Use each word once. Apply algebraic concepts using both real-world problems and "pure" math. 146 _c 1997{2011 EducAide Software Licensed for use by Problem-Attic Algebra1Teachers. Return to Exercises. This worksheet presents a completed function table and a blank graph. They're all free to watch! ↓. Accelerated Algebra II. Chapter 7 PUBLIC RELATIONS MANAGEMENT IN ORGANISATIONS 193 Amisha Mehta and Robina Xavier Considering theory: a guide to practice Whether it is about climate change or planning an anniversary event for an organisation, public relations managers use theory to guide decisions and choices. If there is more than one y value for an x value it is NOT a function. For more information on the EU project in the longer term, see CRS Report R44249, The European Union: Ongoing Challenges and Future Prospects, by Kristin Archick. Describe three ways to represent a function. Similarly, one of the definitions of the term quadratic is a square. Then classify it by degree and by the number of terms. The vocabulary of. Glencoe Algebra 1 Answers ISBN: 9780078651137. 1 Relations and Functions Answers December 13, 2017 January 30, 2019 · Worksheet by Victoria Occasionally a model can be made more accurate but at the cost of simplicity. Pearson Prentice Hall and our other respected imprints provide educational materials, technologies, assessments and related services across the secondary curriculum. A function is a special kind of relation in which each element of the domain is paired with exactly one element in the range. 4 Construct a function to model a linear relationship between two quantities. Lesson 8-1 Exploring Exponential Models. Students learn through discovery and application, developing the skills they need to break down complex challenges and demonstrate their knowledge in new situations. z W 7MeaIdze e zwEictuh h 0IIn 9fci en JiJtbeZ KAjl pg Ie0b6rqa V U2X. Science is the field of study concerned with discovering and describing the world around us by observing and experimenting. 3: Rate of. Worked out by Jakubíková K. Longest side and largest angle are opposite each other, shortest side and. Then determine whether each relation is a function. Decide whether the relation is a function. Is the relation also a function? 2] Rewrite the relation given in the scatter plot as a mapping diagram. Problem 1 A salesman sold twice as much pears in the afternoon than in the morning. Range: - all the y-values (second elements) of a relation. A classic developmental skills text for lower-intermediate and intermediate English language learners. This relation is not a function. relation, function, linear function,vertical line, horizontal line, slope-intercept form of th e equation of a line, rise, run Session 1 Part 1: Fundamentals of Graphing (1 day) 1. of the function is the set of permissible inputs and the. 4, Glencoe Algebra CCSS Math Answers Glencoe Algebra 1 Graphing Relations and Functions Solutions. Choose values for x and find the corresponding values for y. Given a function y = f(x), the. x vaucs 6 is paired Not functions with 2 and 3. BuildingOur Understanding:Key Concepts of Evaluation Whatis it and how do you do it? Imagine that you or your research team has just completed a communication intervention designed to reduce smoking among adolescents. Chapter 6 Test Review (Alg 2) Answer Section 6-7 Inverse Relations and Functions 6-7 Problem 2 Finding an Equation for the Inverse KEY: inverse relation. determine if it is one-to-one. Evaluate the function for a basketball with a radius of 11. Chapter 7 Resource Masters The Fast FileChapter Resource system allows you to conveniently file the resources you use most often. NAME DATE PERIOD D Homework Practice i«i Function Rules Use words and symbols to describe the value of each term as a function of its position. 4 INVERSE FUNCTIONS Inverse Relations Verify that f and g are inverse functions. How to derive and solve equations from worded quadratic problems. Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). >>question 15 a) Graph the function f(x) = 3(x - 1) 2 - 4. Intermediate Algebra Problems With Answers - sample 1: equations, system of equations, percent problems, relations and functions. Graph yx2 2 and find its inverse and graph it. B Graphing Relations, Example 4d 5. "How are you going to win in the period ahead?" That's the key question behind developing strategy. Set, Relations and Functions – Solved Examples Download IIT JEE Solved Examples on Set, Relations and Functions To read more, Buy study materials of Set Relations and Functions comprising study notes, revision notes, video lectures, previous year solved questions etc. Answer Key Graphing Quadratics Practice Quiz Quiz Answer Key Transformations of Quadratic Equations Calculator Exploration Exploration Key Transformations of Quadratic Equations Practice Assignment Completing the Square Guided Notes Guided Notes (completed) Practice Assignment Part 1 Assignment Part 1 Key Practice Assignment Part 2. 