function and relation worksheet with answer key

For example, both the algebraic equations $y = |x| 2$ and $x = |y| + 1$ define relationships between $x$ and $y$. Also sketch a graph for each equation. Algebra 2 relations and functions worksheet answers can be a useful tool for these scholars. 1. % 17The value or algebraic expression used as input when using function notation. Relationships are represented as ordered pairs, tables, mapping diagrams, and graphs. Now consider set A to be the students and B to be the sections. 0000000016 00000 n Questions 4 through 6, give the student 3 graphs (1 discrete and 2 continuous) and ask them the same questions as 1 t, This Daily Lessons in Preschool Mathematics Comparing & Sorting Unitincludes everything you need to teach sorting differentiation skills to your preschooler.Daily Lessons in Preschool Mathematics is a complete and comprehensive curriculum designed to teach your preschooler all five disciplines of math without the boring worksheets!TARGETED SORTING SKILLS IN THE COMPARING & SORTING PRESCHOOL UNIT:Make matchesIdentify setsClassify items by single attributesClassify items by multiple attri, This 7- question, self-grading assignment provides students with practice determining whether or not a relation represents a function. Free trial available at KutaSoftware.com. Let's try the best Worksheet 4.2 relations and. << stream Find $x$ where $g (x) = 0, g (x) = 10$, and $g (x) = 15$. $f ( - 1 ) = - 2 , f ( 0 ) = - 1 , f ( x - 1 ) = \sqrt { x } - 2$, 17. Solutions to Selected Odd Problems. 11. ' 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]. Problems 1 - 6 are on identifying the domain of a relation and problems 7 - 12 are on identifying the range of a relation. Therefore, the domain consists of all $x$-values in the interval $[8,)$. Worksheet #1 Determine whether each relation is a function or not. Chapter 3: Introduction to Functions and Relations. Relations and Functions Worksheet (with Answer Key + PDF) October 12, 2022 by Mathematical Worksheets The relation depicts the connection between input and output. D 25. 5 0 obj {(2, 1), (5, 1), (8, 1), (11, 1), (14, 1), (17, 1)} is a function also. Answers vary, should mention how the function does not always have the same output for a given input. A vertical line can cross the graph of $x=|y|+1$ more than once; therefore, it is not a function. In addition, since we can find a vertical line that intersects the graph more than once, we conclude that the graph is not a function. 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. /Type /Catalog 6 0 obj Answers. Students will be given 20 different relations (graphs, mapping diagrams, tables, ordered pairs) and will need to classify it as a function or a non-function. Interactive simulation the most controversial math riddle ever! The student first takes notes on the definition of a relation and a function. /CSpg /DeviceGray Check to see if any of the x values are repeated to distinguish a function from a relation; if they are not, itis a function. /XObject << A relation is established between two sets when an object from one set is related to one object from another set, resulting in the formation of ordered pairs. . NhSIS+:|2q^>l$ia}^nCLW:'HdfJ)A3X3&X 5Pairs $(x, y)$ that identify position relative to the origin on a rectangular coordinate plane. The zip file contains the worksheet in both .doc format as well as in .pdf. Hi This app,i want said that the app was good ,not good, but excellent choice but i want to said your bad side that improve your app i was so impressed this app but you can't solve this equation but i would like to tell that pls can u erase purchase cause everyone us need to now how to solve it. /Annots 14 0 R If each input has only one line connected to it, then the outputs are a function of the . A relation is a set of one or more ordered pairs. It could also be used as a worksheet for homework. Fast solutions. Who is credited with the