After that, check whether each input value has a corresponding out value. <> 2.1E: Exercises - Relations and Functions - Mathematics LibreTexts Given \(f ( x ) = \sqrt { 2 x + 4 }\), find \(f (2), f (0)\), and \(f \left( \frac { 1 } { 2 } a ^ { 2 } - 2 \right)\). \(\begin{aligned} g ( \color{Cerulean}{- 2}\color{Black}{ )} & = ( \color{Cerulean}{- 2}\color{Black}{ )} ^ { 2 } = 4 \\ g ( \color{Cerulean}{\frac { 1 } { 2 }}\color{Black}{)} & = ( \color{Cerulean}{\frac { 1 } { 2 }} \color{Black}{)} ^ { 2 } = \frac { 1 } { 4 } \\ g (\color{Cerulean}{ x + h}\color{Black}{ )} & = ( \color{Cerulean}{x + h}\color{Black}{ )} ^ { 2 } = x ^ { 2 } + 2 x h + h ^ { 2 } \end{aligned}\), \(g (2) = 4,\: g ( \frac{1}{2} ) = \frac{1}{4} ,\: g (x + h) = x^{2} + 2xh + h^{2}\), At this point, it is important to note that, in general, \(f (x + h) f (x) + f (h)\). Hence, the domain consists of all the real numbers in the set from \([1,5]\). Research and discuss the life and contributions of Ren Descartes. Vocabulary on relations, functions, domain, range, and vertical line test. Function: Domain: 10 Range: Function. [ -c R!z"^Ow,c endobj For relations consisting of points in the plane, the range is the set of all \(y\)-values. Free worksheet(pdf) and answer key on distinguishing functions from relations, stating domain and range and more. 38 0 obj <>stream This helps with the order of operations when simplifying expressions. The student first takes notes on the definition of a relation and a function. Domain: \(\{1, 0, 1, 2\}\); range: \(\{0, 1, 2, 3, 4\}\); function: no, 11. An expression is considered to be unambiguous or well-defined when the definition of the same allocates a unique value or interpretation. An expression is considered to be unambiguous or well-defined when the definition of the same allocates a unique value or interpretation. \(g (4) = 3, g (2) = 0\), and \(g (6) = 2\). Solve Now. If this doesn't solve the problem, visit our Support Center . endobj Explore math program RELATIONS & FUNCTIONS Worksheet. 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 \(f (4), f (0)\), and \(f (2)\).\. Domain: \(\); range: \([0, ]\); function: yes, 27. Then determine the domain and range. . Then the student identifies the domain and range of each example. Given the graph of \(h\), find \(x\) where \(h(x)=-4\). Some filters moved to Formats filters, which is at the top of the page. 2. . Next, we define a relation9 as any set of ordered pairs. Therefore, \(x = |y| + 1\) does not define a function. We can see that \(g(x)=2\) where \(x=5\); in other words, \(g(5)=2\). % 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. 10/10 gives correct answers every time. The representation of a relation on a rectangular coordinate plane, as illustrated above, is called a graph10. What is Meant by Well-defined and Undefined Function? Included are 5 different task sheets. \(\frac { f ( x + h ) - f ( x ) } { h }\). 10. 2. Find \(f (8), f (0)\), and \(f (8)\). 11 0 obj 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. Consider the relations consisting of the seven ordered pair solutions to \(y = |x| 2 \)and \(x = |y| + 1\). endobj The students look at graphs containing dots and decide rather or not the dots form a linear or nonlinear relationship. Simplify \(\frac { p ( x + h ) - p ( x ) } { h }\) given \(p ( x ) = 7 x - 3\). /Annots 14 0 R 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, \(=(,)\). 