 0, which is
CHAPTER 8 Quadratic Equations, Functions, and Inequalities
CHAPTER Quadratic Equations, Functions, and Inequalities Section. Solving Quadratic Equations: Factoring and Special Forms..................... 7 Section. Completing the Square................... 9 Section.
Basic Property: of Rational Expressions. Multiplication and Division of Rational Expressions. The Domain of a Rational Function: P Q WARNING:
Basic roperties of Rational Epressions A rational epression is any epression of the form Q where and Q are polynomials and Q 0. In the following properties, no denominator is allowed to be zero. The Domain
Unit 5 RATIONAL FUNCTIONS. A function with a variable in the denominator Parent function 1 x Graph is a hyperbola
Unit 5 RATIONAL FUNCTIONS A function with a variable in the denominator Parent function 1 x Graph is a hyperbola I will be following the Alg 2 book in this Unit Ch 5 Sections 1-5 Use the Practice Packet
k y = where k is the constant of variation and
Syllabus Objectives: 9. The student will solve a problem by applying inverse and joint variation. 9.6 The student will develop mathematical models involving rational epressions to solve realworld problems.
Project - Math 99 Final Practice Due Thursday 3 rd August
Project - Math 99 Final Practice Summer 017 Project - Math 99 Final Practice Due Thursday rd August Section 1: Multiple Choice Questions Students Name : 1. The epression 10 + when factored fully is:- A.
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
10.1 Adding and Subtracting Rational Expressions
Name Class Date 10.1 Adding and Subtracting Rational Epressions Essential Question: How can you add and subtract rational epressions? A2.7.F Determine the sum, difference of rational epressions with integral
Inverse Variation Read 7.1 Examples 1-4
CC Algebra II HW #52 Name Period Row Date Inverse Variation Read 7.1 Eamples 1-4 Section 7.1 1. Vocabulary Eplain how direct variation equations and inverse variation equations are different. Tell whether
Section 5.0A Factoring Part 1
Section 5.0A Factoring Part 1 I. Work Together A. Multiply the following binomials into trinomials. (Write the final result in descending order, i.e., a + b + c ). ( 7)( + 5) ( + 7)( + ) ( + 7)(3 + 5)
MATH 150 CHAPTER3 Polynomials Section 3.1
MATH 50 CHAPTER Polynomials ------- Section. 4 Degree of a Polynomial 4 Identify the following polynomials: 4 4 Descending order 7 5 4 Leading Term Leading Coefficient The constant (no variable) LEFT AND
Section 4.3: Quadratic Formula
Objective: Solve quadratic equations using the quadratic formula. In this section we will develop a formula to solve any quadratic equation ab c 0 where a b and c are real numbers and a 0. Solve for this
(b) Equation for a parabola: c) Direction of Opening (1) If a is positive, it opens (2) If a is negative, it opens
Section.1 Graphing Quadratics Objectives: 1. Graph Quadratic Functions. Find the ais of symmetry and coordinates of the verte of a parabola.. Model data using a quadratic function. y = 5 I. Think and Discuss
a = B. Examples: 1. Simplify the following expressions using the multiplication rule
Section. Monomials Objectives:. Multiply and divide monomials.. Simplify epressions involving powers of monomials.. Use epressions in scientific notation. I. Negative Eponents and Eponents of Zero A. Rules.
Math 120. x x 4 x. . In this problem, we are combining fractions. To do this, we must have
Math 10 Final Eam Review 1. 4 5 6 5 4 4 4 7 5 Worked out solutions. In this problem, we are subtracting one polynomial from another. When adding or subtracting polynomials, we combine like terms. Remember
2.6 Solving Inequalities Algebraically and Graphically
7_006.qp //07 8:0 AM Page 9 Section.6 Solving Inequalities Algebraically and Graphically 9.6 Solving Inequalities Algebraically and Graphically Properties of Inequalities Simple inequalities were reviewed
Name These exercises cover topics from Algebra I and Algebra II. Complete each question the best you can.