2 To determine if a relation is a function. Then determine whether each relation is a function. 3 Review KEY. Short Answer Questions Write a short answer to each of the following questions. ===== Relations and functions Worksheets for Class 6. If so, you have a function! Watch this tutorial to see how you can determine if a relation is a function. Round to the nearest tenth. 1) How many lefties do you expect? P np 5(0. Determine if the following are functions… Write “function” or “not function” on the line. Yes, the data is a set of ordered pairs. A Practice by Example 9-16. The PDF resources below are password protected. Choose values for x and find the corresponding values for y. Express the relation { 2, 5 , 1, 4 , 1, 3 , 2, 4 } as a table, as a graph, and as a mapping diagram. Lesson Relations and Functions Learning Targets: Represen relations and function using bles, diagrams, and graphs. The height of the curve at x. Year 10 maths Here is a list of all of the maths skills students learn in year 10! These skills are organised into categories, and you can move your mouse over any skill name to preview the skill. Search this site. Problems to work out together in class. Duration: 0 hrs 50 mins Quiz: Graphing Polynomial Functions Take a quiz to assess your understanding of the material. Evaluate the function for a basketball with a radius of 11. 7 Comparing Linear, Quadratic & Exponential Functions Tuesday 4/28. Algebra 2 - Chapter 2 Review Answer Section 2-1 Problem 1 Representing a Relation KEY: relation 2-1 Problem 3 Identifying Functions KEY: function | relation 4. Describe the reflection in each equation. Relations and Functions continued A function is a type of relation where each xvalue (domain) can be paired with only one y value (range). Relations And Functions Worksheets, Relation And Functions Worksheet And Answer Key Free Pdf Distinguishing Functions From, Relations And Functions Card Sort Mrs Newell S Math, Worksheet Functions Using The Veritical Line Test And Mapping Diagrams Algebra Printable, Relations And Functions Worksheet, Fillable Rhsweb Worksheet Domains And Ranges Of Relations And Functions Rhsweb Fax, Topic 2 1. If you like this Site about Solving Math Problems, please let Google know by clicking the +1 button. Math Word Problems and Solutions - Distance, Speed, Time. • Lesson 4-6 Determine whether a relation is a function. 5 Arithmetic Sequences Part 1 Directions: Write a function rule to represent each sequence given below. Graph the inverse for each relation below (put your answer on. If it is a function, determine if it is one -to-one , onto , both , or neither. 1: Relations and Functions Concord High RNBriones • The domain of a relation is the set of all inputs, or x-coordinates, of the ordered pairs. Guided Lesson - It is all about determining if a relation is a function or vice versa. Identify the pattern of change in each of the relations and sort. Algebra I ECA Practice and Test Prep. Need Any Test Bank or Solutions Manual Please contact me email:testbanks [email protected] D = {all real numbers} The y-coordinates of points on the graph are real numbers less than or equal to 4, so the range is. Find the inverse of 4 (2) x g x x Mini Lecture: If fx( ) 3 x and 1 2 x gx §· ¨¸ ©¹ find, a. Welcome to Grade 10 Introduction to Applied and Pre-Calculus Mathematics! This course is a continuation of the concepts you have been studying in previous years, as well as an introduction to new topics. Here is a set of practice problems to accompany the Inverse Functions section of the Graphing and Functions chapter of the notes for Paul Dawkins Algebra course at Lamar University. B Graphing Relations, Example 7 6. 32 36 40 4 0 8 12 16 20 24 28 2004 2006 2008 2010 3. This Homework Practice Workbook gives you additional problems for the concept exercises in each lesson. Basic graphs. Relations 1-6 Represent a Relation A relation is a set of ordered pairs. A relation is a set of inputs and outputs, and a function is a relation with one output for each input. Connect the points. Find the domain and range. Composite Functions What Are Composite Functions? Composition of functions is when one function is inside of another function. 03 CGE 3c, 5a, 5e 10 Instructional Jazz 11 Assessment. You are then asked to identify the functions that are described. 