function and relation worksheet with answer key

Find $x$ where $g (x) = 0, g (x) = 1$, and $g (x) = 4$. Want to buy them separately?Functions and Linear Equations Assessment (15 Questions)Functions and Linear Equations Worksheet (26 Questions)TOPICS BY QUESTION NUMBER:Questions 1-11: Tell whether the relation is a function from a table, graph, or input o, Students will identify functions in 20 YES/NO format problems with multiple representations of function relations: tables, mapping diagrams, graphs and ordered pairs.ANSWER KEY provided.You may also be interested in these Functions resources:Evaluating Functions Coloring ActivityIdentifying Functions Review WorksheetIdentifying Functions Card Sort ActivityFunctions: Multiple Representations Matching ActivityIdentifying Functions PracticeFunction Notation (Task Cards)Functions: Multiple Represent, In this activity, students will determine if relations are functions as they tap into their creative side! /Resources 13 0 R Typically, the coordinates are related by a rule expressed using an algebraic equation. {(3,2), (1, -1), (2, -4), (3, -9), (4, -16)} 4. stream Determine the domain and range of the following relation and state whether it is a function or not: $\{(4, 3), (2, 6), (0, 3), (3, 5), (3, 7)\}$. 7.Lp/; )Q[.[mJ-y)eUt `=PKj~82%.s*`4F/\.{f3O)rQyl8q3ay[T SC ~Gh In this example, the output is given and we are asked to find the input. $f ( x + h ) = x ^ { 3 } + 3 h x ^ { 2 } + 3 h ^ { 2 } x + h ^ { 3 }$, 9. Plus each one comes with an answer key. Mathematics is a way of dealing with tasks that involves numbers and equations. 0 Consider the relations consisting of the seven ordered pair solutions to $y = |x| 2 $and $x = |y| + 1$. 7 0 obj Now, lets begin with the relations functions worksheet. Students will find the range given the domain.Worksheet 3: Function rules and table of valuesStandard. endobj Domain: ; range: ; function: yes, 23. 5 0 obj The uploaded images may not be edited.a hard copy (workshee. [ -c R!z"^Ow,c A visual representation of a pop machine and the connection with functions. 3The vertical number line used as reference in a rectangular coordinate system. 8. Map the following relation and also mention the domain and range. endobj 8Term used in honor of Ren Descartes when referring to the rectangular coordinate system. Explain. 1A system with two number lines at right angles specifying points in a plane using ordered pairs $(x, y)$. Review. <> endobj This relation is not a function. Domain: $\{1, 0, 1, 2\}$; range: $\{0, 1, 2, 3, 4\}$; function: no, 11. For example: $\begin{aligned} h ( \color{Cerulean}{4 a ^ { 3 }}\color{Black}{ )} & = \frac { 1 } { 2 } ( \color{Cerulean}{4 a ^ { 3 } }\color{Black}{)} - 3 = 2 a ^ { 3 } - 3 \\ h ( \color{Cerulean}{2 x - 1}\color{Black}{ )} & = \frac { 1 } { 2 } ( \color{Cerulean}{2 x - 1}\color{Black}{ )} - 3 = x - \frac { 1 } { 2 } - 3 = x - \frac { 7 } { 2 } \end{aligned}$. xULF] 0000000750 00000 n endobj (b) {(2, 1), (4, 2), (6, 3), (8, 4), (10, 5), (12, 6), (14, 7)} is not a function. A function is a relation in which each element of the domain is paired with EXACTLY one element of the range. Quizzes with auto-grading, and real-time student data. so will it will not be a function because -4 will have to pair up with -3. Algebra 2 relations and functions worksheet answers can be a useful tool for these scholars. Questions include sets of ordered pairs, tables, mapping diagrams, and graphs. hb``b``f`a`e`@ rp10D200;> aF`3"W~``xXjau8H20:@| PERIOD. >> All of these worksheets and activities are available for free so long as they are used solely for educational, For instance, x is an object of set A and y is an object from set B. The value of a certain automobile in dollars depends on the number of years since it was