IM 3 Lesson 4.2 Day 3: Graphing Reflections and Connections Unit 4 Polynomial Functions
|
|
- Bonnie Underwood
- 5 years ago
- Views:
Transcription
1 (A) Lesson Context BIG PICTURE of this UNIT: What is a Polynomial and how do they look? What are the attributes of a Polynomial? How do I work with Polynomials? CONTEXT of this LESSON: Where we ve been We have discussed the basics: degree, type, and operations (+,, x) Where we are What are the key attributes of a polynomial and how do these affect the shape? Where we are heading What are the key attributes of a polynomial and how do these affect the shape? (B) Lesson Objectives: a. Begin to analyze the the attributes of a polynomial function and it s effect on the graph. b. Observations and patterns in the graphs of polynomials. c. Solidify our perdictions of how polynomials behave.
2 (C) Drawing Challenge #1: The following challenge is based on the END BEHAVIOURS and MULTIPLICITIES of a polynomial function. From the factored form of each polynomial function, sketch the graph of each function showing clearly the end behaviour and what the function looks like at each root. f (x) = (x 8)(x 2)(x + 4)(x + 9) f (x) = 2(x + 2) 2 (x 2) 2 f (x) = (x 3) 2 (x 1)(x + 5) 2 f (x) = (x + 3)(x 6)(x + 7)(x 1)(x + 4) f (x) = (x 5) 3 (x +1) f (x) = (x + 4) 3 (x 2) 2 (x +1) f (x) = 1 2 (x 4)4 (x + 3) 2 (x 8) f (x) = (x + 6)(x 2) 3 (x +1) 5 *CHALLENGE* f (x) = (x + 5) 2 (2 x)(x + 7) *CHALLENGE* f (x) = (3 x) 2 (x + 9) 2 (6 x) 3
3 (D) Drawing Challenge #2: The following challenge is based on the EXTREMA and ZEROS of a polynomial function. From the description of each polynomial function, sketch a possible graph of each function clearly showing the correct number of extrema or zeros. DO NOT repeat any graphs! IF it is not possible to sketch a function fitting the criteria, EXPLAIN why. (HINT: there are only 2 below that are not possible). 5 th degree polynomial with 4 x-intercepts 5 th degree polynomial with 2 extrema 4 th degree polynomial with 2 x-intercepts 6 th degree polynomial with 3 extrema 4 th degree polynomial with 2 extrema 6 th degree polynomial with 2 x-intercepts 6 th degree polynomial with 1 extrema 5 th degree polynomial with 2 extrema 6 th degree polynomial with 4 x-intercepts 5 th degree polynomial with 1 extrema
4 (E) Matching Challenge #3 Now that we have a grasp on what a polynomail is and we have begun to develop the key vocabulary we can now apply our knowledge WITHOUT the use of technology to see if we can make connections between the two forms of a polynomial and their graphs. You are given a set of 6 factored form equations, 6 standard form equations, and 6 graphs. Your goal is to MATCH a factored form equation to a standard form equation to a graph. Record the combinations below: Factored Form Standard Form Graph
5 Connections and Reflections: 1. Please reflect upon and write about any connections between the factored form equation and the graph. Picture or sketch to support your thinking. Writen Response: 2. Please reflect upon and write about any connections between the standard form equation and the graph. Picture or sketch to support your thinking. Writen Response: 3. Please reflect upon and write about any connections between the x-intercpts equation and the equation. Picture or sketch to support your thinking. Writen Response:
6 4. Please reflect upon and write about any connections between the y-intercpts equation and the equation. Picture or sketch to support your thinking. Writen Response: 5. Please reflect upon and write about any connections between the degree of the polynomial and the shape of the graph. Picture or sketch to support your thinking. Writen Response: 6. Please reflect upon and write about any connections between the sign of the leading coefficient and the end behaviour of the graph. Picture or sketch to support your thinking. Writen Response:
7 Final Consolidaiton Degree and family name 1 st Degree Name: 2 nd Degree Name: 3 rd Degree Name: 4 th Degree Name: 5 th Degree Name: Graph Shape Graph Shape Graph Shape Graph Shape Graph Shape + Leading Coefficient - Leading Coefficient EXT 1. Given the following factored form equation without technology put into standard form and draw a sketch of the graph. f (x) = (x 1)(x 7)(x + 2) EXT 2. Given the following Graph write a possible factored form equaiton or standard form equation.
