function and relation worksheet with answer key

4.0,` 3p H.Hi@A> /AIS false Domain: $[8, 8]$; range: $[3, 3]$; function: no, 33. Functions And Relations Sheet #15-02 Answer Key A visual representation of a pop machine and the connection with functions. trailer If an algebraic equation defines a function, then we can use the notation $f (x) = y$. Worksheet 4.1 Relations and Functions Write each of the following as a relation, state the domain and range, then determine if it is a function. stream Class 6 science chapter 3 extra questions, Solve nonlinear equations matlab symbolic. . The will worksheet will discuss the concept of relations and functions. There is then practice on these topics. Then determine the domain and range. /F10 10 0 R /ColorSpace << 1. We have determined that the set of solutions to $y = |x| 2$ is a function; therefore, using function notation we can write: $\begin{aligned} y & = | x | - 2 \\ \color{Cerulean}{\downarrow} & \\ f ( x ) & = | x | - 2 \end{aligned}$. /Producer ( Q t 5 . Write each of the following as a relation, state the domain and range, then determine if it is a function. Reflections Over Intersecting Lines as Rotations. >> Simplify $\frac { c ( x + h ) - c ( x ) } { h }$ given $c ( x ) = 3 x + 1$. Functions And Relations Worksheet Answer Key - A well-developed Characteristics Worksheet with Solutions will offer individuals with strategies to a number of important queries about https://www.functionworksheets.com/tag/worksheet-4-1-relations-and-functions-answer-key/ Relations And Functions Worksheet Answers - Qstion.co 2 0 obj Domain: $[1,5]$; range: $[3,3]$; function: no. The solutions to $x = |y| + 1$, on the other hand, have values in the domain that correspond to two elements in the range. -2- Worksheet by Kuta Software LLC Find the inverse of each function. Not all relations are functions, and not all functions are relations. The relation depicts the connection between input and output. Quizzes with auto-grading, and real-time student data. A function, on the other hand, is a relation that produces one output for each given input. If asked to find $f(a)$, we substitute the argument $a$ in for the variable and then simplify. Domain and Range Worksheets - Math Worksheets 4 Kids endstream <> Fast solutions. 12 0 obj A Explanations 1. Expression to convert Fahrenheit to Celsius is y = (5x/9) (160/9). 1 2 . Form a relation from A to B to show whether the students belong to any of the four sections. 10 0 obj Determine the domain and range of the following relation and state whether it is a function or not: $\{(4, 3), (2, 6), (0, 3), (3, 5), (3, 7)\}$. Yes 3. For the case of a function, a well-defined function will provide the same result if the input representation is altered, but the input value will not be changed. The maximum $y$-value is $3$ and the minimum is $3$; hence, the range consists of $y$-values in the interval $[3,3]$. Vocabulary on relations, functions, domain, range, and vertical line test. A function is a relation in which each element of the domain is paired with EXACTLY one element of the range. $g (10) = 10$ and $g (5) = 10 ; g (5) = 5$ and $g (10) = 5$. $f ( - 1 ) = - 2 , f ( 0 ) = - 1 , f ( x - 1 ) = \sqrt { x } - 2$, 17. << A relation is any set of ordered pairs. <> Find $x$ where $g (x) = 5, g (x) = 0$, and $g (x) = 10$. Domain: ; range: $[1, 1]$; function: yes, 31. $f ( x + h ) = x ^ { 2 } + 2 x h + h ^ { 2 } + x + h + 1$, 5. As every value of x has a different value of y; it is a function. The given relation is not a function because the $x$-value $3$ corresponds to two $y$-values. Substitute $f (x)$ with $27$ and solve. 