1 Relations and Functions. Notes for Lesson 4-2: Relations and Functions 4-2. C l XARlZlm wrhixgCh itQs B HrXeas Le rNv 1eEd H. • This practice exam is provided by the College Board for AP Exam preparation. y=!3x+2 Domain Range Degree Sign of Leading Coefficient End Behaviour Is the relation a function? 2. Welcome to Edge-Answers, a site for getting through Edgenuity as fast as possible. It would be amazing if you could draw them all in one fell swoop, but we're guessing you don't have that many hands. Worksheet 3. Function Not a function; possible answer: 1, 0 , 1, 2 Reteach 1-6 Relations and Functions (continued) LESSON Draw a vertical line. relations that may be of interest in the 116th Congress. This is done by using the key. SUGGESTED LEARNING STRATEGIES: Visualization, Create Representations, Think-Pair-Share, Interactive Word Wall, Paraphrasing Use this machine to answer the questions below. Then determine whether each relation is a function. —3 Date Class -3 3. Tell whether the relation is a function. This is not a function. 2 To determine if a relation is a function. Write each polynomial in standard form. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. 272 Chapter 5 Nonlinear Functions Lesson 5. A relation is … a function if … Possible answer: There is exactly one range element for each domain element. and Functions. It is predicted that by the year 2030 almost 60 per cent of all people will live in cities. These downloads are arranged subject-wise and topic-wise. v W uA ildl4 Trkiwguhyt xs6 erBeAsEe6r av1ewdb. Title: Microsoft Word - Harolds_Parent_Functions_Cheat_Sheet_2016. Domains can be found algebraically; ranges are often found algebraically and graphically. functions, identities and formulas, graphs: domain, range and transformations. A mapping illustrates how each element of the domain is paired with an element in the range. You will also gain a deeper insight into Mathematics, get to practice using your new skills with lots of examples and questions, and generally improve your mind. OPEN ENDED Draw the graph of a relation that is not a function. 6-7: Inverse Relations and Functions Algebra 2 Mr. In everyday life, many quantities depend on one or more changing variables. The organelles might represent. 1 Determine whether a relationship is a function and identify independent and dependent Practice Solutions. Consequently, if x is in the domain x ≥ 3, then the value of f is in the range f(x) ≥ 0. 2016-2017 Functions and Modeling - Teacher Packet 8 MAFS. Locate the y-intercept on the graph and plot the point. 7e Unit 3 3. Guided Lesson Explanation - There are simple guiding principles that you can use here to determine if it is a go. Quabarl while. 4 INVERSE FUNCTIONS Inverse Relations Verify that f and g are inverse functions. Be careful! 11. Algebra I Notes Relations and Functions Unit 03a Alg I Unit 03a Notes Relations and FunctionsAlg I Unit 03a Notes Relations and Functions Page 4 of 8 9/4/2013 Graphs of Functions: Given the graph, we can use the “vertical line test” to determine if a relation is a function. In Exercises 3 and 4, determine whether the graph represents a function. 3 is paired with 4 and 6. Word problems in quadratic equations and solutions. In everyday life, many quantities depend on one or more changing variables. I can determine the range of a function given the domain A. 1 Relations and Functions Answers December 13, 2017 January 30, 2019 · Worksheet by Victoria Occasionally a model can be made more accurate but at the cost of simplicity. Answer Key 1. For the remainder of class, it's time to practice some algebra skills. 2 The Vertex Form of a Quadratic Relation and The Step Pattern download >> more lesson notes download. 1 Graphing Relations TOP: 2-1 Example 3 KEY: relation | mapping diagram | ordered pair 2. This textbook can help you understand each and every topic in algebra in a very comprehensive manner. Explain how the vertical line test can be used to determine if a relation is a function. Flag for inappropriate content. Answer Keys for Carbon Cycle Assessments Introduction “Answer key” may not be quite the right word to describe the documents we have developed, since the environmental literacy assessments are not primarily about right and wrong answers. Download as PPT, PDF, TXT or read online from Scribd. Relations and Functions answers. INTRODUCTION: Take Notes & Basic Practice. so it is a function. Describe the translation y =∆x« 2 and draw its graph by translating the parent function. 4, Glencoe Algebra CCSS Math Answers Glencoe Algebra 1 Graphing Relations and Functions Solutions. The table shows a relation that is a function, where x is the input and y is the output x —4 -2 o 6 o 3 Which ordered pairs could be included in the table so that the relation remains a function? Select each correct answer. 