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). Set Up. These worksheets cover all the essential concepts related to functions, including domain and range, linear versus nonlinear, graphing stories, and much more. Plus each one comes with an answer key. Students will find the range given the domain.Worksheet 3: Function rules and table of valuesStandard. 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. endstream endobj 27 0 obj <> endobj 28 0 obj <> endobj 29 0 obj <>/Font<>/ProcSet[/PDF/Text/ImageB/ImageC/ImageI]/XObject<>>> endobj 30 0 obj <> endobj 31 0 obj [/ICCBased 34 0 R] endobj 32 0 obj <> endobj 33 0 obj <>stream For example, use the function \(h\) defined by \(h (x) = \frac{1}{2} x 3\)to evaluate for \(x\)-values in the set \(\{2, 0, 7\}\). Domain: \(\); range: \([2, )\); function: yes, 15. Function. xULF] Who is credited with the introduction of the notation \(y = f (x)\)? The will worksheet will discuss the concept of relations and functions. Mathematics is a way of dealing with tasks that involves numbers and equations. Make use of this worksheet to get a better understandingof relations and functions. Is the relation a . Worksheet 7.4 inverse functions answer key - Download worksheet 7.4 inverse functions and more Elementary Mathematics Lecture notes in PDF only on Docsity! ' 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]. Add highlights, virtual manipulatives, and more. As we can see, any vertical line will intersect the graph of \(y=|x|2\) only once; therefore, it is a function. 39. f(x) = 3x2 5x; f(2) Answer 40. g(x) = 4x2 3x; g(3) 41. Here we put an arrow on the ends of our lines to indicate that this set of ordered pairs continues without bounds. PDF RELATIONS & FUNCTIONS Worksheet - School For Excellence 16The notation \(f (x) = y\), which reads \(f\) of \(x\) is equal to \(y\). Given a function, \(y\) and \(f (x)\) can be used interchangeably. 0000001084 00000 n (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. 8Term used in honor of Ren Descartes when referring to the rectangular coordinate system. /SA true Now includes an additional version that uses "y=" notation instead of "f(x)=" notation.This product is part of the Discovery-Based Worksheet Series. Free Math Worksheets (pdfs) with answer keys on Algebra I, Geometry Not all relations are functions, and not all functions are relations. Math is often viewed as a difficult and boring subject, however, with a little effort it can be easy and interesting. (c) All functions are relations, but all relations are not functions. Explain your reasoning for each. 5. /Type /ExtGState 0000000813 00000 n 7) Domain: \(\); range: \([8, ]\); function: yes, 1. There are 9 questions total.The first 3 questions give the student a mapping, a table and a set of ordered pairs and ask them to determine if the relations are functions or not and to find the domain and range of each. This is a relations and functions worksheet. Very interesting and supportful Thank you , haven't gotten one guest one wrong yet, really good app for homework. The value of a is 0.90 and b is 24.5, 11. Worksheet on Relations and Functions. Functions and Relations Worksheet Decide whether the graph represents y as a function of x. /Parent 3 0 R Are you looking for a comprehensive set of worksheets to introduce functions to your students? We can visually identify functions by their graphs using the vertical line test15. 4. Already known sets of ordered pairs are (-2, 0) and (0, 2). 2. 1. D 25. 