On the other hand, an undefined function is the one whose points are outside the domain. Given the linear function defined by \(f(x)=2x-5\), simplify the following. \(\frac { f ( x + h ) - f ( x ) } { h }\). The minimum \(y\)-value represented on the graph is \(0\); thus, the range is \([0,)\). [7A\SwBOK/X/_Q>QG[ `Aaac#*Z;8cq>[&IIMST`kh&45YYF9=X_,,S-,Y)YXmk]c}jc-v};]N"&1=xtv(}'{'IY) -rqr.d._xpUZMvm=+KG^WWbj>:>>>v}/avO8 x{|7>Z]-Ed]-lJVe;qN8v%vb;vnv$@ \CH(w In what year was the value of the car at a minimum? Range: Function: o 2 t 3 3 (3, 3) -2) Relation . Determine the domain and range of the following relation and state whether it is a function or not: \(\{(4, 3), (2, 6), (0, 3), (3, 5), (3, 7)\}\). 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. So, this relation is a function as well. If you're looking for a quick delivery, we've got you covered. \(g (10) = 10\) and \(g (5) = 10 ; g (5) = 5\) and \(g (10) = 5\). 11) f (x) x x y 12) f(x) x x y 13) g(x) x x y 14) g(n) n x y Critical thinking questions: 15) Give an example of a function that doesn't have an inverse. yksL?cS3}s+y43!qgn8Bsr&n/g-|N59J4gt_l>5gI9?Ny=@LKFr. Make a class set of the A Well-Functioning Research Mission: Representing Functions printable. Domain: \(\); range: \((, 3]\); function: yes, 21. endobj Mathematics Homework Helper. Find \(x\) where \(g (x) = 5, g (x) = 4\), and \(g (x) = 4\). /XObject << 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. endobj 0000000750 00000 n >> This 12-question algebra 1 worksheet provides students with practice working with relations and functions. Now, lets begin with the relations functions worksheet. Algebra frequently involves functions, and so the notation becomes useful when performing common tasks. 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 math worksheets on introducing functions are exactly what you need. Then. (e) {(x,y) | x=3 and y is a real number} is both a function and relation. << /Type /Page Relations and Functions tate the domain and range of each relation. 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. This is a multiple choice worksheet where students look at 20 different sets of relationships and decide yes or no rather the relationships are a function. If all these pointers match, then the relation is proved to be a function. Section 3.1. Restart your browser. The relation depicts the connection between input and output. 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. Don't spend your valuable time making your own test or assessmentwe took care of it for you! . NhSIS+:|2q^>l$ia}^nCLW:'HdfJ)A3X3&X Legal. 2. . endobj 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 Plus each one comes with an answer key. Math is often viewed as a difficult and boring subject, however, with a little effort it can be easy and interesting. 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. The maximum \(y\)-value is \(3\) and the minimum is \(3\); hence, the range consists of \(y\)-values in the interval \([3,3]\). No, the input 2 has 2 output values. /MediaBox [0 0 612.000000 792.000000] <> Download Relations and Functions Worksheet PDFs These math worksheets should be practiced regularly and are free to download in PDF formats. 0000006193 00000 n \(f ( - 2 ) = - 7 , f ( 0 ) = - 3 , f ( x - 3 ) = 2 x - 9\), 7. . endstream endobj 35 0 obj <>stream It is important to note that \(y\) and \(f(x)\) are used interchangeably. In this case, we interpret f( 5) = 3 as follows: Figure 2.1.17 Any curve graphed on a rectangular coordinate plane represents a set of ordered pairs and thus defines a relation. Lesson Directions. 