2 0 obj %PDF-1.5 1 2 . Function. D 25. This relation is not a function. endobj 4 0 obj Lesson Directions. \(g ( - 1 ) = 5 , g ( 0 ) = 3 , g \left( \frac { 3 } { 2 } \right) = 0\), 5. Interactive simulation the most controversial math riddle ever! Given the graph of \(g(x)\), find \(g(8), g(0)\), and \(g(8)\). 13 0 obj Relations and function worksheets help students to understand concepts of variable functions, calculus, probability and connect them to the reasoning part of mathematics. 1. Simplify \(\frac { q ( x + h ) - q ( x ) } { h }\) given \(q ( x ) = a x\). Not all relations are functions, and not all functions are relations. D \R(BJIBxCKoo-J-}wwfvv5s9["%VA /F8 8 0 R Section 5.2 Defining Relations and Functions. O*?f`gC/O+FFGGz)~wgbk?J9mdwi?cOO?w| x&mf We can use the given ordered pair solutions to estimate all of the other ordered pairs by drawing a line through the given points. If you're looking for a quick delivery, we've got you covered. 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/` The first number is called the \(x\)-coordinate, and the second number is called the \(y\)-coordinate. 11The set consisting of all of the first components of a relation. 14. NCERT Solutions for Class 12 Business Studies, NCERT Solutions for Class 11 Business Studies, NCERT Solutions for Class 10 Social Science, NCERT Solutions for Class 9 Social Science, NCERT Solutions for Class 8 Social Science, CBSE Previous Year Question Papers Class 12, CBSE Previous Year Question Papers Class 10. This is a relations and functions worksheet. For instance, x is an object of set A and y is an object from set B. Introduction to New Material. Determine the domain and range of the following relation and state whether it is a function or not: \(\{(4, 3), (2, 6), (0, 3), (3, 5), (3, 7)\}\). This will be put in as a formative assessment grade. In this case, we interpret \(f(5) = 3\) as follows: Function notation streamlines the task of evaluating. 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. The set consisting of all of the first components of a relation, in this case the x-values, is called the domain11. 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. Section 3.1. endobj Domain = {-2, 0, 5}, Range = {-1, 3, 4}. Range. 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 \((x, y)\). Let's try the best Worksheet 4.2 relations and functions answer key. (d) P = (1, 2, 3} and Q = {e, f}. Explain your reasoning for each. /CA 1.0 startxref 1. As pictured, the \(x\)-value \(3\) corresponds to more than one \(y\)-value. An expression is considered to be unambiguous or well-defined when the definition of the same allocates a unique value or interpretation. Just print + go! 13. The domain of the graph of \(x=|y|+1\) consists of all x-values greater than or equal to \(1, [1,)\), and the range consists of all real numbers, \(=(,)\). Fast solutions. In what years was the car valued at \($4,000\)? /Pattern << 6. 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. The notation \(f (x)\) is read . 10. /CSpg /DeviceGray Graph the given set of points, then answer the questions that follow. Find \(x\) where \(g (x) = 3, g (x) = 0\), and \(g (x) = 2\). Then determine the domain and range. x y3 -4-52-7 -4-5 7A function is a relation in which each input has exactly one outputThe domain of the function is the set of all input values. We can also recognize functions as relations where no \(x\)-values are repeated. Answers vary, should mention how the function does not always have the same output for a given input. We have determined that the set of solutions to \(y = |x| 2\) is a function; therefore, using function notation we can write: \(\begin{aligned} y & = | x | - 2 \\ \color{Cerulean}{\downarrow} & \\ f ( x ) & = | x | - 2 \end{aligned}\). Find \(f (8), f (0)\), and \(f (8)\). Evaluate the function when x = 3, x = 0, and x = -2. 