function and relation worksheet with answer key

Some filters moved to Formats filters, which is at the top of the page. 26 13 )feOJeB_~n 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. Here we put an arrow on the ends of our lines to indicate that this set of ordered pairs continues without bounds. 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. /Type /ExtGState With a wide variety of practice problems, your students will gain a deep understanding of these fundamental concepts and. \(g ( 0 ) = 2 \sqrt { 2 } , g ( - 8 ) = 0 , g \left( a ^ { 2 } - 8 \right) = | a |\), 19. Domain: \(\{ - 4 , - 1,0,2,3 \}\); range: \(\{ 1,2,3 \}\); function: yes, 9. %PDF-1.5 3. f-1 (x) = (9x/5) + 32 and the inverse is a function also. 1 2 . /Parent 3 0 R You ask, we answer! RELATIONS & FUNCTIONS Worksheet. Function. You must try to solve the questions on your own and later check it with the given practice worksheet relations and functions answer key. endobj 1A system with two number lines at right angles specifying points in a plane using ordered pairs \((x, y)\). In the context of algebra, the relations of interest are sets of ordered pairs \((x, y)\) in the rectangular coordinate plane. 7.Lp/; )Q[.[mJ-y)eUt `=PKj~82%.s*`4F/\.{f3O)rQyl8q3ay[T SC ~Gh To check if a relation is a function, given a mapping diagram of the relation, use the following criterion: 1. \(g (2) = 5, g (3) = 4\) and \(g (1) = 4 , g (5) = 4\) and \(g (1) = 4\), 7. 3 0 obj <> It is a function since no two ordered pairs have the same domain or x-value. <> What was the value of the car when it was new in \(1970\)? The students look at graphs containing dots and decide rather or not the dots form a linear or nonlinear relationship. 0000001693 00000 n 2The horizontal number line used as reference in a rectangular coordinate system. Ex 5. Worksheet on Math Relation | Relations and Functions Worksheets with Answers. 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. \(f ( - 1 ) = 0 , f ( 0 ) = 1 , f \left( a ^ { 2 } \right) = a ^ { 6 } + 1\), 3. /ca 1.0 Yes, each input has exactly 1 output. {(2, 1), (5, 1), (8, 1), (11, 1), (14, 1), (17, 1)} is a function also. This is a relations and functions worksheet. Hence, the domain consists of all the real numbers in the set from \([1,5]\). (5, 4), (8, -1), (7, 3), (0, 5), (10, -2), and __________ 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 \(f (12), f (0)\), and \(f (12)\). 9. Evaluate the function when x = 3, x = 0, and x = -2. [U6Ue:}au&+X[f]p2n3&\ _ Simplify \(\frac { c ( x + h ) - c ( x ) } { h }\) given \(c ( x ) = 3 x + 1\). A relation is any set of ordered pairs. So, this relation is a function as well. . In this case, we interpret \(f(5) = 3\) as follows: Function notation streamlines the task of evaluating. 13 0 obj /GSa 4 0 R Worksheet 4.1 Relations and Functions Write each of the following as a relation, state the domain and range, then determine if it is a function. Expression to convert Fahrenheit to Celsius is y = (5x/9) (160/9). PERIOD. Add another ordered pair to this relation that would make this not a function anymore. %%EOF startxref 2x + y . /Filter /FlateDecode /F9 9 0 R Very interesting and supportful Thank you , haven't gotten one guest one wrong yet, really good app for homework. 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. Identify the input values. The argument could be an algebraic expression. Then looks at examples of the 5 types: a set of ordered pairsa table of valuesa mappinga discrete graphan equation. 2. There are a variety of question types including, multiple- choice, drop down, and select all that apply. Posted: 7/3/17 so 50% off through 7/6/17, Do your students need practice graphing real world quadratics? 