8. Worksheet on Relations and Functions. If you need an answer fast, you can always count on Google. Domain: \(\{ - 4 , - 1,0,2,3 \}\); range: \(\{ 1,2,3 \}\); function: yes, 9. %%EOF 0000000016 00000 n With the definition of a function comes special notation. Also mention whether this relation is a function or not. There are a variety of question types including, multiple- choice, drop down, and select all that apply. 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. %PDF-1.4 2The horizontal number line used as reference in a rectangular coordinate system. It could also be used as a worksheet for homework. <> Decide whether the following relations are functions. <>>> 9. Students will find the range given the domain.Worksheet 3: Function rules and table of valuesStandard. This has been SO helpful when im stuck on problems that i just can't understand. endobj d224f870063a40e098457059835651f2, 055c0d457aa04cdf98c57925f2da174b Explain your reasoning. 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. Domain: \(\); range: \(\); function: yes, 29. We begin with 2 on the y-axis and then read the corresponding x-value. 0000003486 00000 n Functions are often named with different letters; some common names for functions are \(f, g, h, C\), and \(R\). 3. Domain: \(\); range: \([2, )\); function: yes, 15. 6. Answer: the output from the function g when the input is 7 Question: Suppose f(x . /CreationDate (D:20220708141653-04'00') Answers vary, should mention how the function does not always have the same output for a given input. Share a link to a page that you think others may find useful. What was the value of the car when it was new in \(1970\)? 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 >> 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. /AIS false 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/` 10. To determine whether a given relation is a function or not, one needs first to find out the input values, then the output values. 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. 26 0 obj <> endobj 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. The following table contains data of a womans forehand with her respective height. So, this relation is a function as well. If it is a function, give the domain and range. stream Now includes an additional version that uses "y=" notation instead of "f(x)=" notation.This product is part of the Discovery-Based Worksheet Series. 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). Relations Expressed as Graphing. 17The value or algebraic expression used as input when using function notation. But, it's a very good app. /Creator () Find \(f ( 0 ) , f ( 2 )\), and \(f ( 4 )\). 2. endobj If we consider each x-value to be the input that produces exactly one output, then we can use function notation16: The notation \(f(x)\) reads, f of x and should not be confused with multiplication. 5Pairs \((x, y)\) that identify position relative to the origin on a rectangular coordinate plane. Relations and Functions Worksheet Answer Key 1. Analyzing Relations and Functions KEY. 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. DATE. 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. Explain. RELATIONS & FUNCTIONS Worksheet. Relations and Functions Worksheet Answer Key 1. A relation is any set of ordered pairs. Range. Often, we can determine the domain and range of a relation if we are given its graph. Conduct an Internet search for the vertical line test, functions, and evaluating functions. /Title ( I n f i n i t e A l g e b r a 1 - C o n t i n u o u s R e l a t i o n s) In particular, the x-value \(4\) corresponds to two y-values \(3\) and \(3\). . 24. 3. Use the function to determine the value of the car when it is \(4\) years old. We guarantee that your essay will be 100% original. 2 0 obj 6 0 obj % There is then practice on these topics. 