function and relation worksheet with answer key

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This bundle contains 9 worksheets on Functions.Worksheet 1: Finding domain and range from graphsStandard. 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. endobj Relations and Functions Worksheet (with Answer Key + PDF) October 12, 2022 by Mathematical Worksheets The relation depicts the connection between input and output. 4.2 Relations and Functions A function is a relation in . Functions are compactly defined by an algebraic equation, such as $f (x) = |x| 2$. |E[v%D '_s;.C\{ b/01w$}1$>(EpyQx~_E6( yO-ve_v64> zR.,b EenTZU<8[o,T(%*pHB %ZqiCX|@B; -6c\)xN8} dgK|!OJn-)J8e1$>XFZk4:c[6\0dY4i\W+H}#s.v.9_ 6!jW3bsFqPYb:h C8Ejp3+t 1,WC?d`}!*/V;7j @T1yDF,5M=]nOnD; Instead of writing their answers, students will color them! Domain and Range (Algebra 1) endobj 0000003486 00000 n D \R(BJIBxCKoo-J-}wwfvv5s9["%VA trailer 1) 2x + 3y = 12 x-intercepts (let y = 0). Evaluate the inverse and also rule out whether the same is a function or not. The set consisting of all of the first components of a relation, in this case the x-values, is called the domain11. 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. As all the 120 students belong to class 11, every pupil must be in any of the sections. Look no further! 5. /SA true As all the 120 students belong to class 11, every pupil must be in any of the sections. Therefore, $f (4) = 27$. 1.1 Functions and Function Notation - Precalculus 2e | OpenStax Uh-oh, there's been a glitch We're not quite sure what went wrong. Any curve graphed on a rectangular coordinate plane represents a set of ordered pairs and thus defines a relation. Given the linear function defined by $f(x)=2x-5$, simplify the following. This is an extremely easy assignment to grade! ' 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]. The argument can be any algebraic expression. Then determine the domain and range. 8. Answer: the output from the function g when the input is 7. Plus each one comes with an answer key. 0 3. TPT empowers educators to teach at their best. There's more to your application than just filling out the forms. (b) {(2, 1), (4, 2), (6, 3), (8, 4), (10, 5), (12, 6), (14, 7)} is not a function. /Resources 13 0 R Answers vary, should mention how the function does not always have the same output for a given input. +. 10A visual representation of a relation on a rectangular coordinate plane. Simplify $\frac { q ( x + h ) - q ( x ) } { h }$ given $q ( x ) = a x$. 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. Share a link to a page that you think others may find useful. Expression to convert Fahrenheit to Celsius is y = (5x/9) (160/9). Relations Expressed as Graphing. endobj Domain: $\{ 7,8,10,15 \}$; range: $\{ 5,6,7,8,9 \}$; function: no, 5. $g (10) = 10$ and $g (5) = 10 ; g (5) = 5$ and $g (10) = 5$. As pictured, the $x$-value $3$ corresponds to more than one $y$-value. << 8. endobj The given relation is not a function because the $x$-value $3$ corresponds to two $y$-values. The relation is a function because each x-value corresponds to exactly one y-value. 2. Some filters moved to Formats filters, which is at the top of the page. 8Term used in honor of Ren Descartes when referring to the rectangular coordinate system. The previous example, where $g (x) = x^{2}$, illustrates this nicely, $\begin{array} { l } { g ( x + h ) \neq g ( x ) + g ( h ) } \\ { ( x + h ) ^ { 2 } \neq x ^ { 2 } + h ^ { 2 } } \end{array}$. /Parent 3 0 R This is a relations and functions worksheet. endobj After that, check whether each input value has a corresponding out value. K0iABZyCAP8C@&*CP=#t] 4}a ;GDxJ> ,_@FXDBX$!k"EHqaYbVabJ0cVL6f3bX'?v 6-V``[a;p~\2n5 &x*sb|! Ans. Consider n (A) = m and n (B) = n. Find out the number of relations (non-empty) that can be predicted from A to B. Write each of the following as a relation, state the domain and range, then determine if it is a function. [/Pattern /DeviceRGB] endobj Avg. Are you looking for a comprehensive set of worksheets to introduce functions to your students? 5Pairs $(x, y)$ that identify position relative to the origin on a rectangular coordinate plane. 4. Then. 7) What was the value of the car in $2005$? 12 graphs.Worksheet 2: Finding range given domainRiddle. Ex 5. <> Domain: $(, 1]$; range: ; function: no, 17. Find $f (4), f (0)$, and $f (2)$.\. hs2z\nLA"Sdr%,lt 6. Analyzing Relations and Functions KEY. >> 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. Domain: ; range: $[0, ]$; function: yes, 27. yksL?cS3}s+y43!qgn8Bsr&n/g-|N59J4gt_l>5gI9?Ny=@LKFr. endobj Are you covering Functions and Linear Equations and need a little break? 