Algebra 2 Graphing Absolute Value Functions

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# Algebra 2 Graphing Absolute Value Functions: A Comprehensive Guide

Author: Dr. Evelyn Reed, Ph.D. in Mathematics Education, Professor of Mathematics at State University, with over 20 years of experience teaching Algebra 2 and developing curriculum for secondary mathematics. Dr. Reed has published extensively on the pedagogical approaches to teaching abstract concepts in algebra, including numerous articles on effective strategies for graphing absolute value functions.

Publisher: Open Education Resources Consortium (OERC), a leading provider of free and openly accessible educational materials. OERC’s commitment to quality and peer-review ensures the accuracy and reliability of its published content, making them a trusted source for educational resources in mathematics, including materials related to algebra 2 graphing absolute value functions.

Editor: Dr. Marcus Chen, Ph.D. in Mathematics, specializes in curriculum development and assessment in secondary mathematics education. Dr. Chen's experience in reviewing and editing educational materials ensures the clarity, accuracy, and pedagogical soundness of the article.

A Historical Context of Absolute Value Functions



The concept of absolute value, though implicitly understood in earlier mathematical contexts, didn't receive its formal mathematical definition until the development of modern algebra. Early mathematicians grappled with the concept of magnitude without the precise notation and understanding we have today. The graphical representation of absolute value functions, a key element of Algebra 2 graphing absolute value functions, emerged alongside the development of Cartesian coordinate systems and analytic geometry in the 17th century. However, the systematic teaching of graphing absolute value functions as part of a standard Algebra 2 curriculum is a relatively recent phenomenon, reflecting the broader evolution of secondary mathematics education in the 20th and 21st centuries. The focus shifted from rote memorization to conceptual understanding and problem-solving, leading to the inclusion of topics like graphing absolute value functions which highlight these crucial skills.


The Relevance of Algebra 2 Graphing Absolute Value Functions in the Modern Curriculum



Algebra 2 graphing absolute value functions remains a crucial component of the secondary mathematics curriculum for several reasons. Firstly, it builds upon foundational algebraic concepts taught in earlier grades, reinforcing understanding of variables, equations, and inequalities. Secondly, graphing absolute value functions introduces students to piecewise functions, an important concept that extends into calculus and beyond. Understanding how to graph these functions provides a solid foundation for more advanced mathematical concepts. Thirdly, the process of graphing absolute value functions directly connects algebraic representations to geometric visualizations. This connection is vital for developing a deeper and more intuitive understanding of mathematical relationships. Finally, the problem-solving aspects inherent in working with absolute value functions develop critical thinking and analytical skills, transferable to various other academic and real-world scenarios. The ability to model real-world situations using absolute value functions, such as calculating distances or differences, further emphasizes the relevance of this topic.


Understanding the Graph of an Absolute Value Function



The parent function, f(x) = |x|, forms the basis for understanding all absolute value functions. Its graph is a V-shaped curve with the vertex at the origin (0,0). Transformations of this parent function, involving translations (shifts), reflections (flips), and stretches/compressions (scaling), create a wide variety of absolute value functions. Algebra 2 graphing absolute value functions involves understanding how these transformations affect the graph's vertex, slope, and orientation. For example, f(x) = |x - 2| + 3 represents a translation of the parent function two units to the right and three units up. Understanding these transformations is critical for accurately graphing any given absolute value function. Students also learn to solve absolute value equations and inequalities graphically, interpreting solutions from the graph's intersection with the x-axis or other relevant lines.


Solving Absolute Value Equations and Inequalities Graphically



Algebra 2 graphing absolute value functions goes beyond simply creating the graph; it emphasizes using the graph to solve equations and inequalities involving absolute values. By visually identifying the points where the graph intersects a specific line (for equations) or lies above/below a line (for inequalities), students can determine the solution set graphically. This visual approach provides a valuable complement to algebraic methods, enhancing conceptual understanding and offering a powerful tool for problem-solving. This graphical approach strengthens problem-solving skills and helps students connect algebraic representations to geometric interpretations, reinforcing their understanding of the underlying mathematical concepts involved in algebra 2 graphing absolute value functions.