3. xwTS7" %z ;HQIP&vDF)VdTG"cEb PQDEk 5Yg} PtX4X\XffGD=H.d,P&s"7C$ If any of the x values are repeated, but the values that correspond to them in the y-axis are different, then we are dealing with a relation rather than a function. $g ( - 5 ) = 10 , g ( 0 ) = 5 , g ( 5 ) = 0$, 3. Chapter 3: Introduction to Functions and Relations. you CAN do math! Here we put an arrow on the ends of our lines to indicate that this set of ordered pairs continues without bounds. endobj This is a relations and functions worksheet. The vertical line represents a value in the domain, and the number of intersections with the graph represent the number of values to which it corresponds. /Creator () ID: 1480139 Language: English School subject: Math Grade/level: 10 Age: 14-16 Main content: Functions Other contents: Add to my workbooks (78) Download file pdf Embed in my website or blog Add to Google Classroom >> >> <> a. b. . Find $x$ where $g (x) = 5, g (x) = 4$, and $g (x) = 4$.\. Domain: $[5, 1]$; range: $[2, 2]$; function: no, 25. Print a copy of the Answer Key: Think FUNCTIONally printable for your use. %S%m7$3g3: $ Ymk XvH3a, @~^6=Xfw5q@S3JQFLf4 yyE j|8 ] pq Ha L8DCsK4rqf.,jnghC-S_Jh. Not all relations are functions, and not all functions are relations. lOma`M<?L;l"=8o/+}V[*v"WmO%2loCe^Tj.I;e?&){wv Oex`aWgd{D0m:ZL/.]VY-+ 1X(4-VQTUQ] "g5}fov pBv9 tC u>m`o-x%hs-)r_01cc@4s,'""23hn&$n,Jd&!Pir%+ahJB2Zs`sc ?+_F/` 4. The value of a is 0.90 and b is 24.5, 11. Given $g ( x ) = x ^ { 2 }$, find $g (2), g ( \frac{1}{2} )$, and $g (x + h)$. xXnF}-p(p#YBc),Iiy[ 9^:{wqs k8trv-@, Ls?[^~{;%_&d~tfn>C8Mg*d!?M'WHiRK w A! Find the range and domain of a real function f represented by f(x) = root over (x -1). If it is a function, give the domain and range. In what year was the value of the car at a minimum? Worksheet 4.1 relations and functions answer key. Analyzing Relations and Functions KEY. The Vertical Line Test: Given the graph of a relation, if a vertical line can be drawn that crosses the graph in more than one place, then the relation is not a function. You ask, we answer! A1vjp zN6p\W pG@ n $g (2) = 5, g (3) = 4$ and $g (1) = 4 , g (5) = 4$ and $g (1) = 4$, 7. 39. Then looks at examples of the 5 types: a set of ordered pairsa table of valuesa mappinga discrete graphan equation. 26 0 obj <> endobj Find the value of x that will make this relation a function. You must try to solve the questions on your own and later check it with the given practice worksheet relations and functions answer key. Let's try the best Worksheet 4.2 relations and functions answer key. Real World Math Horror Stories from Real encounters, Solve Equations with variables in Exponents, Solve Quadratic Equations by Completing the Square, Mixed Problems on Writing Equations of Lines, Write Equation of Line from the Slope and 1 Point, Equation of Line Parallel to Another Line and Through a Point, Equation of Line Perpendicular to Another Line and Through a Point, Adding and Subtracting Polynomials worksheet, Multiplying Monomials with Polynomials Worksheet, Solve Systems of Equations by Elimination, Solve Systems of Equations (Mixed Review), Sine, Cosine, Tangent, to Find Side Length, Sine Cosine Graphs with Vertical Translations, Sine, Cosine, Tangent Graphs with Phase Shifts, Sine, Cosine, Tangent Graphs with Change in Period, Amplitude and Phase Shifts (All Translations), Graphing Sine, Cosine, Tangent with Change in Period, Cumulative, Summative Worksheet on Periodic Trig Functions, Activity-Explore by Measuring the Relationship of Vertical Angles, Graphic Organizer: Formulas & Theorems of A Circle, Arcs and Angles Formed by Intersecting