Name These eercises cover topics from Algebra I and Algebra II. Complete each question the best you can. Multiple Choice: Place through the letter of the correct answer. You may only use your calculator
Rational Expressions
CHAPTER 6 Rational Epressions 6. Rational Functions and Multiplying and Dividing Rational Epressions 6. Adding and Subtracting Rational Epressions 6.3 Simplifying Comple Fractions 6. Dividing Polynomials:
Define a rational expression: a quotient of two polynomials. ..( 3 10) (3 2) Rational expressions have the same properties as rational numbers:
1 UNIT 7 RATIONAL EXPRESSIONS & EQUATIONS Simplifying Rational Epressions Define a rational epression: a quotient of two polynomials. A rational epression always indicates division EX: 10 means..( 10)
Review for Intermediate Algebra (MATD 0390) Final Exam Oct 2009
Review for Intermediate Algebra (MATD 090) Final Eam Oct 009 Students are epected to know all relevant formulas, including: All special factoring formulas Equation of a circle All formulas for linear equations
Unit 5 RATIONAL FUNCTIONS. A function with a variable in the denominator Parent function 1 x Graph is a hyperbola
Unit 5 RATIONAL FUNCTIONS A function with a variable in the denominator Parent function 1 x Graph is a hyperbola A direct variation is a relationship between two variables x and y that can be written in
Math 1314 Lesson 1: Prerequisites
Math 131 Lesson 1: Prerequisites Prerequisites are topics you should have mastered before you enter this class. Because of the emphasis on technology in this course, there are few skills which you will
Simplifying Rational Expressions
.3 Simplifying Rational Epressions What are the ecluded values of a rational epression? How can you simplify a rational epression? ACTIVITY: Simplifying a Rational Epression Work with a partner. Sample:
Algebra 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
Rational Functions 4.5
Math 4 Pre-Calculus Name Date Rational Function Rational Functions 4.5 g ( ) A function is a rational function if f ( ), where g ( ) and ( ) h ( ) h are polynomials. Vertical asymptotes occur at -values
Unit 9 Study Sheet Rational Expressions and Types of Equations
Algebraic Fractions: Unit 9 Study Sheet Rational Expressions and Types of Equations Simplifying Algebraic Fractions: To simplify an algebraic fraction means to reduce it to lowest terms. This is done by
Equations and Inequalities
Equations and Inequalities Figure 1 CHAPTER OUTLINE 1 The Rectangular Coordinate Systems and Graphs Linear Equations in One Variable Models and Applications Comple Numbers Quadratic Equations 6 Other Types
Complex fraction: - a fraction which has rational expressions in the numerator and/or denominator
Comple fraction: - a fraction which has rational epressions in the numerator and/or denominator o 2 2 4 y 2 + y 2 y 2 2 Steps for Simplifying Comple Fractions. simplify the numerator and/or the denominator
Warm Up Lesson Presentation Lesson Quiz. Holt Algebra 2 2
8-8 Warm Up Lesson Presentation Lesson Quiz 2 Warm Up Simplify each expression. Assume all variables are positive. 1. 2. 3. 4. Write each expression in radical form. 5. 6. Objective Solve radical equations
MA 180 Lecture. Chapter 0. College Algebra and Calculus by Larson/Hodgkins. Fundamental Concepts of Algebra
0.) Real Numbers: Order and Absolute Value Definitions: Set: is a collection of objections in mathematics Real Numbers: set of numbers used in arithmetic MA 80 Lecture Chapter 0 College Algebra and Calculus
Accuplacer 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
Are You Ready for Algebra 3/Trigonometry? Summer Packet **Required for all Algebra 3/Trig CP and Honors students**
Page of Are You Ready for Algebra /Trigonometry? Summer Packet **Required for all Algebra /Trig CP and Honors students** The Algebra /Trigonometry course prepares students for Calculus and college science
LESSON #34 - FINDING RESTRICTED VALUES AND SIMPLIFYING RATIONAL EXPRESSIONS COMMON CORE ALGEBRA II
LESSON #4 - FINDING RESTRICTED VALUES AND SIMPLIFYING RATIONAL EXPRESSIONS COMMON CORE ALGEBRA II A rational epression is a fraction that contains variables. A variable is very useful in mathematics. In
( ) c. m = 0, 1 2, 3 4
G Linear Functions Probably the most important concept from precalculus that is required for differential calculus is that of linear functions The formulas you need to know backwards and forwards are:
TRIG REVIEW NOTES. Co-terminal Angles: Angles that end at the same spot. (sines, cosines, and tangents will equal)
TRIG REVIEW NOTES Convert from radians to degrees: multiply by 0 180 Convert from degrees to radians: multiply by 0. 180 Co-terminal Angles: Angles that end at the same spot. (sines, cosines, and tangents
Unit 3: Rational Expressions
Unit : Rational Epressions Common Denominators Directions: For each of the following, practice finding the LCM necessary for creating a common denominator (Hint: make sure to factor). 1) ; 0. 14; 1 10
Section 7.1 Rational Functions and Simplifying Rational Expressions
Beginning & Intermediate Algebra, 6 th ed., Elayn Martin-Gay Sec. 7.1 Section 7.1 Rational Functions and Simplifying Rational Expressions Complete the outline as you view Video Lecture 7.1. Pause the video
LESSON 8.1 RATIONAL EXPRESSIONS I
LESSON 8. RATIONAL EXPRESSIONS I LESSON 8. RATIONAL EXPRESSIONS I 7 OVERVIEW Here is what you'll learn in this lesson: Multiplying and Dividing a. Determining when a rational expression is undefined Almost
SB CH 2 answers.notebook. November 05, Warm Up. Oct 8 10:36 AM. Oct 5 2:22 PM. Oct 8 9:22 AM. Oct 8 9:19 AM. Oct 8 9:26 AM.