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. endobj 7. xwTS7" %z ;HQIP&vDF)VdTG"cEb PQDEk 5Yg} PtX4X\XffGD=H.d,P&s"7C$ stream With this data, a student maps a relationship between forehand and hand in the form y = ax + b, provided both are constants. Given any function defined by \(h(x) = y\), the value \(x\) is called the argument of the function17. endobj (a) True (b) False (c) True (d) True (e) False, 9. 7. f(x) = x 8. h(x) = x + 7 9. g(x) = x - 2 10. g(x) = 3x 11. Try to test your learnings in the exercises below. \(f ( - 1 ) = - 2 , f ( 0 ) = - 1 , f ( x - 1 ) = \sqrt { x } - 2\), 17. <> /Annots 14 0 R >> 6The point where the \(x\)- and \(y\)-axes cross, denoted by \((0, 0)\). On the other hand, an undefined function is the one whose points are outside the domain. Consider n (A) = m and n (B) = n. Find out the number of relations (non-empty) that can be predicted from A to B. The set of \(x\)-values defines the domain and the set of \(y\)-values defines the range. Legal. Expression to convert Fahrenheit to Celsius is y = (5x/9) (160/9). Here the compact notation \(f(5) = 3\) indicates that where \(x = 5\) (the input), the function results in \(y = 3\) (the output). 13 0 obj Answer. 13. FV>2 u/_$\BCv< 5]s.,4&yUx~xw-bEDCHGKwFGEGME{EEKX,YFZ ={$vrK 2 0 obj The horizontal number line is called the x-axis2, and the vertical number line is called the y-axis3. Solve Now. endobj /Length 12 0 R Lesson Directions. 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. This has been SO helpful when im stuck on problems that i just can't understand. Find \(x\) where \(g (x) = 4, g (x) = 3\), and \(g (x) = 4\). 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. Then they share a relationship and can be written as an ordered pair (x, y). 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. Find \(x\) where \(g (x) = 0, g (x) = 1\), and \(g (x) = 4\). Here we are asked to find the x-value given a particular y-value. 11. The rectangular coordinate system1 consists of two real number lines that intersect at a right angle. 1.1 Functions and Function Notation - Precalculus 2e | OpenStax Uh-oh, there's been a glitch We're not quite sure what went wrong. An expression is considered to be unambiguous or well-defined when the definition of the same allocates a unique value or interpretation. rymprypX;rw[{7]_W|l;G =kz Z$@bPAM.}Bg"52>fC oVKc WB2_we4s3{x )zy9z= 3 _wcs'K7Q% cG;x0]}u qc p--=::\mmD\,\]]km p7uu{ wwO[&mh rs\ 7j\4 W 7w row{{sFGqycq9q^{[w'p{|m l9Oq= 7/rO=p4z11=~ws{\]?v[r;}[>|%.rKo; _{~En.q]\\. Yes 5. Relations and Functions tate the domain and range of each relation. /Type /Page 0000047318 00000 n 2. >> This notation is used as follows: \(\begin{array} { l } { f ( x )\:\: =\:\:\: | x | - 2 } \\ { \:\:\:\:\:\downarrow \quad\quad\quad \downarrow } \\ { f ( \color{Cerulean}{- 5}\color{Black}{ )} = | \color{Cerulean}{- 5}\color{Black}{ |} - 2 = 5 - 2 = 3 } \end{array}\). << \(g (10) = 10\) and \(g (5) = 10 ; g (5) = 5\) and \(g (10) = 5\). 2-1 Skills Practice. You can get arithmetic support online by visiting websites such as Khan Academy or by downloading apps such as Photomath. Therefore, \(x = |y| + 1\) does not define a function. Therefore, the domain consists of all \(x\)-values in the interval \([8,)\). Ans. D \R(BJIBxCKoo-J-}wwfvv5s9["%VA How To Given a relationship between two quantities, determine whether the relationship is a function. The domain is \(\{4, 2, 0, 3\}\) and the range is \(\{3, 3, 5, 6, 7\}\). Find \(f ( 0 ) , f ( 2 )\), and \(f ( 4 )\). endobj 10. In this case, we interpret f( 5) = 3 as follows: Figure 2.1.17 7. If you randomly selected a group of people, you would observe a correlation between their ages and height. 