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. PDF Functions and Relations - Saylor Academy Identify the input values. Worksheet 4.1 relations and functions answer key. The argument can be any algebraic expression. <> relation is a function. "80j]./j\^4z 1. <<9314568F76096D49830FE73A943AC137>]/Prev 83319>> 1. 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. 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. 1. Algebra 2 relations and functions worksheet answers can be a useful tool for these scholars. (a) True (b) False (c) True (d) True (e) False, 9. It is perfect for, This product includes a 10-question assignment with practice over finding domain and range of relations and functions. The google activity may be edited if needed (add/delete questions, change answer type, etc.) Relations and Functions - Liveworksheets If you need an answer fast, you can always count on Google. Are you covering Functions and Linear Equations and need a little break? 1. Domain = {-2, 0, 5}, Range = {-1, 3, 4}. Examples of domain and range, vertical line test, and determining if a relation is a function. . The set consisting of all of the first components of a relation, in this case the x-values, is called the domain11. But, it's a very good app. 2 0 obj 3The vertical number line used as reference in a rectangular coordinate system. Section 5.2 Defining Relations and Functions. /Length 12 0 R stream However, in this course, we will be working with sets of ordered pairs \((x, y)\) in the rectangular coordinate system. Review. Then looks at examples of the 5 types: a set of ordered pairsa table of valuesa mappinga discrete graphan equation. Find \(f (2), f (2)\), and \(f (7)\). A relation is a set of one or more ordered pairs. Recall that when evaluating, it is a best practice to begin by replacing the variables with parentheses and then substitute the appropriate values. We also acknowledge previous National Science Foundation support under grant numbers 1246120, 1525057, and 1413739. This is a relation because if you enter a specific age and check all the persons of that age, you will find that they all have various heights. Given any function defined by \(h(x) = y\), the value \(x\) is called the argument of the function17. /Contents 11 0 R Quizzes with auto-grading, and real-time student data. Legal. They will fill the appropriate box with fun patterns, drawings, and creative ideas! 1 2 . 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. A function is a relation in which each element of the domain is paired with EXACTLY one element of the range. If asked to find \(f(a)\), we substitute the argument \(a\) in for the variable and then simplify. THIS APP IS THE BEST ONE EVER! 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 \(x\) where \(g (x) = 0, g (x) = 10\), and \(g (x) = 15\). A visual representation of a pop machine and the connection with functions. For example, both the algebraic equations \(y = |x| 2\) and \(x = |y| + 1\) define relationships between \(x\) and \(y\). 12 graphs.Worksheet 2: Finding range given domainRiddle. Relations and Functions tate the domain and range of each relation. The minimum \(y\)-value represented on the graph is \(0\); thus, the range is \([0,)\). The ordered pair \((x, y)\) represents the position of points relative to the origin. There is exactly one output for every input. endstream Feel free to download and enjoy these free worksheets on functions and relations. E6S2)212 "l+&Y4P%\%g|eTI (L 0_&l2E 9r9h xgIbifSb1+MxL0oE%YmhYh~S=zU&AYl/ $ZU m@O l^'lsk.+7o9V;?