Warm Up Oct 8 10:36 AM Oct 5 2:22 PM Linear Function Qualities Oct 8 9:22 AM Oct 8 9:19 AM Quadratic Function Qualities Oct 8 9:26 AM Oct 8 9:25 AM 1 Oct 8 9:28 AM Oct 8 9:25 AM Given vertex (-1,4) and
Chapter 9 Notes SN AA U2C9
Chapter 9 Notes SN AA U2C9 Name Period Section 2-3: Direct Variation Section 9-1: Inverse Variation Two variables x and y show direct variation if y = kx for some nonzero constant k. Another kind of variation
Performing well in calculus is impossible without a solid algebra foundation. Many calculus
Chapter Algebra Review Performing well in calculus is impossible without a solid algebra foundation. Many calculus problems that you encounter involve a calculus concept but then require many, many steps
About the Portfolio Activities. About the Chapter Project
Galileo is credited as the first person to notice that the motion of a pendulum depends only upon its length. About the Chapter Project Finding an average is something that most people can do almost instinctively.
Algebra I. Course Outline
Algebra I Course Outline I. The Language of Algebra A. Variables and Expressions B. Order of Operations C. Open Sentences D. Identity and Equality Properties E. The Distributive Property F. Commutative
1 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
Algebra II Notes Unit Nine: Rational Equations and Functions
Syllabus Objectives: 9. The student will solve a problem by applying inverse and joint variation. 9.6 The student will develop mathematical models involving rational epressions to solve realworld problems.
Math 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
UNIT 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
Solve. Label any contradictions or identities. 1) -4x + 2(3x - 3) = 5-9x. 2) 7x - (3x - 1) = 2. 3) 2x 5 - x 3 = 2 4) 15. 5) -4.2q =
Spring 2011 Name Math 115 Elementary Algebra Review Wednesday, June 1, 2011 All problems must me done on 8.5" x 11" lined paper. Solve. Label any contradictions or identities. 1) -4x + 2(3x - 3) = 5-9x
Answers to Sample Exam Problems
Math Answers to Sample Exam Problems () Find the absolute value, reciprocal, opposite of a if a = 9; a = ; Absolute value: 9 = 9; = ; Reciprocal: 9 ; ; Opposite: 9; () Commutative law; Associative law;
MATH 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
Algebra II Notes Rational Functions Unit Rational Functions. Math Background
Algebra II Notes Rational Functions Unit 6. 6.6 Rational Functions Math Background Previously, you Simplified linear, quadratic, radical and polynomial functions Performed arithmetic operations with linear,
Polynomial and Rational Functions. Chapter 3
Polynomial and Rational Functions Chapter 3 Quadratic Functions and Models Section 3.1 Quadratic Functions Quadratic function: Function of the form f(x) = ax 2 + bx + c (a, b and c real numbers, a 0) -30
Section 3.3 Limits Involving Infinity - Asymptotes
76 Section. Limits Involving Infinity - Asymptotes We begin our discussion with analyzing its as increases or decreases without bound. We will then eplore functions that have its at infinity. Let s consider
Adding and Subtracting Rational Expressions
COMMON CORE Locker LESSON 9.1 Adding and Subtracting Rational Epressions Name Class Date 9.1 Adding and Subtracting Rational Epressions Essential Question: How can you add and subtract rational epressions?
Project 2 - Math 99 - Practice Final Due Tuesday 5 th December (100 points) Section 1: Multiple Choice Questions
Project - Math 99 Final Practice Fall 017 Project - Math 99 - Practice Final Due Tuesday 5 th December (100 points) Section 1: Multiple Choice Questions Students Name : 1. The epression 10 + when factored
3 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
Unit 8 Rational Expressions and Equations Examples Introductory Algebra Page 1 of 18
Unit 8 Rational Epressions and Equations Eamples Introductory Algebra Page of 8 When canceling quantities like a, to avoid the division by zero case we usually specify that a 0. a Remember that you can