1: Identifying Key Features of Linear and Exponential Graphs Determine the domain of each function, and then graph the function on graph paper. A function f is a rule which assigns to each element. Exponential functions and logarithmic functions with base b are inverses. Lesson 1 - Polynomial Functions of Degrees Zero, One and Two Lesson 2 - Polynomial Functions of Degree Three Lesson 3 - Modelling Data Using Polynomial Functions Lesson 4 - Angular Measure - Degrees and Radians Lesson 5 - Sinusoidal Functions - Amplitude and Period Lesson 6 - Sinusoidal Functions - Horizontal and Vertical Phase Shifts. WORKSHEET 7. The line passes through two points on the graph, at (1, 1) and (1, 1). 2 Identifying Functions TOP: 2-1 Example 6. Explain why it is not a function. Here is a set of practice problems to accompany the Inverse Functions section of the Graphing and Functions chapter of the notes for Paul Dawkins Algebra course at Lamar University. The 'f' is the name of the function and is not a variable. Try not to look back at your notes if possible. We have developed the assessments because we are trying. 00 nonproportional 2 nonproportional nonproportional −−15 or 15 1 −− 30 or 15 2 −− 45 or 15 3. If the graph is a function, state whether it is discrete, continuous or neither. Functions, Relations, and Transformations 4 Overview In Discovering Advanced Algebra, students study mathematical functions modeling real-world problems. (You will have 3 answers for each problem) 10. Answers may vary. What is the resistance in a circuit when the current is 0. Here's a relation that's a function: Here's a relation that's not a function: Draw a vertical line through each point of the graph. Give the Inverse Functions and. It also covers domain and range, along with the vertical line test. The table shows a relation that is a function, where x is the input and y is the output x —4 -2 o 6 o 3 Which ordered pairs could be included in the table so that the relation remains a function? Select each correct answer. Homework Practice and Problem-Solving Practice Workbook Contents Include: • 120 Homework Practice worksheets- one for each lesson • 120 Problem-Solving Practice worksheets- one for each lesson to apply lesson concepts in a real-world situation Homework Practice and Problem-Solving Practice Workbook. indd i 44/2/08 2:29:30 PM/2/08 2:29:30 PM. Use them in your classroom or at home!. Practice B Relations and Functions Express each relation as a table, as a graph, and as a mapping diagram. OPEN ENDED Draw the graph of a relation that is not a function. 32 36 40 4 0 8 12 16 20 24 28 2004 2006 2008 2010 3. 1 Evaluate Nth Roots and use Rational Exponents Things you should be able to do: - Rewrite radical expressions using rational exponent notation. Show an example of each. Jenise said the graph shows a linear relationship. 5), f(l), and f(7). A function is a relation in which each element of the domain is paired with exactly one element of the range. 233) Key Vocabulary • Lessons 4-1, 4-4, and 4-5 Graph ordered pairs, relations, and equations. All functions are relations, but not all relations are functions. Glencoe Algebra 2 Chapter 8 Worksheet Answers glencoe geometry worksheet answers glencoe geometry workbook answers from the look of the answers it appears to be the glencoe algebra 2 book answers:. Date:— We have seen many different examples of re ations. Round to the nearest hundredth, if necessary. This chapter, on strategic human resource management (SHRM), is really not for the hospitality human resources (HR) director. Chapter 6 Test Review (Alg 2) Answer Section 6-7 Inverse Relations and Functions 6-7 Problem 2 Finding an Equation for the Inverse KEY: inverse relation. The following picture shows the. Glencoe Algebra 1 Answers ISBN: 9780078651137. Set, Relations and Functions – Solved Examples Download IIT JEE Solved Examples on Set, Relations and Functions To read more, Buy study materials of Set Relations and Functions comprising study notes, revision notes, video lectures, previous year solved questions etc. Relations and Functions Practice Exam www. The line passes through no more than one point on the graph. A visual method used to determine whether a relation represented as a graph is a function g. Virtual Nerd's patent-pending tutorial system provides in-context information, hints, and links to supporting tutorials, synchronized with videos, each 3 to 7 minutes long. Find f(x) based on the x-coordinates provided and complete the function tables. Identify the domain and range of each relation. Answers •Page A1 is an answer sheet for the Standardized Test Practice questions that appear in the Student Edition on pages 