introduction of the notation $y = f (x)$? In this example, the output is given and we are asked to find the input. The relation is a function. Relations Expressed as Graphing. %PDF-1.5 d224f870063a40e098457059835651f2, 055c0d457aa04cdf98c57925f2da174b endstream endobj 34 0 obj <>stream 7The four regions of a rectangular coordinate plane partly bounded by the $x$- and $y$-axes and numbered using the Roman numerals I, II, III, and IV. Find $x$ where $g (x) = 4, g (x) = 3$, and $g (x) = 4$. Graph the given set of points, then answer the questions that follow. As every value of x has a different value of y; it is a function. If the function is f (x)= 6x-27, and the domain is {-5, 3, 15, 17}, then find the range. We offer immediate delivery on all orders placed before 3pm. So helpful with my homework. Domain: -6 x 4 Range: -7 y 6 Create your own worksheets like this one with Infinite Algebra 1. 12 graphs.Worksheet 2: Finding range given domainRiddle. >> relation is a function. Plus each one comes with an answer key. What are the Types of Functions in Mathematics? There is exactly one output for every input. In the context of algebra, the relations of interest are sets of ordered pairs $(x, y)$ in the rectangular coordinate plane. 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. endobj $f ( - 1 ) = 0 , f ( 0 ) = 1 , f \left( a ^ { 2 } \right) = a ^ { 6 } + 1$, 3. /Font << Free worksheet(pdf) and answer key on distinguishing functions from relations, stating domain and range and more. 0000000750 00000 n Evaluate the function when x = 3, x = 0, and x = -2. Functions and Relations Worksheet Decide whether the graph represents y as a function of x. Determine the domain and range of the following relation and state whether it is a function or not: $\{(1, 4), (0, 7), (2, 3), (3, 3), (4, 2)\}$. xref We can also recognize functions as relations where no $x$-values are repeated. . For example, use the function $h$ defined by $h (x) = \frac{1}{2} x 3$to evaluate for $x$-values in the set $\{2, 0, 7\}$. We can see that $g(x)=2$ where $x=5$; in other words, $g(5)=2$. The argument could be an algebraic expression. Relations and Functions Worksheet with Answer Key (PDF), Scatter Plot and Line of Best Fit Worksheet (PDF), Absolute Value Equations and Inequalities Worksheet (PDF), 2nd Grade Measuring Worksheet (with Answer Key), Square Numbers Worksheet (with Answer Key), Expanded Form Worksheet (with Answer Key). 1. 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. ~=d91Q0K REYm5s7MV2q-l^m;^&U[~8[LjRdLeujSV)Y)#Q%+j^ER%cD 9*y@-sX&e%C'HJKvCV%v 9@B*@(Qbo)3UGh~0EL^*3(clZ. startxref They will fill the appropriate box with fun patterns, drawings, and creative ideas! 0000006193 00000 n 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. Relations and functions class 11 worksheets with answers - There is Relations and functions class 11 worksheets with answers that can make the technique much. Following are some integers that satisfy both equations: Here two relations consisting of seven ordered pair solutions are obtained: $y=|x|2hassolutions\{(3,1),(2,0),(1,1),(0,2),(1,1),(2,0),(3,1)\}$, $x=|y|+1hassolutions\{(4,3),(3,2),(2,1),(1,0),(2,1),(3,2),(4,3)\}$. Next, we define a relation9 as any set of ordered pairs. 12 graphs.Worksheet 2: Finding range given domainRiddle. RELATIONS & FUNCTIONS Worksheet. Find $x$ where $g (x) = 5, g (x) = 4$, and $g (x) = 4$. Determine whether this relation is a function or not, and find the values of both a and b. The relation is a function because each x-value corresponds to exactly one y-value. 39. Here the compact notation $f(5) = 3$ indicates that where $x = 5$ (the input), the function results in $y = 3$ (the output). Here we can see that the graph of $y=|x|2$ has a domain consisting of all real numbers, $=(,)$, and a range of all y-values greater than or equal to $2, [2,)$. endobj 0000001962 00000 n You can get arithmetic support online by visiting websites such as Khan Academy or by downloading apps such as Photomath. Worksheet on Math Relation | Relations and Functions Worksheets with Answers. 