8 Matching Graphs M
9 Matching Graphs N
10 Matching Graphs O
11 Matching Graphs P
12 Matching Graphs Q
13 Matching Graphs R
IM 3 Assignment 4.3 : Graph Investigation Unit 4 Polynomial Functions
(A) Lesson Context BIG PICTURE of this UNIT: What is a Polynomial and how do they look? What are the attributes of a Polynomial? How do I work with Polynomials? CONTEXT of this LESSON: Where we ve been
More informationIM 3 Assignment 4.3 : Graph Investigation Unit 4 Polynomial Functions
(A) Lesson Context BIG PICTURE of this UNIT: What is a Polynomial and how do they look? What are the attributes of a Polynomial? How do I work with Polynomials? CONTEXT of this LESSON: Where we ve been
More informationPolynomial functions right- and left-hand behavior (end behavior):
Lesson 2.2 Polynomial Functions For each function: a.) Graph the function on your calculator Find an appropriate window. Draw a sketch of the graph on your paper and indicate your window. b.) Identify
More information2.2 BEGINS: POLYNOMIAL
CHAPTER 2.2 HIGHER DEGREE POLY S 2.2 BEGINS: POLYNOMIAL Graphs of Polynomial Functions Polynomial functions are continuous. What this means to us is that the graphs of polynomial functions have no breaks,
More informationIM3 - Lesson 5: Forms of Equations for Linear Functions Unit 1 Basics of Functions
A. Lesson Contet BIG PICTURE of this UNIT: CONTEXT of this LESSON: What is meant by the term FUNCTIONS and how do we work with them? mastery with working with basics & applications of linear functions
More informationGeorgia Department of Education Common Core Georgia Performance Standards Framework CCGPS Advanced Algebra Unit 2
Polynomials Patterns Task 1. To get an idea of what polynomial functions look like, we can graph the first through fifth degree polynomials with leading coefficients of 1. For each polynomial function,
More informationLesson 3: Exploring Quadratic Relations Graphs Unit 5 Quadratic Relations
(A) Lesson Context BIG PICTURE of this UNIT: CONTEXT of this LESSON: How do we analyze and then work with a data set that shows both increase and decrease What is a parabola and what key features do they
More informationIn other words, we are interested in what is happening to the y values as we get really large x values and as we get really small x values.
Polynomial functions: End behavior Solutions NAME: In this lab, we are looking at the end behavior of polynomial graphs, i.e. what is happening to the y values at the (left and right) ends of the graph.
More informationLesson 6: Switching Between Forms of Quadratic Equations Unit 5 Quadratic Functions
(A) Lesson Context BIG PICTURE of this UNIT: CONTEXT of this LESSON: How do we analyze and then work with a data set that shows both increase and decrease What is a parabola and what key features do they
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 informationFoundations of Math II Unit 5: Solving Equations
Foundations of Math II Unit 5: Solving Equations Academics High School Mathematics 5.1 Warm Up Solving Linear Equations Using Graphing, Tables, and Algebraic Properties On the graph below, graph the following
More informationComplete the following table using the equation and graphs given:
L2 1.2 Characteristics of Polynomial Functions Lesson MHF4U Jensen In section 1.1 we looked at power functions, which are single-term polynomial functions. Many polynomial functions are made up of two
More informationSuppose that f is continuous on [a, b] and differentiable on (a, b). Then
Lectures 1/18 Derivatives and Graphs When we have a picture of the graph of a function f(x), we can make a picture of the derivative f (x) using the slopes of the tangents to the graph of f. In this section
More informationPrecalculus Lesson 4.1 Polynomial Functions and Models Mrs. Snow, Instructor
Precalculus Lesson 4.1 Polynomial Functions and Models Mrs. Snow, Instructor Let s review the definition of a polynomial. A polynomial function of degree n is a function of the form P(x) = a n x n + a
More informationTo get horizontal and slant asymptotes algebraically we need to know about end behaviour for rational functions.