6 0 obj 3. x{|7>Z]-Ed]-lJVe;qN8v%vb;vnv$@ \CH(w This notation is used as follows: \(\begin{array} { l } { f ( x )\:\: =\:\:\: | x | - 2 } \\ { \:\:\:\:\:\downarrow \quad\quad\quad \downarrow } \\ { f ( \color{Cerulean}{- 5}\color{Black}{ )} = | \color{Cerulean}{- 5}\color{Black}{ |} - 2 = 5 - 2 = 3 } \end{array}\). (a) Relation {(2, 1), (5, 1), (8, 1), (11, 1), (14, 1), (17, 1)} is a function also. 2. >> Functions are compactly defined by an algebraic equation, such as \(f (x) = |x| 2\). Is the Equation a Function? Relationships are represented as ordered pairs, tables, mapping diagrams, and graphs. stream <> For instance, f(x) = root over x is an undefined function when the value of x is negative. <> The google activity may be edited if needed (add/delete questions, change answer type, etc.) 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. If you randomly selected a group of people, you would observe a correlation between their ages and height. In other words, replace the variable with the value given inside the parentheses. Explain your reasoning. 0000000813 00000 n THIS APP IS THE BEST ONE EVER! For instance, f(x) = root over x is an undefined function when the value of x is negative. A function is a relation in which each input x (domain) has only one output y(range). 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. \(f ( - 2 ) = - 7 , f ( 0 ) = - 3 , f ( x - 3 ) = 2 x - 9\), 7. 2. Explain to a beginning algebra student what the vertical line test is and why it works. How to Calculate the Percentage of Marks? \(\begin{array} { c } { f ( x ) = 5 x + 7 }\\\color{Cerulean}{\downarrow}\quad\quad\quad\:\:\: \\ { 27 = 5 x + 7 } \\ { 20 = 5 x } \\ { 4 = x } \end{array}\). 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. These multiple representation tasks help students see the connections between the equation, table of values, and graph. For example: \(\begin{aligned} h ( \color{Cerulean}{4 a ^ { 3 }}\color{Black}{ )} & = \frac { 1 } { 2 } ( \color{Cerulean}{4 a ^ { 3 } }\color{Black}{)} - 3 = 2 a ^ { 3 } - 3 \\ h ( \color{Cerulean}{2 x - 1}\color{Black}{ )} & = \frac { 1 } { 2 } ( \color{Cerulean}{2 x - 1}\color{Black}{ )} - 3 = x - \frac { 1 } { 2 } - 3 = x - \frac { 7 } { 2 } \end{aligned}\). 10A visual representation of a relation on a rectangular coordinate plane. You can also use mathematical representation for actual scenarios. The uploaded images may not be edited.a hard copy (workshee. Explore math program 12. 3. f-1 (x) = (9x/5) + 32 and the inverse is a function also. 8. The maximum \(y\)-value is \(3\) and the minimum is \(3\); hence, the range consists of \(y\)-values in the interval \([3,3]\). endobj Add another ordered pair to this relation that would make this not a function anymore. The set of \(x\)-values defines the domain and the set of \(y\)-values defines the range. Mathematics is a way of dealing with tasks that involves numbers and equations. Algebra frequently involves functions, and so the notation becomes useful when performing common tasks. It has so many equations and etc that it knows how to do, and has many advantages that other math apps do not. Worksheet on Relations and Functions. 5. xref Sometimes the output is given and we are asked to find the input. 6. 