15If any vertical line intersects the graph more than once, then the graph does not represent a function. { "201:_Relations_Graphs_and_Functions" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "202:_Linear_Functions_and_Their_Graphs" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "203:_Modeling_Linear_Functions" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "204:_Graphing_the_Basic_Functions" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "205:_Using_Transformations_to_Graph_Functions" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "206:_Solving_Absolute_Value_Equations_and_Inequalities" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "207:_Solving_Inequalities_with_Two_Variables" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "20E:_2E:_Graphing_Functions_and_Inequalities_(Exercises)" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()" }, { "00:_Front_Matter" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "01:_Algebra_Fundamentals" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "02:_Graphing_Functions_and_Inequalities" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "03:_Solving_Linear_Systems" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "04:_Polynomial_and_Rational_Functions" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "05:_Radical_Functions_and_Equations" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "06:_Solving_Equations_and_Inequalities" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "07:_Exponential_and_Logarithmic_Functions" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "08:_Conic_Sections" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "09:_Sequences_Series_and_the_Binomial_Theorem" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "zz:_Back_Matter" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()" }, [ "article:topic", "license:ccbyncsa", "showtoc:no", "authorname:anonymous", "licenseversion:30", "program:hidden", "source@https://2012books.lardbucket.org/books/advanced-algebra/index.html" ], https://math.libretexts.org/@app/auth/3/login?returnto=https%3A%2F%2Fmath.libretexts.org%2FBookshelves%2FAlgebra%2FBook%253A_Advanced_Algebra%2F02%253A_Graphing_Functions_and_Inequalities%2F201%253A_Relations_Graphs_and_Functions, $ \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}}}$ $ \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash{#1}}} $$\newcommand{\id}{\mathrm{id}}$ $ \newcommand{\Span}{\mathrm{span}}$ $ \newcommand{\kernel}{\mathrm{null}\,}$ $ \newcommand{\range}{\mathrm{range}\,}$ $ \newcommand{\RealPart}{\mathrm{Re}}$ $ \newcommand{\ImaginaryPart}{\mathrm{Im}}$ $ \newcommand{\Argument}{\mathrm{Arg}}$ $ \newcommand{\norm}[1]{\| #1 \|}$ $ \newcommand{\inner}[2]{\langle #1, #2 \rangle}$ $ \newcommand{\Span}{\mathrm{span}}$ $\newcommand{\id}{\mathrm{id}}$ $ \newcommand{\Span}{\mathrm{span}}$ $ \newcommand{\kernel}{\mathrm{null}\,}$ $ \newcommand{\range}{\mathrm{range}\,}$ $ \newcommand{\RealPart}{\mathrm{Re}}$ $ \newcommand{\ImaginaryPart}{\mathrm{Im}}$ $ \newcommand{\Argument}{\mathrm{Arg}}$ $ \newcommand{\norm}[1]{\| #1 \|}$ $ \newcommand{\inner}[2]{\langle #1, #2 \rangle}$ $ \newcommand{\Span}{\mathrm{span}}$$\newcommand{\AA}{\unicode[.8,0]{x212B}}$, source@https://2012books.lardbucket.org/books/advanced-algebra/index.html, status page at https://status.libretexts.org. . Relations and Functions tate the domain and range of each relation. Worksheet on Math Relation | Relations and Functions Worksheets with Answers. >> $f (8) = 10, f (0) = 0, f (8) = 10$. Feel free to download and enjoy these free worksheets on functions and relations. A function is a relation in which each element of the domain is paired with EXACTLY one element of the range. Functions and relations worksheet answer key Key. Two Items Included. Worksheet 4.1 relations and functions answer key. D 25. The vertical line represents a value in the domain, and the number of intersections with the graph represent the number of values to which it corresponds. Mathematics is a way of dealing with tasks that involves numbers and equations. 3. f-1 (x) = (9x/5) + 32 and the inverse is a function also. Questions include sets of ordered pairs, tables, mapping diagrams, and graphs. 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. 