Concepts: Horizontal Asymptotes, Vertical Asymptotes, Slant (Oblique) Asymptotes, Transforming Reciprocal Function, Sketching Rational Functions, Solving Inequalities using Sign Charts. Rational Function
More informationLesson 3: Working With Linear Relations Day 3 Unit 1 Linear Relations
(A) Lesson Context BIG PICTURE of this UNIT: CONTEXT of this LESSON: mastery with algebraic manipulations/calculations involving linear relations proficiency in working with graphic and numeric representations
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 informationSOL Warm-Up Graphing Calculator Active
A.2c (a) Factoring polynomials SOL Warm-Up 1. Which of the following represents 12x 2 + 6x + 3 in simplified form after factoring out the greatest common factor? A 12(x 2 + 2x + 4) B x(12x 2 + 6x + 3)
More information(b)complete the table to show where the function is positive (above the x axis) or negative (below the x axis) for each interval.
Lesson 3.4 Graph and Equation of Polynomial Functions Part A: Graph of a Polynomial Function the x intercepts of the graph the zeros of the function the roots of the equation Multiplicity (of a zero) A
More informationCHAPTER 2. Polynomial Functions
CHAPTER Polynomial Functions.1 Graphing Polynomial Functions...9. Dividing Polynomials...5. Factoring Polynomials...1. Solving Polynomial Equations...7.5 The Fundamental Theorem of Algebra...5. Transformations
More informationb) since the remainder is 0 I need to factor the numerator. Synthetic division tells me this is true
Section 5.2 solutions #1-10: a) Perform the division using synthetic division. b) if the remainder is 0 use the result to completely factor the dividend (this is the numerator or the polynomial to the
More informationLesson 5: The Graph of the Equation y = f(x)
Lesson 5: The Graph of the Equation y = f(x) Learning targets: I can identify when a function is increasing, decreasing, positive and negative and use interval notation to describe intervals where the
More information7.4 RECIPROCAL FUNCTIONS
7.4 RECIPROCAL FUNCTIONS x VOCABULARY Word Know It Well Have Heard It or Seen It No Clue RECIPROCAL FUNCTION ASYMPTOTE VERTICAL ASYMPTOTE HORIZONTAL ASYMPTOTE RECIPROCAL a mathematical expression or function
More informationSection 4.1: Polynomial Functions and Models
Section 4.1: Polynomial Functions and Models Learning Objectives: 1. Identify Polynomial Functions and Their Degree 2. Graph Polynomial Functions Using Transformations 3. Identify the Real Zeros of a Polynomial
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 informationAbsolute and Local Extrema. Critical Points In the proof of Rolle s Theorem, we actually demonstrated the following
Absolute and Local Extrema Definition 1 (Absolute Maximum). A function f has an absolute maximum at c S if f(x) f(c) x S. We call f(c) the absolute maximum of f on S. Definition 2 (Local Maximum). A function
More informationPolynomial Degree Leading Coefficient. Sign of Leading Coefficient
Chapter 1 PRE-TEST REVIEW Polynomial Functions MHF4U Jensen Section 1: 1.1 Power Functions 1) State the degree and the leading coefficient of each polynomial Polynomial Degree Leading Coefficient y = 2x
More informationWhere we are. a. Introduce cubic functions through a modeling investigation tracking hurricanes
A. Lesson Context BIG PICTURE of this UNIT: How & why do we build NEW knowledge in Mathematics? What NEW IDEAS & NEW CONCEPTS can we now explore with specific references to POLYNOMIAL FUNCTIONS AND RATIONAL
More informationLesson 13: More Factoring Strategies for Quadratic Equations & Expressions
: More Factoring Strategies for Quadratic Equations & Expressions Opening Exploration Looking for Signs In the last lesson, we focused on quadratic equations where all the terms were positive. Juan s examples
More informationLesson 23: The Defining Equation of a Line