1. satisfaction rating 4.7/5; Stay in the Loop 24/7 Functions and Relations Worksheets (Bundle) by Algebra Funsheets 5.0 (26) $14.99 $7.95 Bundle This bundle contains 9 worksheets on Functions.Worksheet 1: Finding domain and range from graphsStandard. We can use the given ordered pair solutions to estimate all of the other ordered pairs by drawing a line through the given points. Free to use Step-by-step explanations for every solution Exclusive how-to animations Sc. Value of [f(0) + f(1)] / 2 is -2, (a) x = 3/2 (b) x = 3 (c) x = , 13. 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. \(f ( x + h ) = x ^ { 3 } + 3 h x ^ { 2 } + 3 h ^ { 2 } x + h ^ { 3 }\), 9. It is NOT a function since two ordered pairs have the same domain or x-value. What was the value of the car in \(2005\)? 120 students are studying in class 11 divided among four sections. If any vertical line intersects the graph more than once, then the graph does not represent a function. If asked to find \(x\) where \(f(x) = a\), we set the function equal to \(a\) and then solve for \(x\). 6. /Type /Catalog 8Term used in honor of Ren Descartes when referring to the rectangular coordinate system. The rectangular coordinate system1 consists of two real number lines that intersect at a right angle. 12. The student first takes notes on the definition of a relation and a function. The students look at graphs containing dots and decide rather or not the dots form a linear or nonlinear relationship. State the domain and range of a relation. \(f ( x + h ) = x ^ { 2 } + 2 x h + h ^ { 2 } + x + h + 1\), 5. endobj Each one has model problems worked out step by step, practice problems, as well as challenge questions at the sheets end. To check if a relation is a function, given a mapping diagram of the relation, use the following criterion: 1. Look no further! /F8 8 0 R You must try to solve the questions on your own and later check it with the given practice worksheet relations and functions answer key. startxref Add another ordered pair to this relation that would make this not a function anymore. Related resources that you mig, This is a 1-1/2 page quiz covering functions & relations, domain & range, discrete & continuous, function notation and independent/dependent variables. 5 0 obj /Font << Given any function defined by \(h(x) = y\), the value \(x\) is called the argument of the function17. /GSa 4 0 R Domain = {-2, 0, 5}, Range = {-1, 3, 4}. How to Determine Whether a Given Relation is a Function or Not? Relation. .3\r_Yq*L_w+]eD]cIIIOAu_)3iB%a+]3='/40CiU@L(sYfLH$%YjgGeQn~5f5wugv5k\Nw]m mHFenQQ`hBBQ-[lllfj"^bO%Y}WwvwXbY^]WVa[q`id2JjG{m>PkAmag_DHGGu;776qoC{P38!9-?|gK9w~B:Wt>^rUg9];}}_~imp}]/}.{^=}^?z8hc' 4. endobj Consider the relations consisting of the seven ordered pair solutions to \(y = |x| 2 \)and \(x = |y| + 1\). 9. 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)}. 0000001693 00000 n In this case, we interpret \(f(5) = 3\) as follows: Function notation streamlines the task of evaluating. The first 3 questions ask students to take a relation (given as a set of ordered pairs) and represent the relation as a table, graph, and mapping diagram. 14 0 obj Math Worksheet 1- FUNCTION versus RELATION Relations . For example: \(\begin{aligned} h ( \color{Cerulean}{4 a ^ { 3 }}\color{Black}{ )} & = \frac { 1 } { 2 } ( \color{Cerulean}{4 a ^ { 3 } }\color{Black}{)} - 3 = 2 a ^ { 3 } - 3 \\ h ( \color{Cerulean}{2 x - 1}\color{Black}{ )} & = \frac { 1 } { 2 } ( \color{Cerulean}{2 x - 1}\color{Black}{ )} - 3 = x - \frac { 1 } { 2 } - 3 = x - \frac { 7 } { 2 } \end{aligned}\). hs2z\nLA"Sdr%,lt 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. Domain: Range: Function: Domain: Range: 15 _ Function: Domain. The solutions to \(x = |y| + 1\), on the other hand, have values in the domain that correspond to two elements in the range. 