406-407. Algebra 1Chapter 5 Lesson 5-2 Practice. Yes (by the vertical line test), Domain = [ 2;2], Range = [ 1;2] 1. Practice PERIOD Analyzing Graphs of Functions and Relations 12 f(x) =21x-3J+1 1. Diffusion, Dialysis and Osmosis Tutorial. Which of the following graphs represents a relation that is NOT a function of x?. 2016-2017 Functions and Modeling - Teacher Packet 8 MAFS. A _____ allows the driver to practice driving, but does not allow him or her to drive a vehicle unaccompanied. docx - ANSWER KEY Algebra II | LESSON 1-1 Relations and functions 1(2 1(1 2(0 3(1 4(2 5 cfw 2 Answers may vary Sample(3. Example: This is read as _____ Evaluating Functions. What do the flat. Chapter 4 is at the core of that study. INTRODUCTION: Take Notes & Basic Practice. but a relation is not always a function. Since each element in the domain is related with. Session 1 Part 2: Functions (2 days) 1. Then determine whether each relation is a function. and Quiz Review Wksht Key Extra Review Practice 8-1 with Key 8-2 with Key. Practice Worksheets 5. Relations and Functions 1. 76 #2-48 (even) & Notes. Final Practice Exam Answer Key. Input 6 7 7 14 Output 5 2 5 2 Find the slope and y-intercept of the line with the given equation. Then determine if the relation represents a function. Choose from 500 different sets of functions inverse relations flashcards on Quizlet. Create the worksheets you need with Infinite Algebra 2. g) None of the above. You can make copies of the Answer Keys to hand out to your class, but please collect them when the students are finished with them. Answer Keys Click on the file name to access the file: If you have difficulty accessing the Google doc via the link, you may download the appropriate PDF file attached to the bottom of this page. B Graphing Relations, Introduction (d) 2. Accelerated Algebra II. Their times and distances are shown in the accompanying graph. 4 Chapter 4: Data and Databases Course 3 chapter 4 functions answer key. 38: Determine when a relation is a. Graph of the linear equation. Lesson Relations and Functions Learning Targets: Represen relations and function using bles, diagrams, and graphs. Here, the abstract idea of a function grows out of students' earlier experiences with linear equations and graphing. Does the relation represent a function? The domain and range are both all real numbers. Name Practice B LESSON Relations and Functions Date Class 8 6 6 8 Express each relation as a table, as a graph, and as a mapping diagram. 4 Practice Quiz KEY. Read the bar graphs on the worksheets and answer questions. Created Date: 8/21/2016 2:54:40 PM. 6561 2) sin Y = 0. Part 1 - Identify Domains, Ranges, and Functions. Domains can be found algebraically; ranges are often found algebraically and graphically. of the function is the set of permissible inputs and the. Have them write the functions they worked with in three ways:. It is predicted that by the year 2030 almost 60 per cent of all people will live in cities. The National Government A. Mugs can be represented by where x is the number of months after January 2001. ANS: {7, 6, 5, 3} PTS: 1 DIF: L2 REF: 4-3 Function Rules, Tables, and Graphs OBJ: 4-3. Domain And Range Answer Key. Writing Explain when a relation is not a function. Over the past month, Matty has randomly opened his piano book to a song in the key of C 80 times, the key of G 30 times, and the key of F 10 times. Guided Lesson - It is all about determining if a relation is a function or vice versa. What does x represent in the inverse function? the amount the. Relations and Functions Let's start by saying that a relation is simply a set or collection of ordered pairs. The identity function. Formalizing Relations and Functions. Choose values for x and find the corresponding values for y. 6561 2) sin Y = 0. 40; Sample answer: The unit rate for the 96-oz container is $0. Graph marginal cost and average total cost and average variable cost. Practice Worksheets 5. B Graphing Relations, Introduction (d) 2. Composite Functions What Are Composite Functions? Composition of functions is when one function is inside of another function. 3 Transformations of Quadratic Relations - conclusions download. Will this give a correct answer from the table? Let us check. Additional Answers (Guided Practice) 2. y = - ⎪x⎥ 7. Home > Articles > Professional Certifications Practice for the NCLEX-RN: Practice Exam 3 and Rationales. Algebra 1 –Unit 2 Homework Packet –Functions and Relations 2. If it is a function, determine if it is one -to-one , onto , both , or neither. Determine whether the eqation is a function, is one-to-oneonto, , both, or. composition of inverse function Problem 4 Problem 5 Further Reading: Composition of Functions Worksheet (25 question pdf with answer key) Functions in Math Inverse. com and save up to 80% off list price and 90% off used textbooks. Test out your knowledge of relations and functions using this interactive quiz and printable worksheet. If the graph is a function, state whether it is discrete, continuous or neither. Answers •Page A1 is an answer sheet for the Standardized Test Practice questions that appear in the Student Edition on pages 406-407. 