purchased in $1970$ according to the following function: 11. A1vjp zN6p\W pG@ << endobj $g (4) = 3, g (2) = 0$, and $g (6) = 2$. <> Let's try the best Worksheet 4.2 relations and. As all the 120 students belong to class 11, every pupil must be in any of the sections. %PDF-1.3 % Consider n (A) = m and n (B) = n. Find out the number of relations (non-empty) that can be predicted from A to B. endobj /ColorSpace << 0000001962 00000 n Answer: the output from the function g when the input is 7. A function, on the other hand, is a relation that produces one output for each given input. /CSpg /DeviceGray . )feOJeB_~n %PDF-1.5 /CSp /DeviceRGB If all these pointers match, then the relation is proved to be a function. For instance, f(x) = root over x is an undefined function when the value of x is negative. 1. As pictured, the $x$-value $3$ corresponds to more than one $y$-value. The horizontal number line is called the x-axis2, and the vertical number line is called the y-axis3. << 10/10 gives correct answers every time. Simplify $\frac { q ( x + h ) - q ( x ) } { h }$ given $q ( x ) = a x$. Interactive simulation the most controversial math riddle ever! . NhSIS+:|2q^>l$ia}^nCLW:'HdfJ)A3X3&X Using the vertical line test, determine if the graph above shows a relation, a function, both a relation and a. /ExtGState << 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. An expression is considered to be unambiguous or well-defined when the definition of the same allocates a unique value or interpretation. 12. Understanding the concept of relation and function will be helpful in real-life situations. 9. Each one has model problems worked out step by step, practice problems, as well as challenge questions at the sheets end. 4. Solving math equations can be challenging, but it's also a great way to improve your problem-solving skills. hs2z\nLA"Sdr%,lt /SA true 3. Questions 4-12 present students with relations in any of the given formats and ask to identify the domain, range, determine whether the relation is a function, and provide an explanation.An answer key is provided!This resource is also i, This ready to use product is a quick, fun way to have your students practice identifying functions. As we can see, any vertical line will intersect the graph of $y=|x|2$ only once; therefore, it is a function. Domain: -6 x 4 Range: -7 y 6 Create your own worksheets like this one with Infinite Algebra 1. If you want more time for your pursuits, consider hiring a virtual assistant. 2. 13. This is a coloring activity for a set of 12 problems on identifying the domain and range for a relation. You can also use mathematical representation for actual scenarios. Range. 2. They will fill the appropriate box with fun patterns, drawings, and creative ideas! Domain: ; range: $[2, )$; function: yes, 15. The previous example, where $g (x) = x^{2}$, illustrates this nicely, $\begin{array} { l } { g ( x + h ) \neq g ( x ) + g ( h ) } \\ { ( x + h ) ^ { 2 } \neq x ^ { 2 } + h ^ { 2 } } \end{array}$. In this case, we interpret $f(5) = 3$ as follows: Function notation streamlines the task of evaluating. 5 0 obj stream I suggest using this as a note guide during the lesson. endstream endobj 35 0 obj <>stream Domain: $\{ 7,8,10,15 \}$; range: $\{ 5,6,7,8,9 \}$; function: no, 5. 4. $g ( - 3 ) = - 1 , g ( 0 ) = 1 , g ( 9 x + 6 ) = 6 x + 5$, 9. 1. If this doesn't solve the problem, visit our Support Center . Simplify $\frac { g ( x + h ) - g ( x ) } { h }$ given $g ( x ) = m x + b$. This system is often called the Cartesian coordinate system8, named after the French mathematician Ren Descartes (15961650). 7. This is because humans get taller throughout time and then stagnate for a period. 0000001728 00000 n Graph the given set of points, then answer the questions that follow. 