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A vertical line can cross the graph of \(x=|y|+1\) more than once; therefore, it is not a function. This 12-question algebra 1 worksheet provides students with practice working with relations and functions. Relations Expressed as Graphing. \(f ( - 1 ) = - 2 , f ( 0 ) = - 1 , f ( x - 1 ) = \sqrt { x } - 2\), 17. Practise Worksheet Relations and Functions, 3. Also sketch a graph for each equation. Holt Algebra 4.2 Relations and Functions PPT + Worksheet. 0000001084 00000 n If asked to find \(f(a)\), we substitute the argument \(a\) in for the variable and then simplify. Therefore, \(f (4) = 27\). Simplify \(\frac { g ( x + h ) - g ( x ) } { h }\) given \(g ( x ) = m x + b\). 0000001693 00000 n Consider the relations consisting of the seven ordered pair solutions to \(y = |x| 2 \)and \(x = |y| + 1\). There is exactly one output for every input. This is a relations and functions worksheet. endobj No, the input 2 has 2 output values. <>/ExtGState<>/XObject<>/ProcSet[/PDF/Text/ImageB/ImageC/ImageI] >>/MediaBox[ 0 0 612 792] /Contents 4 0 R/Group<>/Tabs/S/StructParents 0>> 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. Here \(f\) is the function name, and \(f (x)\) denotes the value in the range associated with the value x in the domain. LCM of 3 and 4, and How to Find Least Common Multiple, What is Simple Interest? 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. Already known sets of ordered pairs are (-2, 0) and (0, 2). We can visually display any relation of this type on a coordinate plane by plotting the points. Not all relations are functions, and not all functions are relations. 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. 0 <>>> Given \(f (x) = 5x + 7\), find \(x\) where \(f (x) = 27\). /SMask /None>> Are you looking for a comprehensive set of worksheets to introduce functions to your students? 1 0 obj [ -c R!z"^Ow,c 8. )feOJeB_~n For example, both the algebraic equations \(y = |x| 2\) and \(x = |y| + 1\) define relationships between \(x\) and \(y\). Are you getting the free resources, updates, and special offers we send out every week in our teacher newsletter? Given any function defined by \(h(x) = y\), the value \(x\) is called the argument of the function17. Worksheet 4.2 relations and functions answer key - Apps can be a great way to help students with their algebra. 24. Then. Given \(g ( x ) = x ^ { 2 }\), find \(g (2), g ( \frac{1}{2} )\), and \(g (x + h)\). 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. Conduct an Internet search for the vertical line test, functions, and evaluating functions. We begin with 2 on the y-axis and then read the corresponding x-value. 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. 10 0 obj \(f ( 0 ) = - 2 , f ( 2 ) = 0 , f ( x + 2 ) = x ^ { 2 } + 3 x\), 13. Here we separate the domain (x-values), and the range (y-values), and depict the correspondence between the values with arrows. 6 . 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. stream endobj 0000000943 00000 n Add highlights, virtual manipulatives, and more. \(f (8) = 10, f (0) = 0, f (8) = 10\). 2 X. Forex weekly compounding profit calculator, How does combining like terms help to simplify expressions, How to calculate compound interest for 20 years, How to calculate the percentage of a number in google sheets, How to solve a system of inequalities word problem, Improper fractions to mixed numbers worksheet, What is the difference between a cas and non cas calculator. \(g ( - 3 ) = - 1 , g ( 0 ) = 1 , g ( 9 x + 6 ) = 6 x + 5\), 9. 7. Print a copy of the Answer Key: Think FUNCTIONally printable for your use. Find \(f ( 0 ) , f ( 2 )\), and \(f ( 4 )\). Look no further! 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 \(2, [2,)\). 