Chords, Tangent, Secant, Arcs and Angles of a Circle, Parallel Chords, Congruent Chords and the Center of a Circle, Relationship Between Tangent, Secant Side Lengths, Arcs and Angles Formed by the Intersection of a Tangent and a Chord, Mixed Review on Formulas of Geometry of the Circle, Graph and Equation of Exponential Growth Functions, Linear Equations - Real World Application Activity, Compare and Contrast Types of Parallelograms, Worksheet Goes Hand in Hand with This Web Page, Side Angle Side and Angle Side Angle Worksheet, System of Linear Equations - Real World Application, Activity - Methods to Solve Systems of Equations, Remote, Exterior and Interior Angles of a Triangle, Sine, Cosine, Tangent (SHOCAHTOA) web page, Activity-Relationship of Angles in a Trapezoid, Compositions of Reflections. 7.Lp/; )Q[.[mJ-y)eUt `=PKj~82%.s*`4F/\.{f3O)rQyl8q3ay[T SC ~Gh endobj endstream endobj 27 0 obj <> endobj 28 0 obj <> endobj 29 0 obj <>/Font<>/ProcSet[/PDF/Text/ImageB/ImageC/ImageI]/XObject<>>> endobj 30 0 obj <> endobj 31 0 obj [/ICCBased 34 0 R] endobj 32 0 obj <> endobj 33 0 obj <>stream (c) All functions are relations, but all relations are not functions. We offer immediate delivery on all orders placed before 3pm. for this concept are Gina wilson 2013 all things algebra answers Our customers say This app saved me from going crazy, it really helps me with my algebra homework I really recommend this app if you struggle with algebra a lot like me, but still good. As all the 120 students belong to class 11, every pupil must be in any of the sections. Algebra Function Worksheets with Answer Keys - mathwarehouse The representation of a relation on a rectangular coordinate plane, as illustrated above, is called a graph10. It is perfect for, This product includes a 10-question assignment with practice over finding domain and range of relations and functions. Algebra frequently involves functions, and so the notation becomes useful when performing common tasks. This product contains a worksheet and an assessment. Domain: ; range: $(, 3]$; function: yes, 21. For instance, f(x) = root over x is an undefined function when the value of x is negative. Find $x$ where $g (x) = 4, g (x) = 3$, and $g (x) = 4$. We also acknowledge previous National Science Foundation support under grant numbers 1246120, 1525057, and 1413739. P These relations and functions guided notes and worksheets cover:relation and function vocabularyways to represent relationshow to determine if a relation is a functioncoordinate plane reviewnotating and evaluating functionsanalyzing graphs (domain, range, continuous, discrete, zeros, intervals of increase and decrease)real-world graphs16 pages + all answer keys includedYou may also like:Functions PostersFunctions Graphic OrganizerTerms of Use:This product should only be used by the teacher who p. This is a yes or no worksheet where the students look at 20 different graphs and use the vertical line test to decide rather or not they are a function. They will fill the appropriate box with fun patterns, drawings, and creative ideas! The following table contains data of a womans forehand with her respective height. 38 0 obj <>stream Illustrate the travelled distance in the form of function t in hours. Section 5.2 Defining Relations and Functions. As all the 120 students belong to class 11, every pupil must be in any of the sections. 4.2 Relations and Functions A function is a relation in . /ExtGState << Add highlights, virtual manipulatives, and more. If this doesn't solve the problem, visit our Support Center . To determine whether a given relation is a function or not, one needs first to find out the input values, then the output values. 