function and relation worksheet with answer key

12The set consisting of all of the second components of a relation. trailer Relations and Functions tate the domain and range of each relation. Evaluate the function when x = 3, x = 0, and x = -2. Given the graph, determine the domain and range and state whether or not it is a function: Domain: \((,15]\); range:\(\); function: no. To define, a function is a binary process or relation that makes each element of one set somehow related to exactly one element from the second one. But, it's a very good app. Explore math program relation is a function. Find out whether the following statements are true or false. endobj /SMask /None>> If it is a function, give the domain and range. A relation is a set of one or more ordered pairs. The uploaded images may not be edited.a hard copy (workshee. ~=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. 6. % (b) {(2, 1), (4, 2), (6, 3), (8, 4), (10, 5), (12, 6), (14, 7)} is not a function. >> Then. Included are 5 different task sheets. 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. 6 0 obj Solving math equations can be challenging, but it's also a great way to improve your problem-solving skills. 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. Find \(f (8), f (0)\), and \(f (8)\). <> For example, use the function \(h\) defined by \(h (x) = \frac{1}{2} x 3\)to evaluate for \(x\)-values in the set \(\{2, 0, 7\}\). 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. /CA 1.0 11 0 obj An expression is considered to be unambiguous or well-defined when the definition of the same allocates a unique value or interpretation. Use the function to determine the value of the car when it is \(4\) years old. 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. [/Pattern /DeviceRGB] \(g ( - 1 ) = 5 , g ( 0 ) = 3 , g \left( \frac { 3 } { 2 } \right) = 0\), 5. Find \(x\) where \(g (x) = 5, g (x) = 0\), and \(g (x) = 10\). Given the graph of \(h\), find \(x\) where \(h(x)=-4\). A relation is a set of one or more ordered pairs. 4.0,` 3p H.Hi@A> Relationships are represented as ordered pairs, tables, mapping diagrams, and graphs. xwTS7" %z ;HQIP&vDF)VdTG"cEb PQDEk 5Yg} PtX4X\XffGD=H.d,P&s"7C$ Feel free to download and enjoy these free worksheets on functions and relations. As we can see, any vertical line will intersect the graph of \(y=|x|2\) only once; therefore, it is a function. We can visually display any relation of this type on a coordinate plane by plotting the points. 1. stream Save money by purchasing. 0000019902 00000 n Simplify \(\frac { c ( x + h ) - c ( x ) } { h }\) given \(c ( x ) = 3 x + 1\). xXnF}-p(p#YBc),Iiy[ 9^:{wqs k8trv-@, Ls?[^~{;%_&d~tfn>C8Mg*d!?M'WHiRK w A! Consider n (A) = m and n (B) = n. Find out the number of relations (non-empty) that can be predicted from A to B. 38 0 obj <>stream 8 0 obj Determine the domain and range of the following relation and state whether it is a function or not: \(\{(1, 4), (0, 7), (2, 3), (3, 3), (4, 2)\}\). Domain: \(\); range: \(\); function: yes, 29. endobj In the context of algebra, the relations of interest are sets of ordered pairs \((x, y)\) in the rectangular coordinate plane. P x Q provides number of relations to be 64. endobj 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. For instance, f(x) = root over x is an undefined function when the value of x is negative. So, this relation is a function as well. This 12-question algebra 1 worksheet provides students with practice working with relations and functions. You can either choose the colors for them to make it unified across the classroom or let them choose their own. >> There's more to your application than just filling out the forms. 6. Graph the given set of points, then answer the questions that follow. Now, lets begin with the relations functions worksheet. If you're looking for a quick delivery, we've got you covered. 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. Also sketch a graph for each equation. Not all relations are functions, and not all functions are relations. Set Up. Our team is dedicated to providing the best possible service to our customers. Then the student identifies the domain and range of each example. 