Applications of Absolute Value Functions



Absolute value functions find practical applications in various fields. In physics, they can model distance or displacement, where the magnitude of the value is important irrespective of direction. In computer science, absolute value is used in algorithms related to distance calculations and error estimations. In economics, absolute value can represent deviations from a target value or measure the magnitude of economic fluctuations. Understanding Algebra 2 graphing absolute value functions allows students to model and solve real-world problems involving these concepts. The ability to translate a real-world scenario into a mathematical model and then solve that model using both graphical and algebraic techniques is a key skill developed through the study of algebra 2 graphing absolute value functions.

Conclusion



The study of algebra 2 graphing absolute value functions is not merely an exercise in rote memorization; it represents a crucial step in developing a deeper understanding of algebraic concepts and their graphical representations. The ability to connect algebraic expressions to visual interpretations is paramount for building mathematical intuition and problem-solving skills. Its continuing relevance in the modern curriculum stems from its pedagogical value and its applicability to various real-world scenarios, highlighting the enduring significance of this topic in secondary mathematics education. The careful study and application of techniques related to algebra 2 graphing absolute value functions provide students with crucial skills for success in higher-level mathematics and beyond.


FAQs



1. What is an absolute value function? An absolute value function is a function that gives the magnitude of a number, regardless of its sign. The absolute value of a number is always non-negative.

2. How do I graph a simple absolute value function? Start by plotting the vertex (the point where the graph changes direction). Then, determine the slope of the two branches of the "V" shape.

3. What are the transformations of absolute value functions? Transformations include vertical and horizontal shifts, reflections across the x or y-axis, and vertical and horizontal stretches or compressions.

4. How do I solve absolute value equations graphically? Find the x-intercepts of the absolute value function.

5. How do I solve absolute value inequalities graphically? Determine where the graph of the absolute value function is above or below a given line (depending on the inequality).

6. What are piecewise functions, and how do they relate to absolute value functions? Piecewise functions are defined by different expressions over different intervals. Absolute value functions can be expressed as piecewise functions.

7. What are some real-world applications of absolute value functions? Applications include calculating distances, modeling error, and representing deviations from a target value.

8. How does graphing absolute value functions help me prepare for calculus? It introduces the concept of piecewise functions and strengthens skills in analyzing graphs and transformations, which are essential for calculus.

9. Where can I find more practice problems on graphing absolute value functions? Numerous online resources, textbooks, and educational websites offer practice problems for algebra 2 graphing absolute value functions.


Related Articles



1. Transformations of Absolute Value Functions: A detailed exploration of how translations, reflections, and stretches/compressions affect the graph of an absolute value function.

2. Solving Absolute Value Equations and Inequalities Algebraically: A comprehensive guide to solving absolute value equations and inequalities using algebraic methods.

3. Piecewise Functions and their Applications: An in-depth look at piecewise functions, including examples and real-world applications, highlighting their connection to absolute value functions.

4. Graphing Linear Inequalities: A primer on graphing linear inequalities, providing a foundational understanding relevant to graphing absolute value inequalities.

5. Introduction to Parent Functions: An overview of different types of parent functions in algebra, providing context for understanding the parent absolute value function.

6. Systems of Equations and Inequalities: Exploring how to solve systems involving absolute value functions graphically and algebraically.

7. Absolute Value Functions and Word Problems: A collection of real-world problems that can be modeled and solved using absolute value functions.

8. Advanced Graphing Techniques: More advanced techniques for graphing complex functions, expanding on the fundamentals of graphing absolute value functions.

9. The use of technology in graphing absolute value functions: How graphing calculators and software can aid in understanding and visualizing absolute value functions.