6 . 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. The students look at 20 different x y tables and decide rather the ordered pairs form a linear or nonlinear relationship. Reflections Over Intersecting Lines as Rotations. Worksheet 4.2 relations and functions answer key - Apps can be a great way to help students with their algebra. Chapter 3: Introduction to Functions and Relations. Find set P and the remaining ordered pairs. 1. Determine the domain and range of the following relation: The minimum \(x\)-value represented on the graph is \(8\) all others are larger. This assignment is also included in my:Algebra 1 Google Forms (, Functions and Relations Worksheets (Bundle), Relations, Functions, Domain and Range | Task Cards, Holt Algebra 4.2 Relations and Functions Worksheet DOC & PDF, Relations and Functions Worksheet (linear/non linear #2), Relations and Functions Notes and Worksheets, Relations and Functions Unit (Algebra 1 Unit 3), Functions and Linear Equations Quiz & Worksheet, Identifying Functions | Function or Not a Function Practice Worksheet, BACK TO SCHOOL | ALGEBRA 1 FUNCTIONS Bundle, Evaluating and Identifying Functions Worksheet, Relations and Functions Introduction Worksheets Bundle (Five Worksheets), Relations and Functions 2 (input-output boxes), Relations and Functions - Algebra 1 Skills Practice Worksheet, Algebra 1 Skills Practice Worksheets Bundle, Identifying Functions - Quick Coloring Activity, Domain and Range of Relations and Functions Quiz for Google Form/Quiz, Relations and Functions Worksheet (linear/non linear #1), RELATIONS AND FUNCTIONS: - IDENTIFY THE DOMAIN AND RANGE COLORING ACTIVITY # 2, Marie's Math Resources and Coloring Activities, Graphing Quadratic Functions in Standard Form Worksheets, Identifying Functions Independent Practice, Functions & Relations, Domain & Range Notes, Functions Unit Bundle - Algebra 1 Curriculum, Functions & Relations, Domain & Range, Function Notation Quiz, Daily Lessons in COMPARING & SORTING Preschool Lesson Plans, Algebra 1 Google Forms Semester 1 Digital Homework and Assessment Bundle. 12 graphs.Worksheet 2: Finding range given domainRiddle. But for the -4 the range is -3 so i did not put that in. . 7. 0000000943 00000 n Find \(f (8), f (0)\), and \(f (8)\). Domain: \(\{1, 0, 1, 2\}\); range: \(\{0, 1, 2, 3, 4\}\); function: no, 11. Form a relation from A to B to show whether the students belong to any of the four sections. Domain: \(\); range: \([8, ]\); function: yes, 1. A function is a relation in which each possible input value leads to exactly one output value. As we have seen, functions are also expressed using graphs. 3. z|OgYG;,_78}:<9}CJ` t\qF_W&]~~'7%EX6hqX=v$ \FLU/)|BtsS*q\B+oF,k=eI)B1tr6h(D 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/ Graph the given set of points, then answer the questions that follow. As all the 120 students belong to class 11, every pupil must be in any of the sections. Domain: \([5, 1]\); range: \([2, 2]\); function: no, 25. There's more to your application than just filling out the forms. /ExtGState << \(\begin{aligned} g ( \color{Cerulean}{- 2}\color{Black}{ )} & = ( \color{Cerulean}{- 2}\color{Black}{ )} ^ { 2 } = 4 \\ g ( \color{Cerulean}{\frac { 1 } { 2 }}\color{Black}{)} & = ( \color{Cerulean}{\frac { 1 } { 2 }} \color{Black}{)} ^ { 2 } = \frac { 1 } { 4 } \\ g (\color{Cerulean}{ x + h}\color{Black}{ )} & = ( \color{Cerulean}{x + h}\color{Black}{ )} ^ { 2 } = x ^ { 2 } + 2 x h + h ^ { 2 } \end{aligned}\), \(g (2) = 4,\: g ( \frac{1}{2} ) = \frac{1}{4} ,\: g (x + h) = x^{2} + 2xh + h^{2}\), At this point, it is important to note that, in general, \(f (x + h) f (x) + f (h)\). 