4. Special relations where every \(x\)-value (input) corresponds to exactly one \(y\)-value (output) are called functions. /F8 8 0 R Find the value of x that will make this relation a function. \(\begin{aligned} g ( \color{Cerulean}{- 2}\color{Black}{ )} & = ( \color{Cerulean}{- 2}\color{Black}{ )} ^ { 2 } = 4 \\ g ( \color{Cerulean}{\frac { 1 } { 2 }}\color{Black}{)} & = ( \color{Cerulean}{\frac { 1 } { 2 }} \color{Black}{)} ^ { 2 } = \frac { 1 } { 4 } \\ g (\color{Cerulean}{ x + h}\color{Black}{ )} & = ( \color{Cerulean}{x + h}\color{Black}{ )} ^ { 2 } = x ^ { 2 } + 2 x h + h ^ { 2 } \end{aligned}\), \(g (2) = 4,\: g ( \frac{1}{2} ) = \frac{1}{4} ,\: g (x + h) = x^{2} + 2xh + h^{2}\), At this point, it is important to note that, in general, \(f (x + h) f (x) + f (h)\). Chapter 1 - Analyzing Functions Answer Key CK-12 Math Analysis Concepts 1 1.1 Relations and Functions Answers 1. 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 Questions include sets of ordered pairs, tables, mapping diagrams, and graphs. This bundle contains 9 worksheets on Functions.Worksheet 1: Finding domain and range from graphsStandard. /Font << Then graph the function and its inverse. If you wish to get more such worksheets of other maths chapters, please make sure to download the Vedantu app today! Then determine whether each relation is a Do my homework for me . Simplify \(\frac { p ( x + h ) - p ( x ) } { h }\) given \(p ( x ) = 7 x - 3\). Use the graph to find the corresponding \(y\)-values where \(x = 8, 0\), and \(8\). 11The set consisting of all of the first components of a relation. Use the function to determine the salespersons income if he sells \(3\) cars this month. Write each of the following as a relation, state the domain and range, then determine if it is a function. The rectangular coordinate system1 consists of two real number lines that intersect at a right angle. Evaluate the inverse and also rule out whether the same is a function or not. Who is credited with the introduction of the notation \(y = f (x)\)? Ans. stream TPT empowers educators to teach at their best. 4. 0000000750 00000 n 14 0 obj If you need an answer fast, you can always count on Google. a. b. Sometimes the output is given and we are asked to find the input. Illustrate the travelled distance in the form of function t in hours. /Type /Catalog The correspondence between the domain and range of each can be pictured as follows: Notice that every element in the domain of the solution set of \(y = |x| 2\) corresponds to only one element in the range; it is a function. Domain. After that, check whether each input value has a corresponding out value. %S%m7$3g3: $ Ymk XvH3a, @~^6=Xfw5q@S3JQFLf4 yyE j|8 ] pq Ha L8DCsK4rqf.,jnghC-S_Jh. 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. 11. So helpful with my homework. Mathematics is a way of dealing with tasks that involves numbers and equations. Range = {4, 16, 25, 36} and Domain = {-2, 2, 4, 5, 6}, 10. Relations Expressed as Graphing. We can easily determine whether or not an equation represents a function by performing the vertical line test on its graph. Each one has model problems worked out step by step, practice problems, as well as challenge questions at the sheets end. There is then practice on these topics. 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. 120 students are studying in class 11 divided among four sections. 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/ What was the value of the car in \(2005\)? Here we put an arrow on the ends of our lines to indicate that this set of ordered pairs continues without bounds. The ordered pair \((x, y)\) represents the position of points relative to the origin. Example: Decide whether the following relations are a function. /GSa 4 0 R 5. 1. hs2z\nLA"Sdr%,lt (d) P = (1, 2, 3} and Q = {e, f}. Find \(f ( 0 ) , f ( 2 )\), and \(f ( 4 )\). Substitute \(f (x)\) with \(27\) and solve. 24. 4. Often, we can determine the domain and range of a relation if we are given its graph. 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. In other words, replace the variable with the value given inside the parentheses. A function, on the other hand, is a relation that produces one output for each given input. 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. 12 graphs.Worksheet 2: Finding range given domainRiddle. Given the graph of a function \(g\), find the \(x\)-values: 2. Review. This is because a person has just one height value at any time in their life. 