1. 7) >> Given the linear function defined by \(f(x)=2x-5\), simplify the following. Recall that when evaluating, it is a best practice to begin by replacing the variables with parentheses and then substitute the appropriate values. Then determine whether each relation is a Do my homework for me . 6. Domain: Range: Function: Domain: Range: 15 _ Function: Domain. This helps with the order of operations when simplifying expressions. 1. Ans. [/Pattern /DeviceRGB] 2. Domain: \(\); range: \([8, ]\); function: yes, 1. 2. . After that, check whether each input value has a corresponding out value. 17The value or algebraic expression used as input when using function notation. Make use of this worksheet to get a better understandingof relations and functions. These math worksheets on introducing functions are exactly what you need. Feel free to download and enjoy these free worksheets on functions and relations. Free to use Step-by-step explanations for every solution Exclusive how-to animations Sc. 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. It not only scans your equation and gives a mathematical answer, but it gives you reasoning behind how it's solved too! Find \(x\) where \(g (x) = 5, g (x) = 4\), and \(g (x) = 4\). There are many \(x\)-values in the domain that correspond to two \(y\)-values. noncommercial purposes and are not distributed outside of a specific teacher's classroom. The student first takes notes on the definition of a relation and a function. 0000000016 00000 n \(g (2) = 4, g (1) = 3, g (0) = 4\), 9. xULF] PERIOD. Plus each one comes with an answer key. Review. endobj Included are 5 different task sheets. endobj 2x + y . Each one has model problems worked out step by step, practice problems, as well as challenge questions at the sheets end. 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. (a) True (b) False (c) True (d) True (e) False, 9. Title: Infinite Algebra 1 - Continuous Relations Created Date: You must try to solve the questions on your own and later check it with the given practice worksheet relations and functions answer key. 4 0 obj We offer the fastest, most expert tutoring in the business. What are the Types of Functions in Mathematics? It is perfect for, This product includes a 10-question assignment with practice over finding domain and range of relations and functions. 0000000750 00000 n /Resources 13 0 R 9. 11 0 obj If all these pointers match, then the relation is proved to be a function. . 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 Domain: \(\{ - 4 , - 1,0,2,3 \}\); range: \(\{ 1,2,3 \}\); function: yes, 9. Analyzing Relations and Functions KEY. /Type /ExtGState 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/ Solve Now. If so, state the domain and range. As a check, we can evaluate \(f (4) = 5 (4) + 7 = 27\). Domain: \(\); range: \(\); function: yes, 29. Students will find the range given the domain.Worksheet 3: Function rules and table of valuesStandard. For relations consisting of points in the plane, the domain is the set of all \(x\)-values. Find \(x\) where \(g (x) = 4, g (x) = 3\), and \(g (x) = 4\). Free worksheet(pdf) and answer key on distinguishing functions from relations, stating domain and range and more. Questions include sets of ordered pairs, tables, mapping diagrams, and graphs. Try to test your learnings in the exercises below. Algebra 2 relations and functions worksheet answers can be a useful tool for these scholars. endobj 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. /PCSp 5 0 R 11 0 obj 4. There's more to your application than just filling out the forms. So, this relation is a function as well. 