5. %S%m7$3g3: $ Ymk XvH3a, @~^6=Xfw5q@S3JQFLf4 yyE j|8 ] pq Ha L8DCsK4rqf.,jnghC-S_Jh. The value of a is 0.90 and b is 24.5, 11. Then looks at examples of the 5 types: a set of ordered pairsa table of valuesa mappinga discrete graphan equation. endobj /AIS false xref With this data, a student maps a relationship between forehand and hand in the form y = ax + b, provided both are constants. Questions include 4 graphs, 2 verbal situations, 1 mapping, 1 equation, and 2 tables/points with both discrete and continuous situations.This product includes:both directions and a link to access a copy of the google form/quiz. This assignment is also included in my:Algebra 1 Google Forms (, Functions and Relations Worksheets (Bundle), Relations, Functions, Domain and Range | Task Cards, Holt Algebra 4.2 Relations and Functions Worksheet DOC & PDF, Relations and Functions Worksheet (linear/non linear #2), Relations and Functions Notes and Worksheets, Relations and Functions Unit (Algebra 1 Unit 3), Functions and Linear Equations Quiz & Worksheet, Identifying Functions | Function or Not a Function Practice Worksheet, BACK TO SCHOOL | ALGEBRA 1 FUNCTIONS Bundle, Evaluating and Identifying Functions Worksheet, Relations and Functions Introduction Worksheets Bundle (Five Worksheets), Relations and Functions 2 (input-output boxes), Relations and Functions - Algebra 1 Skills Practice Worksheet, Algebra 1 Skills Practice Worksheets Bundle, Identifying Functions - Quick Coloring Activity, Domain and Range of Relations and Functions Quiz for Google Form/Quiz, Relations and Functions Worksheet (linear/non linear #1), RELATIONS AND FUNCTIONS: - IDENTIFY THE DOMAIN AND RANGE COLORING ACTIVITY # 2, Marie's Math Resources and Coloring Activities, Graphing Quadratic Functions in Standard Form Worksheets, Identifying Functions Independent Practice, Functions & Relations, Domain & Range Notes, Functions Unit Bundle - Algebra 1 Curriculum, Functions & Relations, Domain & Range, Function Notation Quiz, Daily Lessons in COMPARING & SORTING Preschool Lesson Plans, Algebra 1 Google Forms Semester 1 Digital Homework and Assessment Bundle. [U6Ue:}au&+X[f]p2n3&\ _ For relations consisting of points in the plane, the range is the set of all $y$-values. Add highlights, virtual manipulatives, and more. /Annots 14 0 R So helpful with my homework. We can visually identify functions by their graphs using the vertical line test15. 33. g(x) = 2x + 1 Answer 34. g(x) = 5x 8 35. g(x) = 3x 2 Answer 36. g(x) = 8x + 2 37. g(x) = 3 x Answer 38. g(x) = 7 5x In the following exercises, evaluate the function. This page titled 2.1: Relations, Graphs, and Functions is shared under a CC BY-NC-SA 3.0 license and was authored, remixed, and/or curated by Anonymous via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request. Evaluate the range for the given domain and the function. It is a relation.) Unfortunately, in the last year, adblock has now begun disabling almost all images from loading on our site, which has lead to mathwarehouse becoming unusable for adlbock users. Find $f (4), f (0)$, and $f (2)$.\. A relation is any set of ordered pairs. 9. 4. This relations functions worksheet may act as a last-minute tool to revise the function and relation problems before your exams. Worksheet #1 Determine whether each relation is a function or not. 3. Try to test your learnings in the exercises below. If an algebraic equation defines a function, then we can use the notation $f (x) = y$. Domain: ; range: $[1, 1]$; function: yes, 31. There are many $x$-values in the domain that correspond to two $y$-values. Relations and Functions Worksheet Answer Key 1. Here $f$ is the function name, and $f (x)$ denotes the value in the range associated with the value x in the