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. ' 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]. For example, both the algebraic equations \(y = |x| 2\) and \(x = |y| + 1\) define relationships between \(x\) and \(y\). Each one has model problems worked out step by step, practice problems, as well as challenge questions at the sheets end. Real World Math Horror Stories from Real encounters. In particular, the x-value \(4\) corresponds to two y-values \(3\) and \(3\). D 25. 6 0 obj Simplify \(\frac { q ( x + h ) - q ( x ) } { h }\) given \(q ( x ) = a x\). It could also be used as a worksheet for homework. The \(x\)- and \(y\)-axes break the plane into four regions called quadrants7, named using roman numerals I, II, III, and IV, as pictured. Plus each one comes with an answer key. But for the -4 the range is -3 so i did not put that in. Is the Equation a Function? \(g (10) = 10\) and \(g (5) = 10 ; g (5) = 5\) and \(g (10) = 5\). 0000006193 00000 n Domain: \([1,5]\); range: \([3,3]\); function: no. \(g (2) = 5, g (3) = 4\) and \(g (1) = 4 , g (5) = 4\) and \(g (1) = 4\), 7. Typically, the coordinates are related by a rule expressed using an algebraic equation. \(\begin{array} { c } { f ( x ) = 5 x + 7 }\\\color{Cerulean}{\downarrow}\quad\quad\quad\:\:\: \\ { 27 = 5 x + 7 } \\ { 20 = 5 x } \\ { 4 = x } \end{array}\). Therefore, \(f (4) = 27\). <>>> A visual representation of a pop machine and the connection with functions. 3. Two Items Included. If any vertical line intersects the graph more than once, then the graph does not represent a function. 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. Free trial available at KutaSoftware.com. Given the graph of \(g\), find \(x\) where \(g(x)=2\). It not only scans your equation and gives a mathematical answer, but it gives you reasoning behind how it's solved too! 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! 2The horizontal number line used as reference in a rectangular coordinate system. 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. 0000047318 00000 n /Resources 13 0 R As pictured, the \(x\)-value \(3\) corresponds to more than one \(y\)-value. /Pages 3 0 R 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. 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. 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. 2 0 obj (When solving an equation for y in terms of x, if two or more values of y can be obtained for a given x, then the equation is NOT a function. We can visually identify functions by their graphs using the vertical line test15. FV>2 u/_$\BCv< 5]s.,4&yUx~xw-bEDCHGKwFGEGME{EEKX,YFZ ={$vrK The value of a is 0.90 and b is 24.5, 11. <> Very interesting and supportful Thank you , haven't gotten one guest one wrong yet, really good app for homework. Relations Expressed as Graphing. The solution sets of each equation will form a relation consisting of infinitely many ordered pairs. Math Worksheet 1- FUNCTION versus RELATION Relations . Great resource to use as homework or independent work.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 A, This is a one-sided fill-in-the-blank notes page on differentiating between a function and a relation, exploring the 5 types of functions/relations, and then finding the domain and range of each. Instead of writing their answers, students will color them! satisfaction rating 4.7/5; Stay in the Loop 24/7 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. Domain: \((, 0]\); range: \([1, )\); function: yes, 19. /Contents 11 0 R If you randomly selected a group of people, you would observe a correlation between their ages and height. \(f (8) = 10, f (0) = 0, f (8) = 10\). Free printable worksheets (pdf) with answer keys on Algebra I, Geometry, Trigonometry, Algebra II, and Calculus. P x P is a Cartesian product having nine elements. Equip 8th grade and high school students with this printable practice set to assist them in analyzing relations expressed as ordered pairs, mapping diagrams, input-output tables, graphs and equations to figure out which one of these relations are functions based on the pairing of the domain (x) and range (y). Rational Numbers Between Two Rational Numbers, XXXVII Roman Numeral - Conversion, Rules, Uses, and FAQs, Find Best Teacher for Online Tuition on Vedantu. 0000000016 00000 n Discovery-Based Worksheets have been specially designed to engage students in learnin, Attention 8th grade math teachers! %%EOF 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. 3. 