Classwork Exploratory Challenge/Exercises 1 3 1. Sketch the graph of the equation 9xx +3yy = 18 using intercepts. Then, answer parts (a) (f) that follow. a. Sketch the graph of the equation yy = 3xx +6
More informationLesson 9 Exploring Graphs of Quadratic Functions
Exploring Graphs of Quadratic Functions Graph the following system of linear inequalities: { y > 1 2 x 5 3x + 2y 14 a What are three points that are solutions to the system of inequalities? b Is the point
More informationAlgebra II Chapter 5: Polynomials and Polynomial Functions Part 1
Algebra II Chapter 5: Polynomials and Polynomial Functions Part 1 Chapter 5 Lesson 1 Use Properties of Exponents Vocabulary Learn these! Love these! Know these! 1 Example 1: Evaluate Numerical Expressions
More informationCURVE SKETCHING M.K. HOME TUITION. Mathematics Revision Guides Level: AS / A Level. AQA : C1 Edexcel: C1 OCR: C1 OCR MEI: C1
Mathematics Revision Guides Curve Sketching Page 1 of 11 M.K. HOME TUITION Mathematics Revision Guides Level: AS / A Level AQA : C1 Edexcel: C1 OCR: C1 OCR MEI: C1 CURVE SKETCHING Version :.1 Date: 03-08-007
More informationMath 1314 Lesson 12 Curve Sketching
Math 1314 Lesson 12 Curve Sketching One of our objectives in this part of the course is to be able to graph functions. In this lesson, we ll add to some tools we already have to be able to sketch an accurate
More information1 y = Recitation Worksheet 1A. 1. Simplify the following: b. ( ) a. ( x ) Solve for y : 3. Plot these points in the xy plane:
Math 13 Recitation Worksheet 1A 1 Simplify the following: a ( ) 7 b ( ) 3 4 9 3 5 3 c 15 3 d 3 15 Solve for y : 8 y y 5= 6 3 3 Plot these points in the y plane: A ( 0,0 ) B ( 5,0 ) C ( 0, 4) D ( 3,5) 4
More informationChapter 4E - Combinations of Functions
Fry Texas A&M University!! Math 150!! Chapter 4E!! Fall 2015! 121 Chapter 4E - Combinations of Functions 1. Let f (x) = 3 x and g(x) = 3+ x a) What is the domain of f (x)? b) What is the domain of g(x)?
More informationMath 148. Polynomial Graphs
Math 148 Lab 1 Polynomial Graphs Due: Monday Wednesday, April April 10 5 Directions: Work out each problem on a separate sheet of paper, and write your answers on the answer sheet provided. Submit the
More informationNAME DATE PERIOD. Operations with Polynomials. Review Vocabulary Evaluate each expression. (Lesson 1-1) 3a 2 b 4, given a = 3, b = 2
5-1 Operations with Polynomials What You ll Learn Skim the lesson. Predict two things that you expect to learn based on the headings and the Key Concept box. 1. Active Vocabulary 2. Review Vocabulary Evaluate
More informationSection 3.2 Polynomial Functions and Their Graphs
Section 3.2 Polynomial Functions and Their Graphs EXAMPLES: P (x) = 3, Q(x) = 4x 7, R(x) = x 2 + x, S(x) = 2x 3 6x 2 10 QUESTION: Which of the following are polynomial functions? (a) f(x) = x 3 + 2x +
More informationAnalyzing Functions Maximum & Minimum Points Lesson 75
(A) Lesson Objectives a. Understand what is meant by the term extrema as it relates to functions b. Use graphic and algebraic methods to determine extrema of a function c. Apply the concept of extrema
More informationPolynomial and Rational Functions. Copyright Cengage Learning. All rights reserved.
2 Polynomial and Rational Functions Copyright Cengage Learning. All rights reserved. 2.2 Polynomial Functions of Higher Degree Copyright Cengage Learning. All rights reserved. What You Should Learn Use
More informationThe highest degree term is x $, therefore the function is degree 4 (quartic) c) What are the x-intercepts?
L3 1.3 Factored Form Polynomial Functions Lesson MHF4U Jensen In this section, you will investigate the relationship between the factored form of a polynomial function and the x-intercepts of the corresponding
More informationPlan for Beginning of Year 2: Summer assignment (summative) Cumulative Test Topics 1-4 (IB questions only/no retakes) IA!!