domain. Find $x$ where $g (x) = 0, g (x) = 10$, and $g (x) = 15$. Domain and Range (Algebra 1) So, this relation is a function as well. In mathematics, a student will get to study multiple kinds of functions, which are one one, many one, onto, into, polynomial, linear, identical, quadratic, rational, cubic, algebraic, modulus, signum, greatest integer, fractional part, even and odd, periodic, composite, constant, identity, etc. These multiple representation tasks help students see the connections between the equation, table of values, and graph. Ans. These math worksheets on introducing functions are exactly what you need. 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. But for the -4 the range is -3 so i did not put that in. The monthly income in dollars of a commissioned car salesperson is given by the function $I(n) = 350n + 1,450$ where $n$ represents the number of cars sold in the month. Form a relation from A to B to show whether the students belong to any of the four sections. 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. Then they share a relationship and can be written as an ordered pair (x, y). Given $g ( x ) = x ^ { 2 }$, find $g (2), g ( \frac{1}{2} )$, and $g (x + h)$. Worksheet 4.2 relations and functions answer key - Apps can be a great way to help students with their algebra. Introduction to New Material. Given the graph of $h$, find $x$ where $h(x)=-4$. So, this relation is a function as well. 3. The following table contains data of a womans forehand with her respective height. Of special interest are relations where every $x$-value corresponds to exactly one $y$-value. Print a copy of the Answer Key: Think FUNCTIONally printable for your use. endobj 5. /Length 12 0 R <> Answer: the output from the function g when the input is 7 Question: Suppose f(x . % Find the value of x that will make this relation a function. We offer the fastest, most expert tutoring in the business. Functions and Relations Worksheet Decide whether the graph represents y as a function of x. RELATIONS & FUNCTIONS Worksheet. endobj In particular, the x-value $4$ corresponds to two y-values $3$ and $3$. Find $x$ where $g (x) = 1, g (x) = 0$, and $g (x) = 3$. >> 120 students are studying in class 11 divided among four sections. We say "the output is a function of the input." The input values make up the domain, and the output values make up the range. Given the graph of a function $g$, find the $x$-values: 2. $\{ ( 3,1 ) , ( 5,2 ) , ( 7,3 ) , ( 9,4 ) , ( 12,4 ) \}$, $\{ ( 2,0 ) , ( 4,3 ) , ( 6,6 ) , ( 8,6 ) , ( 10,9 ) \}$, $\{ ( 7,5 ) , ( 8,6 ) , ( 10,7 ) , ( 10,8 ) , ( 15,9 ) \}$, $\{ ( 1,1 ) , ( 2,1 ) , ( 3,1 ) , ( 4,1 ) , ( 5,1 ) \}$, $\{ ( 5,0 ) , ( 5,2 ) , ( 5,4 ) , ( 5,6 ) , ( 5,8 ) \}$, $\{ ( - 3,1 ) , ( - 2,2 ) , ( - 1,3 ) , ( 0,4 ) , ( 0,5 ) \}$, $g ( x ) = | x - 5 | \text { find } g ( - 5 ) , g ( 0 ) , \text { and } g ( 5 )$, $g ( x ) = | x | - 5 ; \text { find } g ( - 5 ) , g ( 0 ) , \text { and } g ( 5 )$, $g ( x ) = | 2 x - 3 | ; \text { find } g ( - 1 ) , g ( 0 ) , \text { and } g \left( \frac { 3 } { 2 } \right)$, $g ( x ) = 3 - | 2 x | ; \text { find } g ( - 3 ) , g ( 0 ) , \text { and } g ( 3 )$, $f ( x ) = 2 x - 3 ; \text { find } f ( - 2 ) , f ( 0 ) , \text { and } f ( x - 3 )$, $f ( x ) = 5 x - 1 ; \text { find } f ( - 2 ) , f ( 0 ) , \text { and } f ( x + 1 )$, $g ( x ) = \frac { 2 } { 3 } x + 1 ; \text { find } g ( - 3 ) , g ( 0 ) , \text { and } f ( 9 x + 6 )$, $g ( x ) = - \frac { 3 } { 4 } x - \frac { 1 } { 2 } ; \text { find } g ( - 4 ) , g ( 0 ) , \text { and } g ( 6 x - 2 )$, $g ( x ) = x ^ { 2 } ; \text { find } g ( - 5 ) , g ( \sqrt { 3 } ) , \text { and } g ( x - 5 )$, $g ( x ) = x ^ { 2 } + 1 ; \text { find } g ( - 1 ) , g ( \sqrt { 6 } ) , \text { and } g ( 2 x - 1 )$, $f ( x ) = x ^ { 2 } - x - 2 ; \text { find } f ( 0 ) , f ( 2 ) , \text { and } f ( x + 2 )$, $f ( x ) = - 2 x ^ { 2 } + x - 4 ; \text { find } f ( - 2 ) , f \left( \frac { 1 } { 2 } \right) , \text { and } f ( x - 3 )$, $h ( t ) = - 16 t ^ { 2 } + 32 ; \text { find } h \left( \frac { 1 } { 4 } \right) , h \left( \frac { 1 } { 2 } \right) , \text { and } h ( 2 a - 1 )$, $h ( t ) = - 16 t ^ { 2 } + 32 ; \text { find } h ( 0 ) , h ( \sqrt { 2 } ) , h ( 2 a + 1 )$, $f ( x ) = \sqrt { x + 1 } - 2 \text { find } f ( - 1 ) , f ( 0 ) , f ( x - 1 )$, $f ( x ) = \sqrt { x - 3 } + 1 ; \text { find } f ( 12 ) , f ( 3 ) , f ( x + 3 )$, $g ( x ) = \sqrt { x + 8 } ; \text { find } g ( 0 ) , g ( - 8 ) , \text { and } g ( x - 8 )$, $g ( x ) = \sqrt { 3 x - 1 } ; \text { find } g \left( \frac { 1 } { 3 } \right) , g \left( \frac { 5 } { 3 } \right) , \text { and } g \left( \frac { 1 } { 3 } a ^ { 2 } + \frac { 1 } { 3 } \right)$, $f ( x ) = x ^ { 3 } + 1 ; \text { find } f ( - 1 ) , f ( 0 ) , f \left( a ^ { 2 } \right)$, $f ( x ) = x ^ { 3 } - 8 ; \text { find } f ( 2 ) , f ( 0 ) , f \left( a ^ { 3 } \right)$, $f ( x ) = 2 x - 3 ; \text { find } x \text { where } f ( x ) = 25$, $f ( x ) = 7 - 3 x ; \text { find } x \text { where } f ( x ) = - 27$, $f ( x ) = 2 x + 5 ; \text { find } x \text { where } f ( x ) = 0$, $f ( x ) = - 2 x + 1 ; \text { find } x \text { where } f ( x ) = 0$, $g ( x ) = 6 x + 2 ; \text { find } x \text { where } g ( x ) = 5$, $g ( x ) = 4 x + 5 ; \text { find } x \text { where } g ( x ) = 2$, $h ( x ) = \frac { 2 } { 3 } x - \frac { 1 } { 2 } ; \text { find } x \text { where } h ( x ) = \frac { 1 } { 6 }$, $h ( x ) = \frac { 5 } { 4 } x + \frac { 1 } { 3 } ; \text { find } x \text { where } h ( x ) = \frac { 1 } { 2 }$. We guarantee that your essay will be 100% original. There are a variety of question types including, multiple- choice, drop down, and select all that apply. If any vertical line intersects the graph more than once, then the graph does not represent a function. Very interesting and supportful Thank you , haven't gotten one guest one wrong yet, really good app for homework. Feel free to download and enjoy these free worksheets on functions and relations. Consider an aeroplane moving at a velocity of 500 km per hour. /Contents 11 0 R The worksheet is also editable if you would like to make any changes. Feel free to download and enjoy these free worksheets on functions and relations .Each one has model problems worked out step by step, practice problems, as well as challenge questions at the sheets end. Examples of domain and range, vertical line test, and determining if a relation is a function. 0000001693 00000 n We offer immediate delivery on all orders placed before 3pm. D \R(BJIBxCKoo-J-}wwfvv5s9["%VA 26 0 obj <> endobj Students will determine if the given relations (shown in mapping diagrams, function tables, graphs, and pairs of points) are a function or not. Worksheet on Relations and Functions. If we consider each x-value to be the input that produces exactly one output, then we can use function notation16: The notation $f(x)$ reads, f of x and should not be confused with multiplication. This is a relations and functions worksheet. Function. . If you're looking for a quick delivery, we've got you covered. $g (2) = 5, g (3) = 4$ and $g (1) = 4 , g (5) = 4$ and $g (1) = 4$, 7. It has so many equations and etc that it knows how to do, and has many advantages that other math apps do not. Domain: $\{5\}$; range: $\{ 0,2,4,6,8 \}$; function: no, 7. Then, they will locate the box with the exercise number in it on the next page and follow the directions for it according to their answer. Relationships are represented as ordered pairs, tables, mapping diagrams, and graphs. Often, we can determine the domain and range of a relation if we are given its graph. Look no further! 