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. The domain is \(\{1, 0, 2, 3, 4\}\) and the range is \(\{2, 3, 4, 7\}\). The best way to learn something new is to break it down into small, manageable steps. Posted: 7/3/17 so 50% off through 7/6/17, Do your students need practice graphing real world quadratics? /ca 1.0 Then they share a relationship and can be written as an ordered pair (x, y). Here we separate the domain (x-values), and the range (y-values), and depict the correspondence between the values with arrows. Ans. <> In what years was the car valued at \($4,000\)? A1vjp zN6p\W pG@ 3. 8Term used in honor of Ren Descartes when referring to the rectangular coordinate system. << Domain: \(\); range: \([1, 1]\); function: yes, 31. <>/ExtGState<>/XObject<>/ProcSet[/PDF/Text/ImageB/ImageC/ImageI] >>/MediaBox[ 0 0 612 792] /Contents 4 0 R/Group<>/Tabs/S/StructParents 0>> A vertical line can cross the graph of \(x=|y|+1\) more than once; therefore, it is not a function. Relations and Functions Worksheet Answer Key, Set P = {-2,0,2} and the remaining elements are {(-2,-2), (-2,2), (0,-2), (0,0), (2,-2), (2,0), (2,2)}. 12 graphs.Worksheet 2: Finding range given domainRiddle. 12. Research and discuss the life and contributions of Ren Descartes. 5. Find \(x\) where \(g (x) = 5, g (x) = 4\), and \(g (x) = 4\). Let's try the best Worksheet 4.2 relations and. 2. Determine the domain and range and state whether the relation is a function or not. 10. Of special interest are relations where every \(x\)-value corresponds to exactly one \(y\)-value. \(f ( 0 ) = - 2 , f ( 2 ) = 0 , f ( x + 2 ) = x ^ { 2 } + 3 x\), 13. 4. To determine whether a given relation is a function or not, one needs first to find out the input values, then the output values. Already known sets of ordered pairs are (-2, 0) and (0, 2). It is a relation.) 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. Find the range and domain of a real function f represented by f(x) = root over (x -1). Map the following relation and also mention the domain and range. Domain: \(\); range: \(\); function: yes, 23. If this doesn't solve the problem, visit our Support Center . Explain your reasoning. Relation. Given the graph of \(g(x)\), find \(g(8), g(0)\), and \(g(8)\). >> PERIOD. 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. Functions Worksheet 1 For exercises 13-18, determine whether each relation is a function. Algebra 2 relations and functions worksheet answers can be a useful tool for these scholars. '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 >> >> /Filter /FlateDecode If an algebraic equation defines a function, then we can use the notation \(f (x) = y\). Relations and function worksheets help students to understand concepts of variable functions, calculus, probability and connect them to the reasoning part of mathematics. Answers vary, should mention how the function does not always have the same output for a given input. /Pattern << Functions and Relations Worksheet Decide whether the graph represents y as a function of x. DATE. What is his income if he does not sell any cars in one month? 13. Not all relations are functions, and not all functions are relations. <> Feel free to download and enjoy these free worksheets on functions and relations. >> /Parent 3 0 R 1. The maximum \(y\)-value is \(3\) and the minimum is \(3\); hence, the range consists of \(y\)-values in the interval \([3,3]\). 13 0 obj 1A system with two number lines at right angles specifying points in a plane using ordered pairs \((x, y)\). 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. After that, check whether each input value has a corresponding out value. Therefore, the domain consists of all \(x\)-values in the interval \([8,)\). R is a relation {(6,4), (8,-1), (x,7), (-3,-6)}. 2. Make use of this worksheet to get a better understandingof relations and functions. << >> The relation is a function. 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/` /AIS false 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. \(g (2) = 4, g (1) = 3, g (0) = 4\), 9. Ex 5. As every value of x has a different value of y; it is a function. Students will determine if the given relations (shown in mapping diagrams, function tables, graphs, and pairs of points) are a function or not. Avg. Relations and Functions tate the domain and range of each relation. Functions and relations answer key - Section 5.2 Defining Relations and Functions. (a) True (b) False (c) True (d) True (e) False, 9. <> Given \(f ( x ) = \sqrt { 2 x + 4 }\), find \(f (2), f (0)\), and \(f \left( \frac { 1 } { 2 } a ^ { 2 } - 2 \right)\). 0000001728 00000 n A function is a relation in which each element of the domain is paired with EXACTLY one element of the range. 