Summer Assignment 018 The IB Math SL class covers six different mathematical topics (Algebra, Functions, Trigonometry, Vectors, Probability and Statistics, and Calculus). In an effort to best prepare you
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 informationChapter 1- Polynomial Functions
Chapter 1- Polynomial Functions WORKBOOK MHF4U W1 1.1 Power Functions MHF4U Jensen 1) Identify which of the following are polynomial functions: a) p x = cos x b) h x = 7x c) f x = 2x, d) y = 3x / 2x 0
More informationGraphing Rational Functions
Unit 1 R a t i o n a l F u n c t i o n s Graphing Rational Functions Objectives: 1. Graph a rational function given an equation 2. State the domain, asymptotes, and any intercepts Why? The function describes
More information= first derivative evaluated at that point: ( )
Calculus 130, section 5.1-5. Functions: Increasing, Decreasing, Extrema notes by Tim Pilachowski Reminder: You will not be able to use a graphing calculator on tests! First, a quick scan of what we know
More informationDistributive property and its connection to areas
February 27, 2009 Distributive property and its connection to areas page 1 Distributive property and its connection to areas Recap: distributive property The distributive property says that when you multiply
More informationWarm Up Lesson Presentation Lesson Quiz. Holt Algebra 2 2
6-7 Warm Up Lesson Presentation Lesson Quiz 2 Warm Up Identify all the real roots of each equation. 1. x 3 7x 2 + 8x + 16 = 0 1, 4 2. 2x 3 14x 12 = 0 1, 2, 3 3. x 4 + x 3 25x 2 27x = 0 4. x 4 26x 2 + 25
More informationch 3 applications of differentiation notebook.notebook January 17, 2018 Extrema on an Interval
Extrema on an Interval Extrema, or extreme values, are the minimum and maximum of a function. They are also called absolute minimum and absolute maximum (or global max and global min). Extrema that occur
More informationName Date. Analyzing Graphs of Polynomial Functions For use with Exploration 2.7
Name Date.7 Analyzing Graphs of Polynomial Functions For use with Eploration.7 Essential Question How many turning points can the graph of a polynomial function have? 1 EXPLORATION: Approimating Turning
More informationPolynomial and Synthetic Division
Polynomial and Synthetic Division Polynomial Division Polynomial Division is very similar to long division. Example: 3x 3 5x 3x 10x 1 3 Polynomial Division 3x 1 x 3x 3 3 x 5x 3x x 6x 4 10x 10x 7 3 x 1
More informationLinear Relationships
Linear Relationships Curriculum Read www.mathletics.com Basics Page questions. Draw the following lines on the provided aes: a Line with -intercept and -intercept -. The -intercept is ( 0and, ) the -intercept
More informationMATH section 4.4 Concavity and Curve Sketching Page 1. is increasing on I. is decreasing on I. = or. x c
MATH 0100 section 4.4 Concavity and Curve Sketching Page 1 Definition: The graph of a differentiable function y = (a) concave up on an open interval I if df f( x) (b) concave down on an open interval I
More informationWarm Up Lesson Presentation Lesson Quiz. Holt Algebra 2 2
6-5 Warm Up Lesson Presentation Lesson Quiz 2 Warm Up Factor completely. 1. 2y 3 + 4y 2 30y 2y(y 3)(y + 5) 2. 3x 4 6x 2 24 Solve each equation. 3(x 2)(x + 2)(x 2 + 2) 3. x 2 9 = 0 x = 3, 3 4. x 3 + 3x
More informationPolynomials Video Lecture. Section 4.1
Polynomials Video Lecture Section 4.1 Course Learning Objectives: 1)Demonstrate an understanding of functional attributes such as domain, range, odd/even, increasing/decreasing, and symmetry. Determine
More informationLesson 2-6: Graphs of Absolute Value Equations
Where we re headed today Today we re going to take the net graphing step we ll learn how to graph absolute value equations. Here are the three things you are going to need to be able to do: 1. Match an
More informationSpring 06/MAT 140/Worksheet 1 Name: Show all your work.