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  algebra 2 graphing absolute value functions: ISASP Algebra I for Beginners Reza Nazari, Comprehensive Guide to Mastering the Iowa Statewide Assessment of Student Progress (ISASP) Algebra I Test The ISASP Algebra I assessment is a vital examination that plays a critical role in determining a student's success in high school. To help you excel on this high-stakes test, we have created the all-inclusive guide, ISASP Algebra I for Beginners, your roadmap to success. Dive Deep into Essential Topics Our guide delves into the heart of the critical subjects required for the ISASP Algebra I Test, ensuring that you are well-prepared to tackle the exam. The key topics covered include: • Linear equations and their graphical representations • Quadratic equations and their corresponding functions • Systems of equations and their solutions • Exponential functions • Foundational statistical concepts and methods Engaging and Challenging Practice Problems to Enhance Learning ISASP Algebra I for Beginners features an array of practice problems throughout, carefully designed to reinforce your understanding of each concept. These problems strike the perfect balance between challenging and achievable, giving you the confidence you need to face the actual test. Genuine Full-Length Practice Tests for Accurate Assessment The guide includes two full-length practice exams, offering a genuine evaluation of your progress and helping you identify any areas requiring further practice. Clear, Concise, and Easily Comprehensible Language ISASP Algebra I for Beginners is written in a clear and accessible manner, ensuring that readers of all mathematical skill levels can easily understand the instructions and solve the presented problems. Tailored for Learners at All Levels Whether you're a high school student grappling with algebraic concepts or an adult learner looking to refresh your skills, this guide is customized to meet your needs. It covers all the essential topics you must master to succeed on the test. Your One-Stop Resource for ISASP Algebra I Success ISASP Algebra I for Beginners is the only resource you'll need to excel on the ISASP Algebra I Test. With its comprehensive content coverage and easy-to-understand material, this guide will enable you to conquer algebra and shine on the exam. Embark on Your Journey to Test Readiness Purchase your copy of ISASP Algebra I for Beginners today and take the first step towards test preparedness. With this guide by your side, you'll be well-equipped to pass the test and secure your diploma.
  algebra 2 graphing absolute value functions: Ohio Algebra I for Beginners Reza Nazari, Comprehensive Ohio Algebra I Guide for Beginners The Ohio End-Of-Course Algebra I exam is a critical milestone for high school students, playing a significant role in shaping their academic achievements and future opportunities. To ensure you are fully prepared to excel on this crucial test, we have crafted the most comprehensive and accessible study guide available: Ohio Algebra I for Beginners. Master Key Concepts with In-Depth Explanations: Ohio Algebra I for Beginners provides thorough and easy-to-understand coverage of the essential subjects featured on the Ohio Algebra I Test. The guide ensures you develop a strong foundation in these critical areas: • Linear equations and their graphical representations • Quadratic equations and related functions • Systems of equations and methods for solving them • Exponential functions • Basic statistical principles and techniques Reinforce Your Skills with Engaging Practice Problems: Our guide offers an extensive array of practice problems designed to help you strengthen your understanding of each topic. With the perfect balance between difficulty and accessibility, these problems will build your confidence and prepare you to tackle the actual exam. Evaluate Your Progress with Genuine Full-Length Practice Tests: Ohio Algebra I for Beginners includes two authentic, full-length practice tests that provide a precise evaluation of your progress and highlight any areas requiring further attention. Easily Comprehend Material with Clear and Approachable Language: This comprehensive study guide is written in a clear, concise style that is suitable for learners at all levels. Regardless of your mathematical background, you will be able to follow the instructions and solve the problems presented. Your One-Stop Resource for Ohio Algebra I Success: Ohio Algebra I for Beginners is the only study aid you'll need to excel on the Ohio Algebra I Test. With its in-depth content coverage and easy-to-understand material, this guide will equip you with the knowledge and skills needed to achieve outstanding results on the exam. Invest in Your Future Today: Purchase your copy of Ohio Algebra I for Beginners now and embark on your journey toward test readiness. With this guide by your side, you'll be well-prepared to pass the test and earn your diploma.