1. Discovery-Based Worksheets have been specially designed to engage students in learnin, Attention 8th grade math teachers! Worksheet 4.2 relations and functions answer key - Apps can be a great way to help students with their algebra. 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 Form a relation from A to B to show whether the students belong to any of the four sections. The students look at 20 different x y tables and decide rather the ordered pairs form a linear or nonlinear relationship. 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 \(h \left( \frac { 1 } { 4 } \right) = 31 , h \left( \frac { 1 } { 2 } \right) = 28 , h ( 2 a - 1 ) = - 64 a ^ { 2 } + 64 a + 16\), 15. Determine whether this relation is a function or not, and find the values of both a and b. endobj Given values for x in the domain, we can quickly calculate the corresponding values in the range. >> 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, \(=(,)\). Domain: {3, 6, 9, 12}; Range: {-4, 0, 4} Mapping Diagrams: given a mapping diagram of a relation, we can tell if it is a function if each input is paired with exactly 1 output. Relations Expressed as Graphing. For example, use the function \(h\) defined by \(h (x) = \frac{1}{2} x 3\)to evaluate for \(x\)-values in the set \(\{2, 0, 7\}\). Relations and Functions Worksheet (with Answer Key + PDF) October 12, 2022 by Mathematical Worksheets The relation depicts the connection between input and output. Relations and Functions Worksheet with Answer Key (PDF), Scatter Plot and Line of Best Fit Worksheet (PDF), Absolute Value Equations and Inequalities Worksheet (PDF), 2nd Grade Measuring Worksheet (with Answer Key), Square Numbers Worksheet (with Answer Key), Expanded Form Worksheet (with Answer Key). There's more to your application than just filling out the forms. Find \(x\) where \(g (x) = 1, g (x) = 0\), and \(g (x) = 3\). endobj D 25. If all these pointers match, then the relation is proved to be a function. Relations and Functions tate the domain and range of each relation. Understanding the concept of relation and function will be helpful in real-life situations. endobj The representation of a relation on a rectangular coordinate plane, as illustrated above, is called a graph10. you CAN do math! 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. If each input has only one line connected to it, then the outputs are a function of the . Domain: \(\{2\}\); range: \(\{4, 2, 0, 2, 4\}\); function: no, 13. \(g ( - 3 ) = - 1 , g ( 0 ) = 1 , g ( 9 x + 6 ) = 6 x + 5\), 9. Given \(f ( x ) = \sqrt { 2 x + 4 }\), find \(f (2), f (0)\), and \(f \left( \frac { 1 } { 2 } a ^ { 2 } - 2 \right)\). To determine whether a given relation is a function or not, one needs first to find out the input values, then the output values. Free trial available at KutaSoftware.com. Functions are compactly defined by an algebraic equation, such as f(x) = | x | 2. 11 0 obj 10. endstream endobj 34 0 obj <>stream This relation is not a function. Domain: \(\{5\}\); range: \(\{ 0,2,4,6,8 \}\); function: no, 7. 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 maximum \(y\)-value is \(3\) and the minimum is \(3\); hence, the range consists of \(y\)-values in the interval \([3,3]\). >> 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. /Resources 13 0 R Step 1: Tell the class a story involving a real-world, linear functional relationship. 