12 0 obj On the other hand, an undefined function is the one whose points are outside the domain. The horizontal number line is called the x-axis2, and the vertical number line is called the y-axis3. 1. Key included. The intersection of the two axes is known as the origin6, which corresponds sto the point \((0, 0)\). 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 (a) True (b) False (c) True (d) True (e) False, 9. 25. It is perfect for, This product includes a 10-question assignment with practice over finding domain and range of relations and functions. Functions Worksheet 1 For exercises 13-18, determine whether each relation is a function. \(\{ ( 3,1 ) , ( 5,2 ) , ( 7,3 ) , ( 9,4 ) , ( 12,4 ) \}\), \(\{ ( 2,0 ) , ( 4,3 ) , ( 6,6 ) , ( 8,6 ) , ( 10,9 ) \}\), \(\{ ( 7,5 ) , ( 8,6 ) , ( 10,7 ) , ( 10,8 ) , ( 15,9 ) \}\), \(\{ ( 1,1 ) , ( 2,1 ) , ( 3,1 ) , ( 4,1 ) , ( 5,1 ) \}\), \(\{ ( 5,0 ) , ( 5,2 ) , ( 5,4 ) , ( 5,6 ) , ( 5,8 ) \}\), \(\{ ( - 3,1 ) , ( - 2,2 ) , ( - 1,3 ) , ( 0,4 ) , ( 0,5 ) \}\), \(g ( x ) = | x - 5 | \text { find } g ( - 5 ) , g ( 0 ) , \text { and } g ( 5 )\), \(g ( x ) = | x | - 5 ; \text { find } g ( - 5 ) , g ( 0 ) , \text { and } g ( 5 )\), \(g ( x ) = | 2 x - 3 | ; \text { find } g ( - 1 ) , g ( 0 ) , \text { and } g \left( \frac { 3 } { 2 } \right)\), \(g ( x ) = 3 - | 2 x | ; \text { find } g ( - 3 ) , g ( 0 ) , \text { and } g ( 3 )\), \(f ( x ) = 2 x - 3 ; \text { find } f ( - 2 ) , f ( 0 ) , \text { and } f ( x - 3 )\), \(f ( x ) = 5 x - 1 ; \text { find } f ( - 2 ) , f ( 0 ) , \text { and } f ( x + 1 )\), \(g ( x ) = \frac { 2 } { 3 } x + 1 ; \text { find } g ( - 3 ) , g ( 0 ) , \text { and } f ( 9 x + 6 )\), \(g ( x ) = - \frac { 3 } { 4 } x - \frac { 1 } { 2 } ; \text { find } g ( - 4 ) , g ( 0 ) , \text { and } g ( 6 x - 2 )\), \(g ( x ) = x ^ { 2 } ; \text { find } g ( - 5 ) , g ( \sqrt { 3 } ) , \text { and } g ( x - 5 )\), \(g ( x ) = x ^ { 2 } + 1 ; \text { find } g ( - 1 ) , g ( \sqrt { 6 } ) , \text { and } g ( 2 x - 1 )\), \(f ( x ) = x ^ { 2 } - x - 2 ; \text { find } f ( 0 ) , f ( 2 ) , \text { and } f ( x + 2 )\), \(f ( x ) = - 2 x ^ { 2 } + x - 4 ; \text { find } f ( - 2 ) , f \left( \frac { 1 } { 2 } \right) , \text { and } f ( x - 3 )\), \(h ( t ) = - 16 t ^ { 2 } + 32 ; \text { find } h \left( \frac { 1 } { 4 } \right) , h \left( \frac { 1 } { 2 } \right) , \text { and } h ( 2 a - 1 )\), \(h ( t ) = - 16 t ^ { 2 } + 32 ; \text { find } h ( 0 ) , h ( \sqrt { 2 } ) , h ( 2 a + 1 )\), \(f ( x ) = \sqrt { x + 1 } - 2 \text { find } f ( - 1 ) , f ( 0 ) , f ( x - 1 )\), \(f ( x ) = \sqrt { x - 3 } + 1 ; \text { find } f ( 12 ) , f ( 3 ) , f ( x + 3 )\), \(g ( x ) = \sqrt { x + 8 } ; \text { find } g ( 0 ) , g ( - 8 ) , \text { and } g ( x - 8 )\), \(g ( x ) = \sqrt { 3 x - 1 } ; \text { find } g \left( \frac { 1 } { 3 } \right) , g \left( \frac { 5 } { 3 } \right) , \text { and } g \left( \frac { 1 } { 3 } a ^ { 2 } + \frac { 1 } { 3 } \right)\), \(f ( x ) = x ^ { 3 } + 1 ; \text { find } f ( - 1 ) , f ( 0 ) , f \left( a ^ { 2 } \right)\), \(f ( x ) = x ^ { 3 } - 8 ; \text { find } f ( 2 ) , f ( 0 ) , f \left( a ^ { 3 } \right)\), \(f ( x ) = 2 x - 3 ; \text { find } x \text { where } f ( x ) = 25\), \(f ( x ) = 7 - 3 x ; \text { find } x \text { where } f ( x ) = - 27\), \(f ( x ) = 2 x + 5 ; \text { find } x \text { where } f ( x ) = 0\), \(f ( x ) = - 2 x + 1 ; \text { find } x \text { where } f ( x ) = 0\), \(g ( x ) = 6 x + 2 ; \text { find } x \text { where } g ( x ) = 5\), \(g ( x ) = 4 x + 5 ; \text { find } x \text { where } g ( x ) = 2\), \(h ( x ) = \frac { 2 } { 3 } x - \frac { 1 } { 2 } ; \text { find } x \text { where } h ( x ) = \frac { 1 } { 6 }\), \(h ( x ) = \frac { 5 } { 4 } x + \frac { 1 } { 3 } ; \text { find } x \text { where } h ( x ) = \frac { 1 } { 2 }\).

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