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! 8. How to Calculate the Percentage of Marks? These worksheets cover all the essential concepts related to functions, including domain and range, linear versus nonlinear, graphing stories, and much more. 3. Given $f (x) = 5x + 7$, find $x$ where $f (x) = 27$. <> $g (2) = 4, g (1) = 3, g (0) = 4$, 9. 0 Are you looking for a comprehensive set of worksheets to introduce functions to your students? so will it will not be a function because -4 will have to pair up with -3. Expression to convert Fahrenheit to Celsius is y = (5x/9) (160/9). The representation of a relation on a rectangular coordinate plane, as illustrated above, is called a graph10. /Type /Page A function is a relation in which each possible input value leads to exactly one output value. Given the graph of $h$, find $x$ where $h(x)=-4$. O*?f`gC/O+FFGGz)~wgbk?J9mdwi?cOO?w| x&mf $g ( 0 ) = 2 \sqrt { 2 } , g ( - 8 ) = 0 , g \left( a ^ { 2 } - 8 \right) = | a |$, 19. Function. 9. 2 0 obj Using the vertical line test, determine if the graph above shows a relation, a function, both a relation and a. This is because a person has just one height value at any time in their life. The first 4 sheets each give:a quadratic equation a partially complete storya space for students to fill in the vertex, y-intercept, and x-intercept a table of values to fill ina space for students to write and answer their own question about the relationThe 5th sheet is a cha, Identifying Functions Independent Practice: Given 25 relations (ordered pairs, graph, table, mapping and equation), students will identify those relations which are NOT A FUNCTION by highlighting the boxes. The value of a is 0.90 and b is 24.5, 11. 6 0 obj We can visually identify functions by their graphs using the vertical line test15. Yes 5. Feel free to download and enjoy these free worksheets on functions and relations. Free printable worksheets (pdf) with answer keys on Algebra I, Geometry, Trigonometry, Algebra II, and Calculus. Find out whether the following statements are true or false. Find $f ( 0 ) , f ( 2 )$, and $f ( 4 )$. 2. . Real World Math Horror Stories from Real encounters. Is the Equation a Function? State the domain and range of a relation. Explain your reasoning for each. Set P = {-2,0,2} and the remaining elements are {(-2,-2), (-2,2), (0,-2), (0,0), (2,-2), (2,0), (2,2)}. 7. Then they share a relationship and can be written as an ordered pair (x, y). /F10 10 0 R Example: Decide whether the following relations are a function. 9. After that, check whether each input value has a corresponding out value. /Producer ( Q t 5 . Worksheet 4.1 relations and functions answer key. If you wish to get more such worksheets of other maths chapters, please make sure to download the Vedantu app today! xULF] Consider n (A) = m and n (B) = n. Find out the number of relations (non-empty) that can be predicted from A to B. $\{ ( 3,1 ) , ( 5,2 ) , ( 7,3 ) , ( 9,4 ) , ( 12,4 ) \}$, $\{ ( 2,0 ) , ( 4,3 ) , ( 6,6 ) , ( 8,6 ) , ( 10,9 ) \}$, $\{ ( 7,5 ) , ( 8,6 ) , ( 10,7 ) , ( 10,8 ) , ( 15,9 ) \}$, $\{ ( 1,1 ) , ( 2,1 ) , ( 3,1 ) , ( 4,1 ) , ( 5,1 ) \}$, $\{ ( 5,0 ) , ( 5,2 ) , ( 5,4 ) , ( 5,6 ) , ( 5,8 ) \}$, $\{ ( - 3,1 ) , ( - 2,2 ) , ( - 1,3 ) , ( 0,4 ) , ( 0,5 ) \}$, $g ( x ) = | x - 5 | \text { find } g ( - 5 ) , g ( 0 ) , \text { and } g ( 5 )$, $g ( x ) = | x | - 5 ; \text { find } g ( - 5 ) , g ( 0 ) , \text { and } g ( 5 )$, $g ( x ) = | 2 x - 3 | ; \text { find } g ( - 1 ) , g ( 0 ) , \text { and } g \left( \frac { 3 } { 2 } \right)$, $g ( x ) = 3 - | 2 x | ; \text { find } g ( - 3 ) , g ( 0 ) , \text { and } g ( 3 )$, $f ( x ) = 2 x - 3 ; \text { find } f ( - 2 ) , f ( 0 ) , \text { and } f ( x - 3 )$, $f ( x ) = 5 x - 1 ; \text { find } f ( - 2 ) , f ( 0 ) , \text { and } f ( x + 1 )$, $g ( x ) = \frac { 2 } { 3 } x + 1 ; \text { find } g ( - 3 ) , g ( 0 ) , \text { and } f ( 9 x + 6 )$, $g ( x ) = - \frac { 3 } { 4 } x - \frac { 1 } { 2 } ; \text { find } g ( - 4 ) , g ( 0 ) , \text { and } g ( 6 x - 2 )$, $g ( x ) = x ^ { 2 } ; \text { find } g ( - 5 ) , g ( \sqrt { 3 } ) , \text { and } g ( x - 5 )$, $g ( x ) = x ^ { 2 } + 1 ; \text { find } g ( - 1 ) , g ( \sqrt { 6 } ) , \text { and } g ( 2 x - 1 )$, $f ( x ) = x ^ { 2 } - x - 2 ; \text { find } f ( 0 ) , f ( 2 ) , \text { and } f ( x + 2 )$, $f ( x ) = - 2 x ^ { 2 } + x - 4 ; \text { find } f ( - 2 ) , f \left( \frac { 1 } { 2 } \right) , \text { and } f ( x - 3 )$, $h ( t ) = - 16 t ^ { 2 } + 32 ; \text { find } h \left( \frac { 1 } { 4 } \right) , h \left( \frac { 1 } { 2 } \right) , \text { and } h ( 2 a - 1 )$, $h ( t ) = - 16 t ^ { 2 } + 32 ; \text { find } h ( 0 ) , h ( \sqrt { 2 } ) , h ( 2 a + 1 )$, $f ( x ) = \sqrt { x + 1 } - 2 \text { find } f ( - 1 ) , f ( 0 ) , f ( x - 1 )$, $f ( x ) = \sqrt { x - 3 } + 1 ; \text { find } f ( 12 ) , f ( 3 ) , f ( x + 3 )$, $g ( x ) = \sqrt { x + 8 } ; \text { find } g ( 0 ) , g ( - 8 ) , \text { and } g ( x - 8 )$, $g ( x ) = \sqrt { 3 x - 1 } ; \text { find } g \left( \frac { 1 } { 3 } \right) , g \left( \frac { 5 } { 3 } \right) , \text { and } g \left( \frac { 1 } { 3 } a ^ { 2 } + \frac { 1 } { 3 } \right)$, $f ( x ) = x ^ { 3 } + 1 ; \text { find } f ( - 1 ) , f ( 0 ) , f \left( a ^ { 2 } \right)$, $f ( x ) = x ^ { 3 } - 8 ; \text { find } f ( 2 ) , f ( 0 ) , f \left( a ^ { 3 } \right)$, $f ( x ) = 2 x - 3 ; \text { find } x \text { where } f ( x ) = 25$, $f ( x ) = 7 - 3 x ; \text { find } x \text { where } f ( x ) = - 27$, $f ( x ) = 2 x + 5 ; \text { find } x \text { where } f ( x ) = 0$, $f ( x ) = - 2 x + 1 ; \text { find } x \text { where } f ( x ) = 0$, $g ( x ) = 6 x + 2 ; \text { find } x \text { where } g ( x ) = 5$, $g ( x ) = 4 x + 5 ; \text { find } x \text { where } g ( x ) = 2$, $h ( x ) = \frac { 2 } { 3 } x - \frac { 1 } { 2 } ; \text { find } x \text { where } h ( x ) = \frac { 1 } { 6 }$, $h ( x ) = \frac { 5 } { 4 } x + \frac { 1 } { 3 } ; \text { find } x \text { where } h ( x ) = \frac { 1 } { 2 }$. 3. Domain: ; range: ; function: yes, 29. If you need an answer fast, you can always count on Google. The students look at graphs containing dots and decide rather or not the dots form a linear or nonlinear relationship. Domain: ; range: $[2, )$; function: yes, 15. Here we put an arrow on the ends of our lines to indicate that this set of ordered pairs continues without bounds. /SM 0.02 9. Answer: the output from the function g when the input is 7. 2?7Co?s[OC7>-o~?_/O>}w7$T']*Y)Q(~5s[e>Os~F}>5m&hJ1/W\sCJq/W\3HrI)rq375G9%%k7~O9i5e~~Ys3fn?*7VYsnOS37fhmj)4R*7a~W.O|a-F1gs/9%Vy>5DD{d-J?=95:'>)S}wxBsf/O|S|ftn~}Qh/fq(4M~BsZm %o(5nU/ <> We also acknowledge previous National Science Foundation support under grant numbers 1246120, 1525057, and 1413739. Then determine whether each relation is a Do my homework for me . It is a function since no two ordered pairs have the same domain or x-value. 10. The ordered pair $(x, y)$ represents the position of points relative to the origin. Solve Now. Legal. 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. Recall that when evaluating, it is a best practice to begin by replacing the variables with parentheses and then substitute the appropriate values. Consider an aeroplane moving at a velocity of 500 km per hour. Given the graph, determine the domain and range and state whether or not it is a function: Domain: $(,15]$; range:; function: no. After that, check whether each input value has a corresponding out value. The students look at 20 different x y tables and decide rather the ordered pairs form a linear or nonlinear relationship. <> xXnF}-p(p#YBc),Iiy[ 9^:{wqs k8trv-@, Ls?