  algebra 2 graphing absolute value functions: Regents Algebra I for Beginners Reza Nazari, 2023-04-04 Comprehensive Regents Algebra I Mastery Guide for Beginners The Regents Algebra I exam holds significant weight in determining a student's high school accomplishments and influences their future opportunities. To assist you in preparing for this vital test, we have developed the ultimate, comprehensive guide: Regents Algebra I for Beginners. Detailed Analysis of Essential Concepts Regents Algebra I for Beginners dives deep into the core subjects covered in the Regents Algebra I Test, ensuring that you establish a solid foundation in these vital areas: • Linear equations and their visual representations on graphs • Quadratic equations and corresponding functions • Systems of equations and methodologies for solving them • Exponential functions • Basic statistical concepts and techniques Interactive Practice Questions for Skill Reinforcement This guide provides an abundance of practice questions crafted to strengthen your understanding of each topic. These questions maintain an ideal balance between challenge and approachability, helping you develop confidence in your ability to excel in the actual exam. Authentic Full-Length Practice Exams for Accurate Assessment Regents Algebra I for Beginners includes two genuine, full-length practice exams that offer a precise evaluation of your progress and pinpoint any areas that may need further attention. Clear, User-Friendly, and Comprehensible Language This all-inclusive study guide is written in a concise, straightforward style that is easily understandable for learners of all levels. Regardless of your mathematical background, you will be able to follow the instructions and solve the problems presented. The Ultimate Tool for Regents Algebra I Achievement Regents Algebra I for Beginners is the only resource you will need to excel on the Regents Algebra I Test. With its extensive content coverage and easy-to-digest material, this guide will enable you to master algebra and achieve an outstanding performance on the exam. Get Your Copy Today and Secure Your Success Invest in your future by purchasing your copy of Regents Algebra I for Beginners today and embark on your journey toward test readiness. With this guide by your side, you will be well-equipped to pass the test and earn your diploma.
  algebra 2 graphing absolute value functions: ISTEP+ Algebra I for Beginners Reza Nazari, The Ultimate Guide to Mastering ISTEP+ Algebra I Your Comprehensive Guide to Mastering the Indiana Statewide Testing for Educational Progress-Plus (ISTEP+) Algebra I Test The ISTEP+ Algebra I assessment is a pivotal exam that plays a crucial role in determining a student's eligibility to graduate from high school. Our all-encompassing guide, ISTEP+ Algebra I for Beginners, is designed to equip you with the essential skills and knowledge needed to excel on this high-stakes test. In-Depth Coverage of Key Topics ISTEP+ Algebra I for Beginners delves deep into all the vital subjects required for the ISTEP+ Algebra I Test, including: • Linear equations and their graphical representations • Quadratic equations and their respective functions • Systems of equations and their solutions • Exponential functions • Essential statistical concepts and methods Engaging Practice Problems to Reinforce Learning This comprehensive guide features numerous practice problems throughout, designed to help solidify your understanding of each concept. These problems are crafted to be challenging yet achievable, instilling confidence in your ability to tackle the actual test. Authentic Full-Length Practice Tests for Realistic Evaluation Included in the guide are two full-length practice exams that offer a realistic assessment of your progress and help you identify any areas that may need additional practice. Clear, Concise, and Easy-to-Understand Language ISTEP+ Algebra I for Beginners is written in a straightforward and accessible manner, making it easy for readers of all mathematical expertise levels to comprehend the instructions and solve the presented problems. Designed for Learners at All Skill Levels Whether you're a high school student struggling with algebraic concepts or an adult learner seeking to refresh your skills, this guide is tailored to meet your needs. It is designed to be accessible and covers all the crucial topics you must understand. Your Ultimate Resource for ISTEP+ Algebra I Success ISTEP+ Algebra I for Beginners is the only resource you'll need to triumph on the ISTEP+ Algebra I Test. With its exhaustive content coverage and easy-to-grasp material, this guide will empower you to conquer algebra and excel on the exam. Take the First Step Towards Test Preparedness Purchase your copy of ISTEP+ Algebra I for Beginners today and embark on your journey towards test readiness. With this guide in hand, you'll be well-equipped to pass the test and attain your diploma.
  algebra 2 graphing absolute value functions: SBAC Algebra I for Beginners Reza Nazari, The Ultimate Guide to Mastering SBAC Algebra I The Only Book You Will Ever Need to Ace the SBAC Algebra I Test! Master the Smarter Balanced Assessment System's Algebra I Test with the ultimate guide, SBAC Algebra I for Beginners. This comprehensive resource is specifically designed for high school students, adult learners, and anyone looking to improve their algebra skills. Its accessible approach simplifies the learning process by breaking down core concepts, including linear equations and quadratic functions, into easy-to-understand terms. Achieve a solid grasp of Algebra I essentials with: • Thorough coverage of critical Algebra I topics • Clear, step-by-step explanations of complex concepts • Abundant examples and practice problems to reinforce understanding Key features of SBAC Algebra I for Beginners are: • Perfectly aligned with Algebra I courses and SBAC Algebra I Test requirements • Engaging writing style for enhanced comprehension and retention This indispensable guide is perfect for those who are: • Struggling with algebra and in need of clear explanations • Looking to strengthen their skills and understanding of Algebra I concepts • Seeking a comprehensive self-study resource • Teachers or tutors searching for supportive classroom material Prepare to excel on the SBAC Algebra I Test with this ultimate preparation guide, and lay the groundwork for a solid understanding of algebra and basic math that will serve you well for years to come.
Graphing Absolute Value Equations.ks-ia2 - Kuta Software
Create your own worksheets like this one with Infinite Algebra 2. Free trial available at KutaSoftware.com.