17The value or algebraic expression used as input when using function notation. This 12-question algebra 1 worksheet provides students with practice working with relations and functions. Are you covering Functions and Linear Equations and need a little break? Relationships are represented as ordered pairs, tables, mapping diagrams, and graphs. [ ] The previous example, where \(g (x) = x^{2}\), illustrates this nicely, \(\begin{array} { l } { g ( x + h ) \neq g ( x ) + g ( h ) } \\ { ( x + h ) ^ { 2 } \neq x ^ { 2 } + h ^ { 2 } } \end{array}\). Free worksheet(pdf) and answer key on distinguishing functions from relations, stating domain and range and more. A1vjp zN6p\W pG@ Interactive simulation the most controversial math riddle ever! We can also recognize functions as relations where no \(x\)-values are repeated. Ordered Pair, Domain, Range, Function Notation, Composite Functions, Real-Life Functions.This 8 page Functions and Relations worksheet (with complete answer key) covers all . We can use the given ordered pair solutions to estimate all of the other ordered pairs by drawing a line through the given points. Range = {4, 16, 25, 36} and Domain = {-2, 2, 4, 5, 6}, 10. Then. The will worksheet will discuss the concept of relations and functions. Answers. +. 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. Class 6 science chapter 3 extra questions, Solve nonlinear equations matlab symbolic. A Explanations 1. Chapter 1 - Analyzing Functions Answer Key CK-12 Math Analysis Concepts 1 1.1 Relations and Functions Answers 1. If all these pointers match, then the relation is proved to be a function. \(\frac { f ( x + h ) - f ( x ) } { h }\). You can also use mathematical representation for actual scenarios. Consider n (A) = m and n (B) = n. Find out the number of relations (non-empty) that can be predicted from A to B. /CreationDate (D:20220708141653-04'00') \(g (10) = 5, g (5) = 0\) and \(g (15) = 0 , g (5) = 10\) and \(g (25) = 10\), 5. [/Pattern /DeviceRGB] 1 0 obj Examples of domain and range, vertical line test, and determining if a relation is a function. Also sketch a graph for each equation. 0000000556 00000 n . Free worksheet(pdf) and answer key on distinguishing functions from relations, stating domain and range and more. 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. Relation. 6. 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. satisfaction rating 4.7/5; Stay in the Loop 24/7 If you're looking for a quick delivery, we've got you covered. Of special interest are relations where every \(x\)-value corresponds to exactly one \(y\)-value. endobj For instance, x is an object of set A and y is an object from set B. Given the graph of \(h\), find \(x\) where \(h(x)=-4\). \(f ( x + h ) = x ^ { 2 } + 2 x h + h ^ { 2 } + x + h + 1\), 5. endobj If this doesn't solve the problem, visit our Support Center . '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 The relation depicts the connection between input and output. Decide whether the relation is a function. Write each of the following as a relation, state the domain and range, then determine if it is a function. /PCSp 5 0 R 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! 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. Use the function to determine the salespersons income if he sells \(3\) cars this month. On the other hand, an undefined function is the one whose points are outside the domain. 39. f(x) = 3x2 5x; f(2) Answer 40. g(x) = 4x2 3x; g(3) 41. \(f (8) = 10, f (0) = 0, f (8) = 10\). Given the graph of \(g(x)\), find \(g(8), g(0)\), and \(g(8)\). In what years was the car valued at \($4,000\)? /Pages 3 0 R 0000000813 00000 n Answer: the output from the function g when the input is 7 Question: Suppose f(x . <> 1. 