1. For the case of a function, a well-defined function will provide the same result if the input representation is altered, but the input value will not be changed. Ans. KEY FEATURES Word problem explanations! hs2z\nLA"Sdr%,lt Share a link to a page that you think others may find useful. To determine whether a given relation is a function or not, one needs first to find out the input values, then the output values. $\{ ( 3,1 ) , ( 5,2 ) , ( 7,3 ) , ( 9,4 ) , ( 12,4 ) \}$, $\{ ( 2,0 ) , ( 4,3 ) , ( 6,6 ) , ( 8,6 ) , ( 10,9 ) \}$, $\{ ( 7,5 ) , ( 8,6 ) , ( 10,7 ) , ( 10,8 ) , ( 15,9 ) \}$, $\{ ( 1,1 ) , ( 2,1 ) , ( 3,1 ) , ( 4,1 ) , ( 5,1 ) \}$, $\{ ( 5,0 ) , ( 5,2 ) , ( 5,4 ) , ( 5,6 ) , ( 5,8 ) \}$, $\{ ( - 3,1 ) , ( - 2,2 ) , ( - 1,3 ) , ( 0,4 ) , ( 0,5 ) \}$, $g ( x ) = | x - 5 | \text { find } g ( - 5 ) , g ( 0 ) , \text { and } g ( 5 )$, $g ( x ) = | x | - 5 ; \text { find } g ( - 5 ) , g ( 0 ) , \text { and } g ( 5 )$, $g ( x ) = | 2 x - 3 | ; \text { find } g ( - 1 ) , g ( 0 ) , \text { and } g \left( \frac { 3 } { 2 } \right)$, $g ( x ) = 3 - | 2 x | ; \text { find } g ( - 3 ) , g ( 0 ) , \text { and } g ( 3 )$, $f ( x ) = 2 x - 3 ; \text { find } f ( - 2 ) , f ( 0 ) , \text { and } f ( x - 3 )$, $f ( x ) = 5 x - 1 ; \text { find } f ( - 2 ) , f ( 0 ) , \text { and } f ( x + 1 )$, $g ( x ) = \frac { 2 } { 3 } x + 1 ; \text { find } g ( - 3 ) , g ( 0 ) , \text { and } f ( 9 x + 6 )$, $g ( x ) = - \frac { 3 } { 4 } x - \frac { 1 } { 2 } ; \text { find } g ( - 4 ) , g ( 0 ) , \text { and } g ( 6 x - 2 )$, $g ( x ) = x ^ { 2 } ; \text { find } g ( - 5 ) , g ( \sqrt { 3 } ) , \text { and } g ( x - 5 )$, $g ( x ) = x ^ { 2 } + 1 ; \text { find } g ( - 1 ) , g ( \sqrt { 6 } ) , \text { and } g ( 2 x - 1 )$, $f ( x ) = x ^ { 2 } - x - 2 ; \text { find } f ( 0 ) , f ( 2 ) , \text { and } f ( x + 2 )$, $f ( x ) = - 2 x ^ { 2 } + x - 4 ; \text { find } f ( - 2 ) , f \left( \frac { 1 } { 2 } \right) , \text { and } f ( x - 3 )$, $h ( t ) = - 16 t ^ { 2 } + 32 ; \text { find } h \left( \frac { 1 } { 4 } \right) , h \left( \frac { 1 } { 2 } \right) , \text { and } h ( 2 a - 1 )$, $h ( t ) = - 16 t ^ { 2 } + 32 ; \text { find } h ( 0 ) , h ( \sqrt { 2 } ) , h ( 2 a + 1 )$, $f ( x ) = \sqrt { x + 1 } - 2 \text { find } f ( - 1 ) , f ( 0 ) , f ( x - 1 )$, $f ( x ) = \sqrt { x - 3 } + 1 ; \text { find } f ( 12 ) , f ( 3 ) , f ( x + 3 )$, $g ( x ) = \sqrt { x + 8 } ; \text { find } g ( 0 ) , g ( - 8 ) , \text { and } g ( x - 8 )$, $g ( x ) = \sqrt { 3 x - 1 } ; \text { find } g \left( \frac { 1 } { 3 } \right) , g \left( \frac { 5 } { 3 } \right) , \text { and } g \left( \frac { 1 } { 3 } a ^ { 2 } + \frac { 1 } { 3 } \right)$, $f ( x ) = x ^ { 3 } + 1 ; \text { find } f ( - 1 ) , f ( 0 ) , f \left( a ^ { 2 } \right)$, $f ( x ) = x ^ { 3 } - 8 ; \text { find } f ( 2 ) , f ( 0 ) , f \left( a ^ { 3 } \right)$, $f ( x ) = 2 x - 3 ; \text { find } x \text { where } f ( x ) = 25$, $f ( x ) = 7 - 3 x ; \text { find } x \text { where } f ( x ) = - 27$, $f ( x ) = 2 x + 5 ; \text { find } x \text { where } f ( x ) = 0$, $f ( x ) = - 2 x + 1 ; \text { find } x \text { where } f ( x ) = 0$, $g ( x ) = 6 x + 2 ; \text { find } x \text { where } g ( x ) = 5$, $g ( x ) = 4 x + 5 ; \text { find } x \text { where } g ( x ) = 2$, $h ( x ) = \frac { 2 } { 3 } x - \frac { 1 } { 2 } ; \text { find } x \text { where } h ( x ) = \frac { 1 } { 6 }$, $h ( x ) = \frac { 5 } { 4 } x + \frac { 1 } { 3 } ; \text { find } x \text { where } h ( x ) = \frac { 1 } { 2 }$. - Example, Formula, Solved Examples, and FAQs, Line Graphs - Definition, Solved Examples and Practice Problems, Cauchys Mean Value Theorem: Introduction, History and Solved Examples. PDF Functions and Relations Worksheet - Santa Ana College 1) 2x + 3y = 12 x-intercepts (let y = 0). Function. /Pages 3 0 R So helpful with my homework. 