Absolute Value Functions
Make a plan for how to choose x-values for a table when graphing an absolute value function. Explain your reasoning. Step 1 Make a table of values. Step 2 Plot the ordered pairs. Step 3 …

Algebra 2 Worksheets
Basics Order of operations Evaluating expressions Simplifying algebraic expressions Linear Relations and Functions Review of linear equations Graphing absolute value functions …

F.BF.B.3.GraphingAbsoluteValueF - JMAP
11. 3 2 1 -2 -1 1 2 3 4 5 6 -1 Which equation does the graph above represent?

Absolute Value Functions and Graphs Guided Notes
Sep 2, 2016 · Absolute Value Functions and Graphs Guided Notes 1. What is meant by absolute value? ro iv s (or z bs lute valu

2.1 Graphing Absolute Value Functions - Weebly
Essential Question: How can you identify the features of the graph of an absolute value function? Graphing and Analyzing the Parent Absolute Value Function. written as ⎟ represents the …

Name_______________________ Graphing Absolute Value Functions
On this worksheet the students will analyze the characteristics of the absolute value function then translate the graph using the rules developed in Activity 6 for f(x ± h) and f(x) ± k. Then they will …

Graphing Absolute Value Equations
All graphs for absolute value functions begin with this graph. 1. Observe the graphs and equations and answer the questions that follow. 2. Pretend that each of the graphs above began with the …

Infinite Algebra 2 - Graphing Absolute Value Functions HW
©C O2q0J1t6T fKJu`tuaM bSsonfjtowKa^rTer FLKLoCz.k c qAul^lq EraiughhYtYs^ YrBezsaeXrivZeFd`.T n fMhaOd[e] bwVittihR `IQn`fhiXnXiEtUeJ ZAmlvgMeQbgrmaJ L2k.

Graphing Abs Value
6 4 2 −6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6 −2 −4 −6

Microsoft Word - PACKET 2 GRAPHING ABSOLUTE VALUE …
Absolute Value Functions In order to graph an absolute value function, you will be using many of the same methods you did for quadratics. The standard form of an absolute value function is …

ABSOLUTE VALUE FUNCTIONS AND GRAPHS
Sep 2, 2016 · KEY VOCABULARY: Absolute Value Functions and Graphs Write absolute value function Sketch the graphs from a given absolute value function

Function Families Worksheet #2 Algebra 2: Absolute Value
Function Families Worksheet #2 Algebra 2: Absolute Value Graph each “family” of equations on a graphing calculator. Try to discover what makes each one different. Then try to sketch them on …

F.IF.C.7: Graphing Absolute Value Functions - JMAP
F.IF.C.7: Graphing Absolute Value Functions 3 Which graph represents the equation 1) 2)

Graphing Absolute Value Functions - bhs.rcschools.net
Sep 19, 2018 · ©V \2L0V1s5w WKjujt]aR ZSEoyfWtZwFaWrVeZ QLXLhCx.` j hA\lDlZ Zr^ifgNhit_sB NrIegsueSrVviewd`.] -1- R KMIaRdrez mw`ihtWhK QICn[fqinn[iytpe[ …

Graphing Absolute-Value Functions
Absolute-value graphs can translate up or down, and to the right or left. Graph the function and give the coordinates of the vertex. f x x 1 2 Make a table of values then plot the resulting points. …

Transformations of Linear and 1.2 Absolute Value Functions
Transformations of the Parent Absolute Value Function Work with a partner. Compare the graph of the function

3.7 Graphing Absolute Value Functions - Jackson School District
Combine transformations of graphs of absolute value functions. An absolute value function is a function that contains an absolute value expression. The parent absolute value function is f(x) x …

Solving absolute Value equations by Graphing
Apter 5 absolute Value equations by Graphing Absolute value equations in the form ax 1 b 5 c, where a, b, and c are constants, can be solved by graphing corresponding functions in the for. …

Absolute Value Functions and Graphs - Algebra2Coach.com
Sep 2, 2016 · Absolute Value Functions and Graphs Bell work Choose the suitable option: The absolute value of a number is always ( negative / positive ). The shape of the graph of an …

Graphing Absolute Value Equations.ks-ia2 - Kuta Software
Create your own worksheets like this one with Infinite Algebra 2. Free trial available at KutaSoftware.com.