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. Yes 3. << 7. The intersection of the two axes is known as the origin6, which corresponds sto the point \((0, 0)\). You can also use mathematical representation for actual scenarios. Form a relation from A to B to show whether the students belong to any of the four sections. \(f ( x + h ) = x ^ { 3 } + 3 h x ^ { 2 } + 3 h ^ { 2 } x + h ^ { 3 }\), 9. With the definition of a function comes special notation. /Type /Page \(f ( - 1 ) = - 2 , f ( 0 ) = - 1 , f ( x - 1 ) = \sqrt { x } - 2\), 17. Are you covering Functions and Linear Equations and need a little break? 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. If the function is f (x)= 6x-27, and the domain is {-5, 3, 15, 17}, then find the range. For example, the ordered pair \((4, 3)\) represents the position \(4\) units to the left of the origin, and \(3\) units above in the second quadrant. 39. (e) {(x,y) | x=3 and y is a real number} is both a function and relation. The zip file contains the worksheet in both .doc format as well as in .pdf. These multiple representation tasks help students see the connections between the equation, table of values, and graph. \(\frac { f ( x + h ) - f ( x ) } { h }\). \(\{ ( 3,1 ) , ( 5,2 ) , ( 7,3 ) , ( 9,4 ) , ( 12,4 ) \}\), \(\{ ( 2,0 ) , ( 4,3 ) , ( 6,6 ) , ( 8,6 ) , ( 10,9 ) \}\), \(\{ ( 7,5 ) , ( 8,6 ) , ( 10,7 ) , ( 10,8 ) , ( 15,9 ) \}\), \(\{ ( 1,1 ) , ( 2,1 ) , ( 3,1 ) , ( 4,1 ) , ( 5,1 ) \}\), \(\{ ( 5,0 ) , ( 5,2 ) , ( 5,4 ) , ( 5,6 ) , ( 5,8 ) \}\), \(\{ ( - 3,1 ) , ( - 2,2 ) , ( - 1,3 ) , ( 0,4 ) , ( 0,5 ) \}\), \(g ( x ) = | x - 5 | \text { find } g ( - 5 ) , g ( 0 ) , \text { and } g ( 5 )\), \(g ( x ) = | x | - 5 ; \text { find } g ( - 5 ) , g ( 0 ) , \text { and } g ( 5 )\), \(g ( x ) = | 2 x - 3 | ; \text { find } g ( - 1 ) , g ( 0 ) , \text { and } g \left( \frac { 3 } { 2 } \right)\), \(g ( x ) = 3 - | 2 x | ; \text { find } g ( - 3 ) , g ( 0 ) , \text { and } g ( 3 )\), \(f ( x ) = 2 x - 3 ; \text { find } f ( - 2 ) , f ( 0 ) , \text { and } f ( x - 3 )\), \(f ( x ) = 5 x - 1 ; \text { find } f ( - 2 ) , f ( 0 ) , \text { and } f ( x + 1 )\), \(g ( x ) = \frac { 2 } { 3 } x + 1 ; \text { find } g ( - 3 ) , g ( 0 ) , \text { and } f ( 9 x + 6 )\), \(g ( x ) = - \frac { 3 } { 4 } x - \frac { 1 } { 2 } ; \text { find } g ( - 4 ) , g ( 0 ) , \text { and } g ( 6 x - 2 )\), \(g ( x ) = x ^ { 2 } ; \text { find } g ( - 5 ) , g ( \sqrt { 3 } ) , \text { and } g ( x - 5 )\), \(g ( x ) = x ^ { 2 } + 1 ; \text { find } g ( - 1 ) , g ( \sqrt { 6 } ) , \text { and } g ( 2 x - 1 )\), \(f ( x ) = x ^ { 2 } - x - 2 ; \text { find } f ( 0 ) , f ( 2 ) , \text { and } f ( x + 2 )\), \(f ( x ) = - 2 x ^ { 2 } + x - 4 ; \text { find } f ( - 2 ) , f \left( \frac { 1 } { 2 } \right) , \text { and } f ( x - 3 )\), \(h ( t ) = - 16 t ^ { 2 } + 32 ; \text { find } h \left( \frac { 1 } { 4 } \right) , h \left( \frac { 1 } { 2 } \right) , \text { and } h ( 2 a - 1 )\), \(h ( t ) = - 16 t ^ { 2 } + 32 ; \text { find } h ( 0 ) , h ( \sqrt { 2 } ) , h ( 2 a + 1 )\), \(f ( x ) = \sqrt { x + 1 } - 2 \text { find } f ( - 1 ) , f ( 0 ) , f ( x - 1 )\), \(f ( x ) = \sqrt { x - 3 } + 1 ; \text { find } f ( 12 ) , f ( 3 ) , f ( x + 3 )\), \(g ( x ) = \sqrt { x + 8 } ; \text { find } g ( 0 ) , g ( - 8 ) , \text { and } g ( x - 8 )\), \(g ( x ) = \sqrt { 3 x - 1 } ; \text { find } g \left( \frac { 1 } { 3 } \right) , g \left( \frac { 5 } { 3 } \right) , \text { and } g \left( \frac { 1 } { 3 } a ^ { 2 } + \frac { 1 } { 3 } \right)\), \(f ( x ) = x ^ { 3 } + 1 ; \text { find } f ( - 1 ) , f ( 0 ) , f \left( a ^ { 2 } \right)\), \(f ( x ) = x ^ { 3 } - 8 ; \text { find } f ( 2 ) , f ( 0 ) , f \left( a ^ { 3 } \right)\), \(f ( x ) = 2 x - 3 ; \text { find } x \text { where } f ( x ) = 25\), \(f ( x ) = 7 - 3 x ; \text { find } x \text { where } f ( x ) = - 27\), \(f ( x ) = 2 x + 5 ; \text { find } x \text { where } f ( x ) = 0\), \(f ( x ) = - 2 x + 1 ; \text { find } x \text { where } f ( x ) = 0\), \(g ( x ) = 6 x + 2 ; \text { find } x \text { where } g ( x ) = 5\), \(g ( x ) = 4 x + 5 ; \text { find } x \text { where } g ( x ) = 2\), \(h ( x ) = \frac { 2 } { 3 } x - \frac { 1 } { 2 } ; \text { find } x \text { where } h ( x ) = \frac { 1 } { 6 }\), \(h ( x ) = \frac { 5 } { 4 } x + \frac { 1 } { 3 } ; \text { find } x \text { where } h ( x ) = \frac { 1 } { 2 }\).

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