#I3eEKDd9i,UQ h6'~khu_ }9PIo= C#$n?z}[1 Chapter 1 - Analyzing Functions Answer Key CK-12 Math Analysis Concepts 1 1.1 Relations and Functions Answers 1. Then. The domain is \(\{4, 2, 0, 3\}\) and the range is \(\{3, 3, 5, 6, 7\}\). 2.1: Relations, Graphs, and Functions - Mathematics LibreTexts \(g ( 0 ) = 2 \sqrt { 2 } , g ( - 8 ) = 0 , g \left( a ^ { 2 } - 8 \right) = | a |\), 19. K0iABZyCAP8C@&*CP=#t] 4}a ;GDxJ> ,_@FXDBX$!k"EHqaYbVabJ0cVL6f3bX'?v 6-V``[a;p~\2n5 &x*sb|! /MediaBox [0 0 612.000000 792.000000] In what years was the car valued at \($4,000\)? 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. Relations and Functions Worksheet | Worksheet on Relations - BYJUS 3 0 obj <> endobj >> Find set P and the remaining ordered pairs. 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. Also sketch a graph for each equation. Substitute \(f (x)\) with \(27\) and solve. Find \(x\) where \(g (x) = 4, g (x) = 3\), and \(g (x) = 4\). Write each of the following as a relation, state the domain and range, then determine if it is a function. \(g (10) = 10\) and \(g (5) = 10 ; g (5) = 5\) and \(g (10) = 5\). A1vjp zN6p\W pG@ Domain. The first number is called the \(x\)-coordinate, and the second number is called the \(y\)-coordinate. Real World Math Horror Stories from Real encounters, Solve Equations with variables in Exponents, Solve Quadratic Equations by Completing the Square, Mixed Problems on Writing Equations of Lines, Write Equation of Line from the Slope and 1 Point, Equation of Line Parallel to Another Line and Through a Point, Equation of Line Perpendicular to Another Line and Through a Point, Adding and Subtracting Polynomials worksheet, Multiplying Monomials with Polynomials Worksheet, Solve Systems of Equations by Elimination, Solve Systems of Equations (Mixed Review), Sine, Cosine, Tangent, to Find Side Length, Sine Cosine Graphs with Vertical Translations, Sine, Cosine, Tangent Graphs with Phase Shifts, Sine, Cosine, Tangent Graphs with Change in Period, Amplitude and Phase Shifts (All Translations), Graphing Sine, Cosine, Tangent with Change in Period, Cumulative, Summative Worksheet on Periodic Trig Functions, Activity-Explore by Measuring the Relationship of Vertical Angles, Graphic Organizer: Formulas & Theorems of A Circle, Arcs and Angles Formed by Intersecting Chords, Tangent, Secant, Arcs and Angles of a Circle, Parallel Chords, Congruent Chords and the Center of a Circle, Relationship Between Tangent, Secant Side Lengths, Arcs and Angles Formed by the Intersection of a Tangent and a Chord, Mixed Review on Formulas of Geometry of the Circle, Graph and Equation of Exponential Growth Functions, Linear Equations - Real World Application Activity, Compare and Contrast Types of Parallelograms, Worksheet Goes Hand in Hand with This Web Page, Side Angle Side and Angle Side Angle Worksheet, System of Linear Equations - Real World Application, Activity - Methods to Solve Systems of Equations, Remote, Exterior and Interior Angles of a Triangle, Sine, Cosine, Tangent (SHOCAHTOA) web page, Activity-Relationship of Angles in a Trapezoid, Compositions of Reflections. Here we are asked to find the x-value given a particular y-value. \(g (2) = 4, g (1) = 3, g (0) = 4\), 9. PDF Functions and Relations Worksheet - Santa Ana College xYMo6WQFH8n Find \(x\) where \(g (x) = 5, g (x) = 0\), and \(g (x) = 10\). 