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. 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. 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. Legal. 5 0 obj Worksheet 4.1 relations and functions answer key. /SA true DATE. In what year was the value of the car at a minimum? 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). The students will crea, In this concept-building, evaluating and identifying functions discovery worksheet, students will be able to evaluate functions for specific values; represent relations as a set of ordered pairs, table, graph, and mapping; and identify functions versus relations. Functions and relations answer key - Section 5.2 Defining Relations and Functions. Posted: 7/3/17 so 50% off through 7/6/17, Do your students need practice graphing real world quadratics? RELATIONS & FUNCTIONS Worksheet. This bundle contains 9 worksheets on Functions.Worksheet 1: Finding domain and range from graphsStandard. 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. 39. 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 \(\begin{aligned} g ( \color{Cerulean}{- 2}\color{Black}{ )} & = ( \color{Cerulean}{- 2}\color{Black}{ )} ^ { 2 } = 4 \\ g ( \color{Cerulean}{\frac { 1 } { 2 }}\color{Black}{)} & = ( \color{Cerulean}{\frac { 1 } { 2 }} \color{Black}{)} ^ { 2 } = \frac { 1 } { 4 } \\ g (\color{Cerulean}{ x + h}\color{Black}{ )} & = ( \color{Cerulean}{x + h}\color{Black}{ )} ^ { 2 } = x ^ { 2 } + 2 x h + h ^ { 2 } \end{aligned}\), \(g (2) = 4,\: g ( \frac{1}{2} ) = \frac{1}{4} ,\: g (x + h) = x^{2} + 2xh + h^{2}\), At this point, it is important to note that, in general, \(f (x + h) f (x) + f (h)\). A function is a relation in which each element of the domain is paired with EXACTLY one element of the range. Special relations where every \(x\)-value (input) corresponds to exactly one \(y\)-value (output) are called functions. \(\begin{array} { c } { h ( \color{Cerulean}{- 2}\color{Black}{ )} = \frac { 1 } { 2 } ( \color{Cerulean}{- 2}\color{Black}{ )} - 3 = - 1 - 3 = - 4 } \\ { h ( \color{Cerulean}{0}\color{Black}{ )} = \frac { 1 } { 2 } ( \color{Cerulean}{0}\color{Black}{ )} - 3 = 0 - 3 = - 3 } \\ { h ( \color{Cerulean}{7}\color{Black}{ )} = \frac { 1 } { 2 } ( \color{Cerulean}{7}\color{Black}{ )} - 3 = \frac { 7 } { 2 } - 3 = \frac { 1 } { 2 } } \end{array}\). d224f870063a40e098457059835651f2, 055c0d457aa04cdf98c57925f2da174b 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 . However, if you took a certain persons height over time, the height would be a function of age. /Producer ( Q t 5 . >> \(h \left( \frac { 1 } { 4 } \right) = 31 , h \left( \frac { 1 } { 2 } \right) = 28 , h ( 2 a - 1 ) = - 64 a ^ { 2 } + 64 a + 16\), 15. In the following exercises, evaluate the function: a. g(h2) b. g(x + 2) c. g(x) + g(2). Also mention whether this relation is a function or not. Find \(f (4), f (0)\), and \(f (2)\).\. Step 1: Tell the class a story involving a real-world, linear functional relationship. What is his income if he does not sell any cars in one month? Make a class set of the A Well-Functioning Research Mission: Representing Functions printable. Use the function to determine the value of the car when it is \(4\) years old. The students look at graphs containing dots and decide rather or not the dots form a linear or nonlinear relationship. Don't spend your valuable time making your own test or assessmentwe took care of it for you! hs2z\nLA"Sdr%,lt x][%9r~_q6Ge 7zYz}! Of special interest are relations where every \(x\)-value corresponds to exactly one \(y\)-value. (e) {(x,y) | x=3 and y is a real number} is both a function and relation. ~=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. 