[^~{;%_&d~tfn>C8Mg*d!?M'WHiRK w A! There's more to your application than just filling out the forms. The first number is called the $x$-coordinate, and the second number is called the $y$-coordinate. In the following exercises, evaluate the function: a. g(h2) b. g(x + 2) c. g(x) + g(2). The solutions to $x = |y| + 1$, on the other hand, have values in the domain that correspond to two elements in the range. $\begin{aligned} f ( \color{Cerulean}{- 2}\color{Black}{ )} & = \sqrt { 2 ( \color{Cerulean}{- 2}\color{Black}{ )} + 4 } = \sqrt { - 4 + 4 } = \sqrt { 0 } = 0 \\ f ( \color{Cerulean}{0}\color{Black}{ )} & = \sqrt { 2 ( \color{Cerulean}{0}\color{Black}{ )} + 4 } = \sqrt { 0 + 4 } = \sqrt { 4 } = 2 \\ f ( \color{Cerulean}{\frac { 1 } { 2 } a ^ { 2 } - 2}\color{Black}{ )} & = \sqrt { 2( \color{Cerulean}{ \frac { 1 } { 2 } a ^ { 2 } - 2}\color{Black}{)} + 4 } = \sqrt { a ^ { 2 } - 4 + 4 } = \sqrt { a ^ { 2 } } = | a | \end{aligned}$, $f (2) = 0,\: f (0) = 2,\: f \left( \frac { 1 } { 2 } a ^ { 2 } - 2 \right)= |a|$. How will the Relations and Functions Worksheet with Answer Key (PDF) help you?The learners will know if a given problem or situation is a relation or a function. Then determine the domain and range. The solution sets of each equation will form a relation consisting of infinitely many ordered pairs. THIS APP IS THE BEST ONE EVER! 3. f-1 (x) = (9x/5) + 32 and the inverse is a function also. Answer. 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. 8. Each one has model problems worked out step by step, practice problems, as well as challenge questions at the sheets end. 1. We can easily determine whether or not an equation represents a function by performing the vertical line test on its graph. <>>> endobj /Creator () z|OgYG;,_78}:<9}CJ` t\qF_W&]~~'7%EX6hqX=v$ \FLU/)|BtsS*q\B+oF,k=eI)B1tr6h(D Vocabulary on relations, functions, domain, range, and vertical line test. 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. |E[v%D '_s;.C\{ b/01w$}1$>(EpyQx~_E6( yO-ve_v64> zR.,b EenTZU<8[o,T(%*pHB %ZqiCX|@B; -6c\)xN8} dgK|!OJn-)J8e1$>XFZk4:c[6\0dY4i\W+H}#s.v.9_ 6!jW3bsFqPYb:h C8Ejp3+t 1,WC?d`}!*/V;7j @T1yDF,5M=]nOnD; Form a relation from A to B to show whether the students belong to any of the four sections. 7) Functions are often named with different letters; some common names for functions are $f, g, h, C$, and $R$. Also mention whether this relation is a function or not. The LibreTexts libraries arePowered by NICE CXone Expertand are supported by the Department of Education Open Textbook Pilot Project, the UC Davis Office of the Provost, the UC Davis Library, the California State University Affordable Learning Solutions Program, and Merlot. What is his income if he does not sell any cars in one month? I suggest using this as a note guide during the lesson. To check if a relation is a function, given a mapping diagram of the relation, use the following criterion: 1. 1A system with two number lines at right angles specifying points in a plane using ordered pairs $(x, y)$. 'y`u#$u:x7K#^o-6o%z}'It DOI^=--g@BB*V]& \>l w)y(K$D Zs&XI g"Dv+zZN7Oo,\u4BS\eYK.}%D\pV)UO^>-W3ud>JS%YE4n:P?ta\`UR;2M[!m?f4z+ao6>}khBqjY]~\ X+>XZC;I!4j|um=#b5>v5{umK)V+$6 Solving math equations can be challenging, but it's also a great way to improve your problem-solving skills. Let's try the best Worksheet 4.2 relations and functions answer key. 4 0 obj Review. 0000001693 00000 n Save money by purchasing. Functions and relations worksheet answer key Key. A function is a relation in which each element of the domain is paired with EXACTLY one element of the range. endstream endobj 35 0 obj <>stream 4. /Contents 11 0 R $f ( x + h ) = x ^ { 3 } + 3 h x ^ { 2 } + 3 h ^ { 2 } x + h ^ { 3 }$, 9. stream We provide you year-long structured coaching classes for CBSE and ICSE Board & JEE and NEET entrance exam preparation at affordable tuition fees, with an exclusive session for clearing doubts, ensuring that neither you nor the topics remain unattended. 1. << Given values for x in the domain, we can quickly calculate the corresponding values in the range. 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. { "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.