1. 5. The ordered pair $(x, y)$ represents the position of points relative to the origin. /Type /Page (c) All functions are relations, but all relations are not functions. /PCSp 5 0 R Then determine the domain and range. Find $f (2), f (2)$, and $f (7)$. <> DATE. >> These two number lines define a flat surface called a plane4, and each point on this plane is associated with an ordered pair5 of real numbers $(x, y)$. Class 6 science chapter 3 extra questions, Solve nonlinear equations matlab symbolic. <> Function: Domain: 10 Range: Function. What was the value of the car new? For example, use the function $h$ defined by $h (x) = \frac{1}{2} x 3$to evaluate for $x$-values in the set $\{2, 0, 7\}$. /F10 10 0 R Use the graph to find the corresponding $y$-values where $x = 8, 0$, and $8$. $h \left( \frac { 1 } { 4 } \right) = 31 , h \left( \frac { 1 } { 2 } \right) = 28 , h ( 2 a - 1 ) = - 64 a ^ { 2 } + 64 a + 16$, 15. Given the graph, determine the domain and range and state whether or not it is a function: Domain: $(,15]$; range:; function: no. Find $x$ where $g (x) = 5, g (x) = 4$, and $g (x) = 4$.\. 6. /Producer ( Q t 5 . Domain. Explore math program endobj $g ( - 1 ) = 5 , g ( 0 ) = 3 , g \left( \frac { 3 } { 2 } \right) = 0$, 5. Yes, each input has exactly 1 output. The relation is a function because each x-value corresponds to exactly one y-value. 0000001084 00000 n LCM of 3 and 4, and How to Find Least Common Multiple, What is Simple Interest? Some filters moved to Formats filters, which is at the top of the page. There is exactly one output for every input. New: $$22,000$; $4$ years old: $$14,800$. Relations and function worksheets help students to understand concepts of variable functions, calculus, probability and connect them to the reasoning part of mathematics. Given $f ( x ) = \sqrt { 2 x + 4 }$, find $f (2), f (0)$, and $f \left( \frac { 1 } { 2 } a ^ { 2 } - 2 \right)$. Therefore, $x = |y| + 1$ does not define a function. << You can get arithmetic support online by visiting websites such as Khan Academy or by downloading apps such as Photomath. 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. 2 0 obj {(2, 1), (5, 1), (8, 1), (11, 1), (14, 1), (17, 1)} is a function also. The domain is $\{4, 2, 0, 3\}$ and the range is $\{3, 3, 5, 6, 7\}$. <<9314568F76096D49830FE73A943AC137>]/Prev 83319>> Therefore, $f (4) = 27$. Yes 3. To determine whether a given relation is a function or not, one needs first to find out the input values, then the output values. 0000006193 00000 n An expression is considered to be unambiguous or well-defined when the definition of the same allocates a unique value or interpretation. Not all relations are functions, and not all functions are relations. Then determine whether each relation is a Do my homework for me . Special relations where every $x$-value (input) corresponds to exactly one $y$-value (output) are called functions. Instead of writing their answers, students will color them! $g (10) = 10$ and $g (5) = 10 ; g (5) = 5$ and $g (10) = 5$. Relation. Share a link to a page that you think others may find useful. Given the linear function defined by $f(x)=2x-5$, simplify the following. Calculate the range for the function f (x)= (3x-2)/5, if its domain is {-6, -1, 4, 9, 19} Check whether the set of ordered pair represent the function, and state . z|OgYG;,_78}:<9}CJ` t\qF_W&]~~'7%EX6hqX=v$ \FLU/)|BtsS*q\B+oF,k=eI)B1tr6h(D In the following exercises, evaluate the function: a. g(h2) b. g(x + 2) c. g(x) + g(2). xwTS7" %z ;HQIP&vDF)VdTG"cEb PQDEk 5Yg} PtX4X\XffGD=H.d,P&s"7C$ 17The value or algebraic expression used as input when using function notation. 39. startxref { "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.