Spring 06/MAT 140/Worksheet 1 Name: Show all your work. 1. (4pts) Write two examples of each kind of number: natural integer rational irrational 2. (12pts) Simplify: ( a) 3 4 2 + 4 2 ) = 3 b) 3 20 7 15
More informationSolution Choose several values for x, and find the corresponding values of (x), or y.
Example 1 GRAPHING FUNCTIONS OF THE FORM (x) = ax n Graph the function. 3 a. f ( x) x Solution Choose several values for x, and find the corresponding values of (x), or y. f ( x) x 3 x (x) 2 8 1 1 0 0
More informationSolving Systems of Linear and Quadratic Equations
9.5 Solving Systems of Linear and Quadratic Equations How can you solve a system of two equations when one is linear and the other is quadratic? ACTIVITY: Solving a System of Equations Work with a partner.
More informationIMP 3 Function POW #1 Linear, Quadratic and Cubic Functions with some extension to higher degree polynomials
IMP 3 Function POW # Linear, Quadratic and Cubic Functions with some extension to higher degree polynomials Directions: ) Graphing: Use a graphing calculator to do all the graphing. This will save you
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. 3x 4 2x 3 3x 2 x 7 b. x 1 c. 0.2x 1.x 2 3.2x 3 d. 20 16x 2 20x e. x x 2 x 3 x 4 x f. x 2 6x 2x 6 3x 4 8
More informationExploring Graphs of Polynomial Functions
Name Period Exploring Graphs of Polynomial Functions Instructions: You will be responsible for completing this packet by the end of the period. You will have to read instructions for this activity. Please
More informationDaily WeBWorK. 1. Below is the graph of the derivative f (x) of a function defined on the interval (0, 8).
Daily WeBWorK 1. Below is the graph of the derivative f (x) of a function defined on the interval (0, 8). (a) On what intervals is f (x) concave down? f (x) is concave down where f (x) is decreasing, so
More informationSimilar Shapes and Gnomons
Similar Shapes and Gnomons May 12, 2013 1. Similar Shapes For now, we will say two shapes are similar if one shape is a magnified version of another. 1. In the picture below, the square on the left is
More informationSolving Polynomial and Rational Inequalities Algebraically. Approximating Solutions to Inequalities Graphically
10 Inequalities Concepts: Equivalent Inequalities Solving Polynomial and Rational Inequalities Algebraically Approximating Solutions to Inequalities Graphically (Section 4.6) 10.1 Equivalent Inequalities
More informationYou are looking at a textile fabric pattern. Please answer the following questions.
Introductory Activity: You are looking at a textile fabric pattern. Please answer the following questions. 1.) What different patterns do you see inside the fabric? 2.) How are the shapes in the pattern
More information) 2 ( 2x 3 y 5 12x 9 y 12
(A) Lesson Context BIG PICTURE of this UNIT: Do mathematical operations transfer to polnomials? How can we appl polnomials to area and perimeter? Where we ve been Where we are Where we are heading CONTEXT
More informationChapter 2 Polynomial and Rational Functions
Chapter 2 Polynomial and Rational Functions Section 1 Section 2 Section 3 Section 4 Section 5 Section 6 Section 7 Quadratic Functions Polynomial Functions of Higher Degree Real Zeros of Polynomial Functions
More informationPrecalculus. How to do with no calculator 1a)
Precalculus UNIT 2 Review NAME PERIOD This assessment covers many concepts which you must be able to understand without the use of your calculator to view the graph. Please complete the following table
More informationPolynomials Patterns Task
Polynomials Patterns Task Mathematical Goals Roughly sketch the graphs of simple polynomial functions by hand Graph polynomial functions using technology Identify key features of the graphs of polynomial
More informationChapter REVIEW ANSWER KEY
TEXTBOOK HELP Pg. 313 Chapter 3.2-3.4 REVIEW ANSWER KEY 1. What qualifies a function as a polynomial? Powers = non-negative integers Polynomial functions of degree 2 or higher have graphs that are smooth
More informationCurve Sketching. Warm up
Curve Sketching Warm up Below are pictured six functions: f,f 0,f 00,g,g 0, and g 00. Pick out the two functions that could be f and g, andmatchthemtotheir first and second derivatives, respectively. (a)
More informationTennessee Department of Education
Tennessee Department of Education Task: Fourth Degree Polynomial Algebra II Pre Problem Work: Create up with a second degree polynomial that has an x 2 and a constant term, but not an x term, and that
More informationPeriod: Date: Lesson 3B: Properties of Dilations and Equations of lines
Name: Period: Date: : Properties of Dilations and Equations of lines Learning Targets I can identify the properties of dilation mentioned as followed: dilation takes a line not passing through the center
More informationGeometry Summer Assignment 2018
Geometry Summer Assignment 2018 The following packet contains topics and definitions that you will be required to know in order to succeed in Geometry this year. You are advised to be familiar with each
More informationLearning Target: I can sketch the graphs of rational functions without a calculator. a. Determine the equation(s) of the asymptotes.