1 Relations and Functions When the two number lines are place on a plane, a gridded map is formed. Solved examples with detailed answer description, explanation are given and it would be easy to understand. This is the Aptitude Questions & Answers section on & Sets, Relations and Functions& with explanation for various interview, competitive examination and entrance test. Then, test to see if each element in the domain is matched with exactly one element in the range. Describe three ways to represent a function. Their times and distances are shown in the accompanying graph. Additional Answers (Guided Practice) 2. Identify the domain and range for the relation. Please change your browser settings and reload. Domain and Range • The range of a relation is the set of all outputs, or y-coordinates, of the ordered pairs. Glencoe geometry worksheet answer key chapter 11 january 8. 12; 5; 9 Use the graph of h to find the domain and range of each function. Express the relation { 2, 5 , 1, 4 , 1, 3 , 2, 4 } as a table, as a graph, and as a mapping diagram. 2 - Find Slope and Rate of Change - pg. • The answers for the lesson-by-lesson masters are provided as reduced pages with answers appearing in red. Relations and Functions Lesson 4-2 Learning Targets: I can identify functions. Review key concepts and strategies After handing in test, students get and brain teaser puzzle to work on. Secondary Mathematics III: An Integrated Approach. Functions are written using function notation. • Lesson 4-2 Transform figures on a coordinate plane. 2 Turn the fold to the left and write the title of the chapter on the front. 1 Worksheet by Kuta Software LLC. SUGGESTED LEARNING STRATEGIES: Visualization, Create Representations, Think-Pair-Share, Interactive Word Wall, Paraphrasing Use this machine to answer the questions below. Also, for each problem, determine if the relation given represents a function and record your answers in the appropriate spaces provided for each problem. The other answer was 2. Find the domain and range of the relation and determine whether it is a function? Answers are Domain x>1 range y>0yes it is a function Domain all real numbers,range all real numbers yes it is a function Domain positive integers, asked by snow on March 12, 2014; Algebra-I'm still stuck. Here is a graphic preview for all of the Linear Equations Worksheets. A function is a relation if for each x-value there is exactly one y-value. Sample answer: The graph of h is a translation 2 units up of the graph of the parent linear function. Relations and Functions 1. i & v, ii & vi, and iii and iv. So what are you going to learn here? You will learn about Numbers, Polynomials, Inequalities, Sequences and Sums, many types of Functions, and how to solve them. 1: “Veggie-Tables” 1. The vertical line test states that a relation is a function if and only if a vertical line does not pass through more than one point on the graph of the relation. Students respond to multiple-choice items using the Answer Sheets on pages 44 and 45 and constructed-response items using pages 40 to 43 of Session 3. WRITING FUNCTIONS Practice A 1. 77 Day 1 Inverse Relations and Functions 11 March 03, 2009 Feb 2812:59 PM Get It? Got It? Good! The graph of the inverse of a relation is the reflection over the line y = x of the graph of the relation. CHAPTER 3 Functions and Patterns Understand the concepts of a relation and a function, and determine whether a given relation defined by a graph, a set of ordered pairs, or a symbolic expression is a function. To start, write the ratio of sin D. Please note that some chapters address several areas of KSAs. The Chapter 7 Resource Mastersincludes the core materials needed for Chapter 7. is the set of resulting outputs. Guided Reading Activity Answer Key I. Range: Function. 3 Practice - Inverse Functions State if the given functions are inverses. The total cost for 5 months with both services is $53. 1 Functions and Function Notation In this section you will learn to: • find the domain and range of relations and functions • identify functions given ordered pairs, graphs, and equations • use function notation and evaluate functions • use the Vertical Line Test (VLT) to identify functions • apply the difference quotient.