12 graphs.Worksheet 2: Finding range given domainRiddle. 10. Find $x$ where $g (x) = 0, g (x) = 10$, and $g (x) = 15$. We guarantee that your essay will be 100% original. This is because humans get taller throughout time and then stagnate for a period. <> 5. Of special interest are relations where every $x$-value corresponds to exactly one $y$-value. Students will identify function rules by, Relations, Functions, Domain and Range Task CardsThese 20 task cards cover the following objectives:1) Identify the domain and range of ordered pairs, tables, mappings, graphs, and equations.2) Determine whether a relation is a function given ordered pairs, tables, mappings, graphs, and equations.A recording worksheet is also included for students to write down their answers as they use the task cards. PDF RELATIONS & FUNCTIONS Worksheet - School For Excellence Functions and Relations Worksheets (Bundle) by Algebra Funsheets 5.0 (26) $14.99 $7.95 Bundle This bundle contains 9 worksheets on Functions.Worksheet 1: Finding domain and range from graphsStandard. 1. $f ( - 1 ) = 0 , f ( 0 ) = 1 , f \left( a ^ { 2 } \right) = a ^ { 6 } + 1$, 3. Math Worksheet 1- FUNCTION versus RELATION Relations . For instance, x is an object of set A and y is an object from set B. All of these worksheets and activities are available for free so long as they are used solely for educational, 25. /CSp /DeviceRGB This is a relation because if you enter a specific age and check all the persons of that age, you will find that they all have various heights. endobj Relations and function worksheets help students to understand concepts of variable functions, calculus, probability and connect them to the reasoning part of mathematics. The first 3 questions ask students to take a relation (given as a set of ordered pairs) and represent the relation as a table, graph, and mapping diagram. Given a function rule, students will complete a table of values or given a table of values, students will find the function rule.Worksheet 4: Function rules and table of values 2Riddle. Review. Domain = {-2, 0, 5}, Range = {-1, 3, 4}. Find $f (4), f (0)$, and $f (2)$.\. Domain: {3, 6, 9, 12}; Range: {-4, 0, 4} Mapping Diagrams: given a mapping diagram of a relation, we can tell if it is a function if each input is paired with exactly 1 output. 120 students are studying in class 11 divided among four sections. % Lesson Directions. 2. The Vertical Line Test: Given the graph of a relation, if a vertical line can be drawn that crosses the graph in more than one place, then the relation is not a function. Yes 5. 6. This is a relations and functions worksheet. /Type /Catalog So, this relation is a function as well. << LCM of 3 and 4, and How to Find Least Common Multiple, What is Simple Interest? 3. f-1 (x) = (9x/5) + 32 and the inverse is a function also. Look no further! relation is a function. Pre-made digital activities. 2. Set P = {-2,0,2} and the remaining elements are { (-2,-2), (-2,2), (0,-2), (0,0), (2,-2), (2,0), (2,2)} 2. 0000003486 00000 n This is a multiple choice worksheet where students look at 20 different sets of relationships and decide yes or no rather the relationships are a function. yksL?cS3}s+y43!qgn8Bsr&n/g-|N59J4gt_l>5gI9?Ny=@LKFr. Domain: $\{ 7,8,10,15 \}$; range: $\{ 5,6,7,8,9 \}$; function: no, 5. Save money by purchasing. endobj ' Zk! $l$T4QOt"y\b)AI&NI$R$)TIj"]&=&!:dGrY@^O$ _%?P(&OJEBN9J@y@yCR nXZOD}J}/G3k{%Ow_.'