Learning Target: I can sketch the graphs of rational functions without a calculator Consider the graph of y= f(x), where f(x) = 3x 3 (x+2) 2 a. Determine the equation(s) of the asymptotes. b. Find the
More informationA. Graph the parabola. B. Where are the solutions to the equation, 0= x + 1? C. What does the Fundamental Theorem of Algebra say?
Hart Interactive Honors Algebra 1 Lesson 6 M4+ Opening Exercises 1. Watch the YouTube video Imaginary Numbers Are Real [Part1: Introduction] by Welch Labs (https://www.youtube.com/watch?v=t647cgsuovu).
More informationSecondary Math 3 Honors Unit 10: Functions Name:
Secondary Math 3 Honors Unit 10: Functions Name: Parent Functions As you continue to study mathematics, you will find that the following functions will come up again and again. Please use the following
More informationDescribe in words how the graph of each function below would differ from the graph of f (x).
MATH 111 Exam # Review (4.1-4.4, 6.1, 6.) Describe in words how the graph of each function below would differ from the graph of f (. 1. f ( x 7). f (. f ( 5 4. f ( 5. 7 f ( 6. f ( x ) 9 7. f ( 8. f ( 9.
More informationPower Functions and Polynomial Functions
CHAPTER Power Functions and Polynomial Functions Estuaries form when rivers and streams meet the sea, resulting in a mix of salt and fresh water. On the coast of Georgia, large estuaries have formed where
More informationThe degree of the polynomial function is n. We call the term the leading term, and is called the leading coefficient. 0 =
Math 1310 A polynomial function is a function of the form = + + +...+ + where 0,,,, are real numbers and n is a whole number. The degree of the polynomial function is n. We call the term the leading term,
More information2, or x 5, 3 x 0, x 2
Pre-AP Algebra 2 Lesson 2 End Behavior and Polynomial Inequalities Objectives: Students will be able to: use a number line model to sketch polynomials that have repeated roots. use a number line model
More informationHow do limits demonstrate the dynamic nature of Calculus? How will the three processes confirm the uniqueness of a limit?
WDHS Curriculum Map: created by Andrea Kappre Course: Honors Calculus March 2012 Time Interval/ Content Standards/ Strands Essential Questions Skills Assessment Unit 1: Limits Sections 2-1 -2-5 F-IF.7.
More informationName Date. Logarithms and Logarithmic Functions For use with Exploration 3.3
3.3 Logarithms and Logarithmic Functions For use with Eploration 3.3 Essential Question What are some of the characteristics of the graph of a logarithmic function? Every eponential function of the form
More informationName Period Date. polynomials of the form x ± bx ± c. Use guess and check and logic to factor polynomials of the form 2
Name Period Date POLYNOMIALS Student Packet 3: Factoring Polynomials POLY3 STUDENT PAGES POLY3.1 An Introduction to Factoring Polynomials Understand what it means to factor a polynomial Factor polynomials
More informationRATIONAL FUNCTIONS AND
RATIONAL FUNCTIONS AND GRAPHS ALGEBRA 5 INU0114/514 (MATHS 1) Dr Adrian Jannetta MIMA CMath FRAS Rational functions and graphs 1/ 20 Adrian Jannetta Objectives In this lecture (and next seminar) we will
More informationSection 1.8/1.9. Linear Transformations
Section 1.8/1.9 Linear Transformations Motivation Let A be a matrix, and consider the matrix equation b = Ax. If we vary x, we can think of this as a function of x. Many functions in real life the linear
More information( ) 0. Section 3.3 Graphs of Polynomial Functions. Chapter 3
76 Chapter 3 Section 3.3 Graphs of Polynomial Functions In the previous section we explored the short run behavior of quadratics, a special case of polynomials. In this section we will explore the short
More informationAim: Mean value theorem. HW: p 253 # 37, 39, 43 p 272 # 7, 8 p 308 # 5, 6
Mr. Apostle 12/14/16 Do Now: Aim: Mean value theorem HW: p 253 # 37, 39, 43 p 272 # 7, 8 p 308 # 5, 6 test 12/21 Determine all x values where f has a relative extrema. Identify each as a local max or min:
More informationMidterm Review. Name: Class: Date: ID: A. Short Answer. 1. For each graph, write the equation of a radical function of the form y = a b(x h) + k.