13 0 obj 24. Explain your reasoning. P Is the relation a function? Each one has model problems worked out step by step, practice problems, as well as challenge questions at the sheets end. The students look at graphs containing dots and decide rather or not the dots form a linear or nonlinear relationship. Functions and relations answer key - Section 5.2 Defining Relations and Functions. This is a relations and functions worksheet. Each one has model problems worked out step by step, practice problems, as well as challenge questions at the sheets end. Determine the domain and range of the following relation: The minimum \(x\)-value represented on the graph is \(8\) all others are larger. As every value of x has a different value of y; it is a function. endobj . In the context of algebra, the relations of interest are sets of ordered pairs \((x, y)\) in the rectangular coordinate plane. This has been SO helpful when im stuck on problems that i just can't understand. We offer the fastest, most expert tutoring in the business. %PDF-1.3 % \(\begin{array} { c } { h ( \color{Cerulean}{- 2}\color{Black}{ )} = \frac { 1 } { 2 } ( \color{Cerulean}{- 2}\color{Black}{ )} - 3 = - 1 - 3 = - 4 } \\ { h ( \color{Cerulean}{0}\color{Black}{ )} = \frac { 1 } { 2 } ( \color{Cerulean}{0}\color{Black}{ )} - 3 = 0 - 3 = - 3 } \\ { h ( \color{Cerulean}{7}\color{Black}{ )} = \frac { 1 } { 2 } ( \color{Cerulean}{7}\color{Black}{ )} - 3 = \frac { 7 } { 2 } - 3 = \frac { 1 } { 2 } } \end{array}\). Given \(g ( x ) = x ^ { 2 }\), find \(g (2), g ( \frac{1}{2} )\), and \(g (x + h)\). 7. In this case, we interpret f( 5) = 3 as follows: Figure 2.1.17 These cards are most appropriate for Math 8-Algebra 1.Task cards are very versatile, and can, This r squared creation is the complementary worksheet for our 4.2 PowerPoint, which students will complete as homework. 11 0 obj . NhSIS+:|2q^>l$ia}^nCLW:'HdfJ)A3X3&X Accessibility StatementFor more information contact us atinfo@libretexts.orgor check out our status page at https://status.libretexts.org. Given the graph of \(g\), find \(x\) where \(g(x)=2\). 13. 11. With this data, a student maps a relationship between forehand and hand in the form y = ax + b, provided both are constants. We can easily determine whether or not an equation represents a function by performing the vertical line test on its graph. There is then practice on these topics. 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 \(2, [2,)\). /F7 7 0 R 4. Key included. <> Domain: \(\{ - 4 , - 1,0,2,3 \}\); range: \(\{ 1,2,3 \}\); function: yes, 9. It could also be used as a worksheet for homework. KEY FEATURES Word problem explanations! There are a variety of question types including, multiple- choice, drop down, and select all that apply. Vedantu LIVE Online Master Classes is an incredibly personalized tutoring platform for you, while you are staying at your home. The argument could be an algebraic expression. Build bright future aspects You can build a bright future by taking advantage of opportunities and planning for success. 26 13 It has so many equations and etc that it knows how to do, and has many advantages that other math apps do not. . 7 0 obj In the following exercises, evaluate the function: a. g(h2) b. g(x + 2) c. g(x) + g(2). /Type /Page If it is a function, give the domain and range. What will be the domain and range of the following relation? 