_!JQ@SVF=IEbbbb5Q%O@%!ByM:e0G7 e%e[(R0`3R46i^)*n*|"fLUomO0j&jajj.w_4zj=U45n4hZZZ^0Tf%9->=cXgN]. I've finished math now so I'm deleting the app, but I wanted to leave a good review as a thank you , used it for high school Precalc, it'll be hard to resist to use for every problem, it's a very helpful and easy to use app since i struggle with online class(recently) this app helped me to solve my Math homeworks with ease:) I recommend this to people who are confused about the math solutions or wants to check if there answers are right. These multiple representation tasks help students see the connections between the equation, table of values, and graph. This worksheet is practice for the students on how to find the domain and range of a relation, decide if something is a function or not, and to express a relation using a table, graph, and mapping diagram. Feel free to download and enjoy these free worksheets on functions and relations. so will it will not be a function because -4 will have to pair up with -3. This download also includes a PDF "worksheet" with the exact same questions as the Google Form. Consider the relations consisting of the seven ordered pair solutions to $y = |x| 2 $and $x = |y| + 1$. /Font << <> d224f870063a40e098457059835651f2, 055c0d457aa04cdf98c57925f2da174b Very interesting and supportful Thank you , haven't gotten one guest one wrong yet, really good app for homework. Explain your reasoning for each. There are 9 questions total.The first 3 questions give the student a mapping, a table and a set of ordered pairs and ask them to determine if the relations are functions or not and to find the domain and range of each. These math worksheets on introducing functions are exactly what you need. The students look at graphs containing dots and decide rather or not the dots form a linear or nonlinear relationship. Decide whether the following relations are functions. /Pattern << This is because a person has just one height value at any time in their life. Relations Expressed as Graphing. 0000047318 00000 n (d) P = (1, 2, 3} and Q = {e, f}. So, this relation is a function as well. State the domain and range of a relation. (a) Relation {(2, 1), (5, 1), (8, 1), (11, 1), (14, 1), (17, 1)} is a function also. 2. Applying for a job is more than just filling out an application. << $h \left( \frac { 1 } { 4 } \right) = 31 , h \left( \frac { 1 } { 2 } \right) = 28 , h ( 2 a - 1 ) = - 64 a ^ { 2 } + 64 a + 16$, 15. (x) = (9x/5) + 32 and the inverse is a function also. As we have seen, functions are also expressed using graphs. Relations and Functions tate the domain and range of each relation. 9. Then. The solution sets of each equation will form a relation consisting of infinitely many ordered pairs. This is a coloring activity for a set of 12 problems on identifying the domain and range for a relation. /F7 7 0 R Typically, the coordinates are related by a rule expressed using an algebraic equation. There is exactly one output for every input. D 25. x{|7>Z]-Ed]-lJVe;qN8v%vb;vnv$@ \CH(w Are you getting the free resources, updates, and special offers we send out every week in our teacher newsletter? www.rhnet.org We offer the fastest, most expert tutoring in the business. >> Evaluate the inverse and also rule out whether the same is a function or not. Domain. We can visually identify functions by their graphs using the vertical line test15. Is the relation a function? Practise Worksheet Relations and Functions, 3. Each one has model problems worked out step by step, practice problems, as well as challenge questions at the sheets