Name: Class: Date: ID: A Midterm Review Short Answer 1. For each graph, write the equation of a radical function of the form y = a b(x h) + k. a) b) c) 2. Determine the domain and range of each function.
More information1. Graph (on graph paper) the following equations by creating a table and plotting points on a coordinate grid y = -2x 2 4x + 2 x y.
1. Graph (on graph paper) the following equations by creating a table and plotting points on a coordinate grid y = -2x 2 4x + 2 x y y = x 2 + 6x -3 x y domain= range= -4-3 -2-1 0 1 2 3 4 domain= range=
More informationAlgebra I Chapter 6: Solving and Graphing Linear Inequalities
Algebra I Chapter 6: Solving and Graphing Linear Inequalities Jun 10 9:21 AM Chapter 6 Lesson 1 Solve Inequalities Using Addition and Subtraction Vocabulary Words to Review: Inequality Solution of an Inequality
More information3.2. Polynomial Functions and Their Graphs. Copyright Cengage Learning. All rights reserved.
3.2 Polynomial Functions and Their Graphs Copyright Cengage Learning. All rights reserved. Objectives Graphing Basic Polynomial Functions End Behavior and the Leading Term Using Zeros to Graph Polynomials
More information1. Find all critical numbers of the function. 2. Find any critical numbers of the function.
1. Find all critical numbers of the function. a. critical numbers: *b. critical numbers: c. critical numbers: d. critical numbers: e. no critical numbers 2. Find any critical numbers of the function. a.
More informationChapter 7 Polynomial Functions. Factoring Review. We will talk about 3 Types: ALWAYS FACTOR OUT FIRST! Ex 2: Factor x x + 64
Chapter 7 Polynomial Functions Factoring Review We will talk about 3 Types: 1. 2. 3. ALWAYS FACTOR OUT FIRST! Ex 1: Factor x 2 + 5x + 6 Ex 2: Factor x 2 + 16x + 64 Ex 3: Factor 4x 2 + 6x 18 Ex 4: Factor
More informationAlgebra 1B notes and problems March 12, 2009 Factoring page 1
March 12, 2009 Factoring page 1 Factoring Last class, you worked on a set of problems where you had to do multiplication table calculations in reverse. For example, given the answer x 2 + 4x + 2x + 8,
More informationf (x) = 2x x = 2x2 + 4x 6 x 0 = 2x 2 + 4x 6 = 2(x + 3)(x 1) x = 3 or x = 1.
F16 MATH 15 Test November, 016 NAME: SOLUTIONS CRN: Use only methods from class. You must show work to receive credit. When using a theorem given in class, cite the theorem. Reminder: Calculators are not
More informationDaily Lessons and Assessments for AP* Calculus AB, A Complete Course Page 119 Mark Sparks 2012
Unit # Understanding the Derivative Homework Packet f ( h) f ( Find lim for each of the functions below. Then, find the equation of the tangent line to h 0 h the graph of f( at the given value of. 1. f
More informationLesson 15: Structure in Graphs of Polynomial Functions
150 Lesson 15: Structure in Graphs of Polynomial Functions Student Outcomes Students graph polynomial functions and describe end behavior based upon the degree of the polynomial. Lesson Notes So far in
More information