Absolute Value Functions
Make a plan for how to choose x-values for a table when graphing an absolute value function. Explain your reasoning. Step 1 Make a table of values. Step 2 Plot the ordered pairs. Step 3 …

Algebra 2 Worksheets
Basics Order of operations Evaluating expressions Simplifying algebraic expressions Linear Relations and Functions Review of linear equations Graphing absolute value functions …

F.BF.B.3.GraphingAbsoluteValueF - JMAP
11. 3 2 1 -2 -1 1 2 3 4 5 6 -1 Which equation does the graph above represent?

Absolute Value Functions and Graphs Guided Notes
Sep 2, 2016 · Absolute Value Functions and Graphs Guided Notes 1. What is meant by absolute value? ro iv s (or z bs lute valu

2.1 Graphing Absolute Value Functions - Weebly
Essential Question: How can you identify the features of the graph of an absolute value function? Graphing and Analyzing the Parent Absolute Value Function. written as ⎟ represents the …

Name_______________________ Graphing Absolute Value …
On this worksheet the students will analyze the characteristics of the absolute value function then translate the graph using the rules developed in Activity 6 for f(x ± h) and f(x) ± k. Then they …

Graphing Absolute Value Equations
All graphs for absolute value functions begin with this graph. 1. Observe the graphs and equations and answer the questions that follow. 2. Pretend that each of the graphs above began with the …

Infinite Algebra 2 - Graphing Absolute Value Functions HW
©C O2q0J1t6T fKJu`tuaM bSsonfjtowKa^rTer FLKLoCz.k c qAul^lq EraiughhYtYs^ YrBezsaeXrivZeFd`.T n fMhaOd[e] bwVittihR `IQn`fhiXnXiEtUeJ ZAmlvgMeQbgrmaJ L2k.

Graphing Abs Value
6 4 2 −6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6 −2 −4 −6

Microsoft Word - PACKET 2 GRAPHING ABSOLUTE VALUE …
Absolute Value Functions In order to graph an absolute value function, you will be using many of the same methods you did for quadratics. The standard form of an absolute value function is …

ABSOLUTE VALUE FUNCTIONS AND GRAPHS
Sep 2, 2016 · KEY VOCABULARY: Absolute Value Functions and Graphs Write absolute value function Sketch the graphs from a given absolute value function

Function Families Worksheet #2 Algebra 2: Absolute Value
Function Families Worksheet #2 Algebra 2: Absolute Value Graph each “family” of equations on a graphing calculator. Try to discover what makes each one different. Then try to sketch them on …

F.IF.C.7: Graphing Absolute Value Functions - JMAP
F.IF.C.7: Graphing Absolute Value Functions 3 Which graph represents the equation 1) 2)

Graphing Absolute Value Functions - bhs.rcschools.net
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Graphing Absolute-Value Functions
Absolute-value graphs can translate up or down, and to the right or left. Graph the function and give the coordinates of the vertex. f x x 1 2 Make a table of values then plot the resulting …

Transformations of Linear and 1.2 Absolute Value Functions
Transformations of the Parent Absolute Value Function Work with a partner. Compare the graph of the function

3.7 Graphing Absolute Value Functions - Jackson School …
Combine transformations of graphs of absolute value functions. An absolute value function is a function that contains an absolute value expression. The parent absolute value function is f(x) …

Solving absolute Value equations by Graphing
Apter 5 absolute Value equations by Graphing Absolute value equations in the form ax 1 b 5 c, where a, b, and c are constants, can be solved by graphing corresponding functions in the for. …

Absolute Value Functions and Graphs - Algebra2Coach.com
Sep 2, 2016 · Absolute Value Functions and Graphs Bell work Choose the suitable option: The absolute value of a number is always ( negative / positive ). The shape of the graph of an …