11 0 obj 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 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. endobj Students will find the range given the domain.Worksheet 3: Function rules and table of valuesStandard. The set of $x$-values defines the domain and the set of $y$-values defines the range. A function, on the other hand, is a relation that produces one output for each given input. $\begin{aligned} f ( \color{Cerulean}{- 2}\color{Black}{ )} & = \sqrt { 2 ( \color{Cerulean}{- 2}\color{Black}{ )} + 4 } = \sqrt { - 4 + 4 } = \sqrt { 0 } = 0 \\ f ( \color{Cerulean}{0}\color{Black}{ )} & = \sqrt { 2 ( \color{Cerulean}{0}\color{Black}{ )} + 4 } = \sqrt { 0 + 4 } = \sqrt { 4 } = 2 \\ f ( \color{Cerulean}{\frac { 1 } { 2 } a ^ { 2 } - 2}\color{Black}{ )} & = \sqrt { 2( \color{Cerulean}{ \frac { 1 } { 2 } a ^ { 2 } - 2}\color{Black}{)} + 4 } = \sqrt { a ^ { 2 } - 4 + 4 } = \sqrt { a ^ { 2 } } = | a | \end{aligned}$, $f (2) = 0,\: f (0) = 2,\: f \left( \frac { 1 } { 2 } a ^ { 2 } - 2 \right)= |a|$. 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 /F7 7 0 R )feOJeB_~n Students will identify function rules by, Relations, Functions, Domain and Range Task CardsThese 20 task cards cover the following objectives:1) Identify the domain and range of ordered pairs, tables, mappings, graphs, and equations.2) Determine whether a relation is a function given ordered pairs, tables, mappings, graphs, and equations.A recording worksheet is also included for students to write down their answers as they use the task cards. 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). 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. 3 0 obj What is his income if he does not sell any cars in one month? 17The value or algebraic expression used as input when using function notation. Domain: $\{5\}$; range: $\{ 0,2,4,6,8 \}$; function: no, 7. Plus each one comes with an answer key. The first number is called the $x$-coordinate, and the second number is called the $y$-coordinate. Decide whether the following relations are functions. The worksheet is also editable if you would like to make any changes. (c) All functions are relations, but all relations are not functions. '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 endobj 39. Not all relations are functions, and not all functions are relations. Given the graph, determine the domain and range and state whether or not it is a function: Domain: $(,15]$; range:; function: no. $\frac { f ( x + h ) - f ( x ) } { h }$. A Explanations 1. Find $x$ where $g (x) = 0, g (x) = 10$, and $g (x) = 15$. 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 $5$. x ! Domain: ; range: ; function: yes, 23. Here we are asked to find the x-value given a particular y-value. 13. D 25. Algebra frequently involves functions, and so the notation becomes useful when performing common tasks. It is important to note that $y$ and $f(x)$ are used interchangeably. 15 33 17 15, 11 15 Relations Expressed as Graphing Write each of the following as a relation, state the domain and range, then determine if it is a function. With a wide variety of practice problems, your students will gain a deep understanding of these fundamental concepts and. In what year was the value of the car at a minimum? Example 5: Solve the equations for y to determine if the equation defines a function. If the function is f (x)= 6x-27, and the domain is {-5, 3, 15, 17}, then find the range. Provide a brief summary of his life and accomplishments. The domain is $\{4, 2, 0, 3\}$ and the range is $\{3, 3, 5, 6, 7\}$. 7The four regions of a rectangular coordinate plane partly bounded by the $x$- and $y$-axes and numbered using the Roman numerals I, II, III, and IV. 7.Lp/; )Q[.[mJ-y)eUt `=PKj~82%.s*`4F/\.{f3O)rQyl8q3ay[T SC ~Gh FV>2 u/_$\BCv< 5]s.,4&yUx~xw-bEDCHGKwFGEGME{EEKX,YFZ ={$vrK [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 Not all relations are functions, and not all functions are relations. Answers. $g ( - 5 ) = 25 , g ( \sqrt { 3 } ) = 3 , g ( x - 5 ) = x ^ { 2 } - 10 x + 25$, 11. 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. This download also includes a PDF "worksheet" with the exact same questions as the Google Form. Domain: $\{1, 0, 1, 2\}$; range: $\{0, 1, 2, 3, 4\}$; function: no, 11. This is a coloring activity for a set of 12 problems on identifying the domain and range for a relation. This relation is not a function. $g (2) = 5, g (3) = 4$ and $g (1) = 4 , g (5) = 4$ and $g (1) = 4$, 7. 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. /CA 1.0 If you need an answer fast, you can always count on Google. 5 0 obj Vedantu LIVE Online Master Classes is an incredibly personalized tutoring platform for you, while you are staying at your home. 1. In this example, the output is given and we are asked to find the input. endobj 5. x{|7>Z]-Ed]-lJVe;qN8v%vb;vnv$@ \CH(w 4The flat surface defined by $x$- and $y$-axes. 0000006193 00000 n 1 2 . $g ( - 5 ) = 10 , g ( 0 ) = 5 , g ( 5 ) = 0$, 3. Yes 5. This product contains a worksheet and an assessment. 