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 following table contains data of a womans forehand with her respective height. \(g (10) = 5, g (5) = 0\) and \(g (15) = 0 , g (5) = 10\) and \(g (25) = 10\), 5. 2-1 Skills Practice. With the definition of a function comes special notation. Understanding the concept of relation and function will be helpful in real-life situations. \(\{ ( 3,1 ) , ( 5,2 ) , ( 7,3 ) , ( 9,4 ) , ( 12,4 ) \}\), \(\{ ( 2,0 ) , ( 4,3 ) , ( 6,6 ) , ( 8,6 ) , ( 10,9 ) \}\), \(\{ ( 7,5 ) , ( 8,6 ) , ( 10,7 ) , ( 10,8 ) , ( 15,9 ) \}\), \(\{ ( 1,1 ) , ( 2,1 ) , ( 3,1 ) , ( 4,1 ) , ( 5,1 ) \}\), \(\{ ( 5,0 ) , ( 5,2 ) , ( 5,4 ) , ( 5,6 ) , ( 5,8 ) \}\), \(\{ ( - 3,1 ) , ( - 2,2 ) , ( - 1,3 ) , ( 0,4 ) , ( 0,5 ) \}\), \(g ( x ) = | x - 5 | \text { find } g ( - 5 ) , g ( 0 ) , \text { and } g ( 5 )\), \(g ( x ) = | x | - 5 ; \text { find } g ( - 5 ) , g ( 0 ) , \text { and } g ( 5 )\), \(g ( x ) = | 2 x - 3 | ; \text { find } g ( - 1 ) , g ( 0 ) , \text { and } g \left( \frac { 3 } { 2 } \right)\), \(g ( x ) = 3 - | 2 x | ; \text { find } g ( - 3 ) , g ( 0 ) , \text { and } g ( 3 )\), \(f ( x ) = 2 x - 3 ; \text { find } f ( - 2 ) , f ( 0 ) , \text { and } f ( x - 3 )\), \(f ( x ) = 5 x - 1 ; \text { find } f ( - 2 ) , f ( 0 ) , \text { and } f ( x + 1 )\), \(g ( x ) = \frac { 2 } { 3 } x + 1 ; \text { find } g ( - 3 ) , g ( 0 ) , \text { and } f ( 9 x + 6 )\), \(g ( x ) = - \frac { 3 } { 4 } x - \frac { 1 } { 2 } ; \text { find } g ( - 4 ) , g ( 0 ) , \text { and } g ( 6 x - 2 )\), \(g ( x ) = x ^ { 2 } ; \text { find } g ( - 5 ) , g ( \sqrt { 3 } ) , \text { and } g ( x - 5 )\), \(g ( x ) = x ^ { 2 } + 1 ; \text { find } g ( - 1 ) , g ( \sqrt { 6 } ) , \text { and } g ( 2 x - 1 )\), \(f ( x ) = x ^ { 2 } - x - 2 ; \text { find } f ( 0 ) , f ( 2 ) , \text { and } f ( x + 2 )\), \(f ( x ) = - 2 x ^ { 2 } + x - 4 ; \text { find } f ( - 2 ) , f \left( \frac { 1 } { 2 } \right) , \text { and } f ( x - 3 )\), \(h ( t ) = - 16 t ^ { 2 } + 32 ; \text { find } h \left( \frac { 1 } { 4 } \right) , h \left( \frac { 1 } { 2 } \right) , \text { and } h ( 2 a - 1 )\), \(h ( t ) = - 16 t ^ { 2 } + 32 ; \text { find } h ( 0 ) , h ( \sqrt { 2 } ) , h ( 2 a + 1 )\), \(f ( x ) = \sqrt { x + 1 } - 2 \text { find } f ( - 1 ) , f ( 0 ) , f ( x - 1 )\), \(f ( x ) = \sqrt { x - 3 } + 1 ; \text { find } f ( 12 ) , f ( 3 ) , f ( x + 3 )\), \(g ( x ) = \sqrt { x + 8 } ; \text { find } g ( 0 ) , g ( - 8 ) , \text { and } g ( x - 8 )\), \(g ( x ) = \sqrt { 3 x - 1 } ; \text { find } g \left( \frac { 1 } { 3 } \right) , g \left( \frac { 5 } { 3 } \right) , \text { and } g \left( \frac { 1 } { 3 } a ^ { 2 } + \frac { 1 } { 3 } \right)\), \(f ( x ) = x ^ { 3 } + 1 ; \text { find } f ( - 1 ) , f ( 0 ) , f \left( a ^ { 2 } \right)\), \(f ( x ) = x ^ { 3 } - 8 ; \text { find } f ( 2 ) , f ( 0 ) , f \left( a ^ { 3 } \right)\), \(f ( x ) = 2 x - 3 ; \text { find } x \text { where } f ( x ) = 25\), \(f ( x ) = 7 - 3 x ; \text { find } x \text { where } f ( x ) = - 27\), \(f ( x ) = 2 x + 5 ; \text { find } x \text { where } f ( x ) = 0\), \(f ( x ) = - 2 x + 1 ; \text { find } x \text { where } f ( x ) = 0\), \(g ( x ) = 6 x + 2 ; \text { find } x \text { where } g ( x ) = 5\), \(g ( x ) = 4 x + 5 ; \text { find } x \text { where } g ( x ) = 2\), \(h ( x ) = \frac { 2 } { 3 } x - \frac { 1 } { 2 } ; \text { find } x \text { where } h ( x ) = \frac { 1 } { 6 }\), \(h ( x ) = \frac { 5 } { 4 } x + \frac { 1 } { 3 } ; \text { find } x \text { where } h ( x ) = \frac { 1 } { 2 }\).