8Term used in honor of Ren Descartes when referring to the rectangular coordinate system. Domain: \([1,5]\); range: \([3,3]\); function: no. Given the graph, state the domain and range and determine whether or not it represents a function: From the graph we can see that the minimum \(x\)-value is \(1\) and the maximum \(x\)-value is \(5\). As we have seen, functions are also expressed using graphs. In other words, replace the variable with the value given inside the parentheses. Simplify \(\frac { g ( x + h ) - g ( x ) } { h }\) given \(g ( x ) = m x + b\). Functions and Relations Worksheet Decide whether the graph represents y as a function of x. Find out whether the following statements are true or false. Simplify \(\frac { q ( x + h ) - q ( x ) } { h }\) given \(q ( x ) = a x\). /CSp /DeviceRGB What are the Types of Functions in Mathematics? Don't spend your valuable time making your own test or assessmentwe took care of it for you! This is because a person has just one height value at any time in their life. yksL?cS3}s+y43!qgn8Bsr&n/g-|N59J4gt_l>5gI9?Ny=@LKFr. \(\{ ( 3,1 ) , ( 5,2 ) , ( 7,3 ) , ( 9,4 ) , ( 12,4 ) \}\), \(\{ ( 2,0 ) , ( 4,3 ) , ( 6,6 ) , ( 8,6 ) , ( 10,9 ) \}\), \(\{ ( 7,5 ) , ( 8,6 ) , ( 10,7 ) , ( 10,8 ) , ( 15,9 ) \}\), \(\{ ( 1,1 ) , ( 2,1 ) , ( 3,1 ) , ( 4,1 ) , ( 5,1 ) \}\), \(\{ ( 5,0 ) , ( 5,2 ) , ( 5,4 ) , ( 5,6 ) , ( 5,8 ) \}\), \(\{ ( - 3,1 ) , ( - 2,2 ) , ( - 1,3 ) , ( 0,4 ) , ( 0,5 ) \}\), \(g ( x ) = | x - 5 | \text { find } g ( - 5 ) , g ( 0 ) , \text { and } g ( 5 )\), \(g ( x ) = | x | - 5 ; \text { find } g ( - 5 ) , g ( 0 ) , \text { and } g ( 5 )\), \(g ( x ) = | 2 x - 3 | ; \text { find } g ( - 1 ) , g ( 0 ) , \text { and } g \left( \frac { 3 } { 2 } \right)\), \(g ( x ) = 3 - | 2 x | ; \text { find } g ( - 3 ) , g ( 0 ) , \text { and } g ( 3 )\), \(f ( x ) = 2 x - 3 ; \text { find } f ( - 2 ) , f ( 0 ) , \text { and } f ( x - 3 )\), \(f ( x ) = 5 x - 1 ; \text { find } f ( - 2 ) , f ( 0 ) , \text { and } f ( x + 1 )\), \(g ( x ) = \frac { 2 } { 3 } x + 1 ; \text { find } g ( - 3 ) , g ( 0 ) , \text { and } f ( 9 x + 6 )\), \(g ( x ) = - \frac { 3 } { 4 } x - \frac { 1 } { 2 } ; \text { find } g ( - 4 ) , g ( 0 ) , \text { and } g ( 6 x - 2 )\), \(g ( x ) = x ^ { 2 } ; \text { find } g ( - 5 ) , g ( \sqrt { 3 } ) , \text { and } g ( x - 5 )\), \(g ( x ) = x ^ { 2 } + 1 ; \text { find } g ( - 1 ) , g ( \sqrt { 6 } ) , \text { and } g ( 2 x - 1 )\), \(f ( x ) = x ^ { 2 } - x - 2 ; \text { find } f ( 0 ) , f ( 2 ) , \text { and } f ( x + 2 )\), \(f ( x ) = - 2 x ^ { 2 } + x - 4 ; \text { find } f ( - 2 ) , f \left( \frac { 1 } { 2 } \right) , \text { and } f ( x - 3 )\), \(h ( t ) = - 16 t ^ { 2 } + 32 ; \text { find } h \left( \frac { 1 } { 4 } \right) , h \left( \frac { 1 } { 2 } \right) , \text { and } h ( 2 a - 1 )\), \(h ( t ) = - 16 t ^ { 2 } + 32 ; \text { find } h ( 0 ) , h ( \sqrt { 2 } ) , h ( 2 a + 1 )\), \(f ( x ) = \sqrt { x + 1 } - 2 \text { find } f ( - 1 ) , f ( 0 ) , f ( x - 1 )\), \(f ( x ) = \sqrt { x - 3 } + 1 ; \text { find } f ( 12 ) , f ( 3 ) , f ( x + 3 )\), \(g ( x ) = \sqrt { x + 8 } ; \text { find } g ( 0 ) , g ( - 8 ) , \text { and } g ( x - 8 )\), \(g ( x ) = \sqrt { 3 x - 1 } ; \text { find } g \left( \frac { 1 } { 3 } \right) , g \left( \frac { 5 } { 3 } \right) , \text { and } g \left( \frac { 1 } { 3 } a ^ { 2 } + \frac { 1 } { 3 } \right)\), \(f ( x ) = x ^ { 3 } + 1 ; \text { find } f ( - 1 ) , f ( 0 ) , f \left( a ^ { 2 } \right)\), \(f ( x ) = x ^ { 3 } - 8 ; \text { find } f ( 2 ) , f ( 0 ) , f \left( a ^ { 3 } \right)\), \(f ( x ) = 2 x - 3 ; \text { find } x \text { where } f ( x ) = 25\), \(f ( x ) = 7 - 3 x ; \text { find } x \text { where } f ( x ) = - 27\), \(f ( x ) = 2 x + 5 ; \text { find } x \text { where } f ( x ) = 0\), \(f ( x ) = - 2 x + 1 ; \text { find } x \text { where } f ( x ) = 0\), \(g ( x ) = 6 x + 2 ; \text { find } x \text { where } g ( x ) = 5\), \(g ( x ) = 4 x + 5 ; \text { find } x \text { where } g ( x ) = 2\), \(h ( x ) = \frac { 2 } { 3 } x - \frac { 1 } { 2 } ; \text { find } x \text { where } h ( x ) = \frac { 1 } { 6 }\), \(h ( x ) = \frac { 5 } { 4 } x + \frac { 1 } { 3 } ; \text { find } x \text { where } h ( x ) = \frac { 1 } { 2 }\).

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