end. Worksheet 4.2 relations and functions answer key - Apps can be a great way to help students with their algebra. Key included. PDF Infinite Algebra 1 - Continuous Relations - Kuta Software endobj Use the graph to find the corresponding $y$-values where $x = 8, 0$, and $8$. The value of a new car in dollars is given by the function $V(t) = 1,800t + 22,000$ where $t$ represents the age of the car in years. { "201:_Relations_Graphs_and_Functions" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "202:_Linear_Functions_and_Their_Graphs" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "203:_Modeling_Linear_Functions" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "204:_Graphing_the_Basic_Functions" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "205:_Using_Transformations_to_Graph_Functions" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "206:_Solving_Absolute_Value_Equations_and_Inequalities" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "207:_Solving_Inequalities_with_Two_Variables" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "20E:_2E:_Graphing_Functions_and_Inequalities_(Exercises)" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()" }, { "00:_Front_Matter" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "01:_Algebra_Fundamentals" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "02:_Graphing_Functions_and_Inequalities" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "03:_Solving_Linear_Systems" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "04:_Polynomial_and_Rational_Functions" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "05:_Radical_Functions_and_Equations" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "06:_Solving_Equations_and_Inequalities" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "07:_Exponential_and_Logarithmic_Functions" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "08:_Conic_Sections" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "09:_Sequences_Series_and_the_Binomial_Theorem" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "zz:_Back_Matter" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()" }, [ "article:topic", "license:ccbyncsa", "showtoc:no", "authorname:anonymous", "licenseversion:30", "program:hidden", "source@https://2012books.lardbucket.org/books/advanced-algebra/index.html" ], https://math.libretexts.org/@app/auth/3/login?returnto=https%3A%2F%2Fmath.libretexts.org%2FBookshelves%2FAlgebra%2FBook%253A_Advanced_Algebra%2F02%253A_Graphing_Functions_and_Inequalities%2F201%253A_Relations_Graphs_and_Functions, $ \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}}}$ $ \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash{#1}}} $$\newcommand{\id}{\mathrm{id}}$ $ \newcommand{\Span}{\mathrm{span}}$ $ \newcommand{\kernel}{\mathrm{null}\,}$ $ \newcommand{\range}{\mathrm{range}\,}$ $ \newcommand{\RealPart}{\mathrm{Re}}$ $ \newcommand{\ImaginaryPart}{\mathrm{Im}}$ $ \newcommand{\Argument}{\mathrm{Arg}}$ $ \newcommand{\norm}[1]{\| #1 \|}$ $ \newcommand{\inner}[2]{\langle #1, #2 \rangle}$ $ \newcommand{\Span}{\mathrm{span}}$ $\newcommand{\id}{\mathrm{id}}$ $ \newcommand{\Span}{\mathrm{span}}$ $ \newcommand{\kernel}{\mathrm{null}\,}$ $ \newcommand{\range}{\mathrm{range}\,}$ $ \newcommand{\RealPart}{\mathrm{Re}}$ $ \newcommand{\ImaginaryPart}{\mathrm{Im}}$ $ \newcommand{\Argument}{\mathrm{Arg}}$ $ \newcommand{\norm}[1]{\| #1 \|}$ $ \newcommand{\inner}[2]{\langle #1, #2 \rangle}$ $ \newcommand{\Span}{\mathrm{span}}$$\newcommand{\AA}{\unicode[.8,0]{x212B}}$, source@https://2012books.lardbucket.org/books/advanced-algebra/index.html, status page at https://status.libretexts.org.