4. endstream endobj 34 0 obj <>stream Relations And Functions Worksheet Teaching Resources | TPT 2 0 obj 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 relation depicts the connection between input and output. State the domain and range of a relation. Now, lets begin with the relations functions worksheet. Worksheet 4.2 relations and functions answer key <>/ExtGState<>/XObject<>/ProcSet[/PDF/Text/ImageB/ImageC/ImageI] >>/MediaBox[ 0 0 612 792] /Contents 4 0 R/Group<>/Tabs/S/StructParents 0>> Interactive simulation the most controversial math riddle ever! /Font << What was the value of the car new? \(\{ ( 3,1 ) , ( 5,2 ) , ( 7,3 ) , ( 9,4 ) , ( 12,4 ) \}\), \(\{ ( 2,0 ) , ( 4,3 ) , ( 6,6 ) , ( 8,6 ) , ( 10,9 ) \}\), \(\{ ( 7,5 ) , ( 8,6 ) , ( 10,7 ) , ( 10,8 ) , ( 15,9 ) \}\), \(\{ ( 1,1 ) , ( 2,1 ) , ( 3,1 ) , ( 4,1 ) , ( 5,1 ) \}\), \(\{ ( 5,0 ) , ( 5,2 ) , ( 5,4 ) , ( 5,6 ) , ( 5,8 ) \}\), \(\{ ( - 3,1 ) , ( - 2,2 ) , ( - 1,3 ) , ( 0,4 ) , ( 0,5 ) \}\), \(g ( x ) = | x - 5 | \text { find } g ( - 5 ) , g ( 0 ) , \text { and } g ( 5 )\), \(g ( x ) = | x | - 5 ; \text { find } g ( - 5 ) , g ( 0 ) , \text { and } g ( 5 )\), \(g ( x ) = | 2 x - 3 | ; \text { find } g ( - 1 ) , g ( 0 ) , \text { and } g \left( \frac { 3 } { 2 } \right)\), \(g ( x ) = 3 - | 2 x | ; \text { find } g ( - 3 ) , g ( 0 ) , \text { and } g ( 3 )\), \(f ( x ) = 2 x - 3 ; \text { find } f ( - 2 ) , f ( 0 ) , \text { and } f ( x - 3 )\), \(f ( x ) = 5 x - 1 ; \text { find } f ( - 2 ) , f ( 0 ) , \text { and } f ( x + 1 )\), \(g ( x ) = \frac { 2 } { 3 } x + 1 ; \text { find } g ( - 3 ) , g ( 0 ) , \text { and } f ( 9 x + 6 )\), \(g ( x ) = - \frac { 3 } { 4 } x - \frac { 1 } { 2 } ; \text { find } g ( - 4 ) , g ( 0 ) , \text { and } g ( 6 x - 2 )\), \(g ( x ) = x ^ { 2 } ; \text { find } g ( - 5 ) , g ( \sqrt { 3 } ) , \text { and } g ( x - 5 )\), \(g ( x ) = x ^ { 2 } + 1 ; \text { find } g ( - 1 ) , g ( \sqrt { 6 } ) , \text { and } g ( 2 x - 1 )\), \(f ( x ) = x ^ { 2 } - x - 2 ; \text { find } f ( 0 ) , f ( 2 ) , \text { and } f ( x + 2 )\), \(f ( x ) = - 2 x ^ { 2 } + x - 4 ; \text { find } f ( - 2 ) , f \left( \frac { 1 } { 2 } \right) , \text { and } f ( x - 3 )\), \(h ( t ) = - 16 t ^ { 2 } + 32 ; \text { find } h \left( \frac { 1 } { 4 } \right) , h \left( \frac { 1 } { 2 } \right) , \text { and } h ( 2 a - 1 )\), \(h ( t ) = - 16 t ^ { 2 } + 32 ; \text { find } h ( 0 ) , h ( \sqrt { 2 } ) , h ( 2 a + 1 )\), \(f ( x ) = \sqrt { x + 1 } - 2 \text { find } f ( - 1 ) , f ( 0 ) , f ( x - 1 )\), \(f ( x ) = \sqrt { x - 3 } + 1 ; \text { find } f ( 12 ) , f ( 3 ) , f ( x + 3 )\), \(g ( x ) = \sqrt { x + 8 } ; \text { find } g ( 0 ) , g ( - 8 ) , \text { and } g ( x - 8 )\), \(g ( x ) = \sqrt { 3 x - 1 } ; \text { find } g \left( \frac { 1 } { 3 } \right) , g \left( \frac { 5 } { 3 } \right) , \text { and } g \left( \frac { 1 } { 3 } a ^ { 2 } + \frac { 1 } { 3 } \right)\), \(f ( x ) = x ^ { 3 } + 1 ; \text { find } f ( - 1 ) , f ( 0 ) , f \left( a ^ { 2 } \right)\), \(f ( x ) = x ^ { 3 } - 8 ; \text { find } f ( 2 ) , f ( 0 ) , f \left( a ^ { 3 } \right)\), \(f ( x ) = 2 x - 3 ; \text { find } x \text { where } f ( x ) = 25\), \(f ( x ) = 7 - 3 x ; \text { find } x \text { where } f ( x ) = - 27\), \(f ( x ) = 2 x + 5 ; \text { find } x \text { where } f ( x ) = 0\), \(f ( x ) = - 2 x + 1 ; \text { find } x \text { where } f ( x ) = 0\), \(g ( x ) = 6 x + 2 ; \text { find } x \text { where } g ( x ) = 5\), \(g ( x ) = 4 x + 5 ; \text { find } x \text { where } g ( x ) = 2\), \(h ( x ) = \frac { 2 } { 3 } x - \frac { 1 } { 2 } ; \text { find } x \text { where } h ( x ) = \frac { 1 } { 6 }\), \(h ( x ) = \frac { 5 } { 4 } x + \frac { 1 } { 3 } ; \text { find } x \text { where } h ( x ) = \frac { 1 } { 2 }\).
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