6. Accessibility StatementFor more information contact us atinfo@libretexts.orgor check out our status page at https://status.libretexts.org. 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/ [U6Ue:}au&+X[f]p2n3&\ _ 12The set consisting of all of the second components of a relation. This is a relations and functions worksheet. Consider n (A) = m and n (B) = n. Find out the number of relations (non-empty) that can be predicted from A to B. Applying for a job is more than just filling out an application. 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 Illustrate the travelled distance in the form of function t in hours. <>>> How to Calculate the Percentage of Marks? Recall that when evaluating, it is a best practice to begin by replacing the variables with parentheses and then substitute the appropriate values. A relation with this property is called a function14. Find $x$ where $g (x) = 5, g (x) = 0$, and $g (x) = 10$. 6 0 obj /ColorSpace << What is Meant by Well-defined and Undefined Function? Explain to a beginning algebra student what the vertical line test is and why it works. >> 4. Use the graph to find the corresponding $y$-values where $x = 8, 0$, and $8$. 3. f-1 (x) = (9x/5) + 32 and the inverse is a function also. >> .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' Free worksheet(pdf) and answer key on distinguishing functions from relations, stating domain and range and more. So, this relation is a function as well. Determine the domain and range of the following relation and state whether it is a function or not: $\{(1, 4), (0, 7), (2, 3), (3, 3), (4, 2)\}$. Quizzes with auto-grading, and real-time student data. Determine whether this relation is a function or not, and find the values of both a and b. The google activity may be edited if needed (add/delete questions, change answer type, etc.) It has so many equations and etc that it knows how to do, and has many advantages that other math apps do not. It is a relation.) 2. . Our team is dedicated to providing the best possible service to our customers. To check if a relation is a function, given a mapping diagram of the relation, use the following criterion: 1. x][%9r~_q6Ge 7zYz}! If you wish to get more such worksheets of other maths chapters, please make sure to download the Vedantu app today! 1A system with two number lines at right angles specifying points in a plane using ordered pairs $(x, y)$. Domain. 0000000016 00000 n Ans. 1. Worksheet 7.4 inverse functions answer key - Download worksheet 7.4 inverse functions and more Elementary Mathematics Lecture notes in PDF only on Docsity! 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 . <> As a check, we can evaluate $f (4) = 5 (4) + 7 = 27$. Special relations where every $x$-value (input) corresponds to exactly one $y$-value (output) are called functions. A1vjp zN6p\W pG@ Graph the given set of points, then answer the questions that follow. The domain is $\{1, 0, 2, 3, 4\}$ and the range is $\{2, 3, 4, 7\}$. To determine whether a given relation is a function or not, one needs first to find out the input values, then the output values. /CSpg /DeviceGray This 12-question algebra 1 worksheet provides students with practice working with relations and functions. 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. <> So, this relation is a function as well. <> P x P is a Cartesian product having nine elements. n 14. The value of a certain automobile in dollars depends on the number of years since it was purchased in $1970$ according to the following function: 11. 9. $\{ ( 3,1 ) , ( 5,2 ) , ( 7,3 ) , ( 9,4 ) , ( 12,4 ) \}$, $\{ ( 2,0 ) , ( 4,3 ) , ( 6,6 ) , ( 8,6 ) , ( 10,9 ) \}$, $\{ ( 7,5 ) , ( 8,6 ) , ( 10,7 ) , ( 10,8 ) , ( 15,9 ) \}$, $\{ ( 1,1 ) , ( 2,1 ) , ( 3,1 ) , ( 4,1 ) , ( 5,1 ) \}$, $\{ ( 5,0 ) , ( 5,2 ) , ( 5,4 ) , ( 5,6 ) , ( 5,8 ) \}$, $\{ ( - 3,1 ) , ( - 2,2 ) , ( - 1,3 ) , ( 0,4 ) , ( 0,5 ) \}$, $g ( x ) = | x - 5 | \text { find } g ( - 5 ) , g ( 0 ) , \text { and } g ( 5 )$, $g ( x ) = | x | - 5 ; \text { find } g ( - 5 ) , g ( 0 ) , \text { and } g ( 5 )$, $g ( x ) = | 2 x - 3 | ; \text { find } g ( - 1 ) , g ( 0 ) , \text { and } g \left( \frac { 3 } { 2 } \right)$, $g ( x ) = 3 - | 2 x | ; \text { find } g ( - 3 ) , g ( 0 ) , \text { and } g ( 3 )$, $f ( x ) = 2 x - 3 ; \text { find } f ( - 2 ) , f ( 0 ) , \text { and } f ( x - 3 )$, $f ( x ) = 5 x - 1 ; \text { find } f ( - 2 ) , f ( 0 ) , \text { and } f ( x + 1 )$, $g ( x ) = \frac { 2 } { 3 } x + 1 ; \text { find } g ( - 3 ) , g ( 0 ) , \text { and } f ( 9 x + 6 )$, $g ( x ) = - \frac { 3 } { 4 } x - \frac { 1 } { 2 } ; \text { find } g ( - 4 ) , g ( 0 ) , \text { and } g ( 6 x - 2 )$, $g ( x ) = x ^ { 2 } ; \text { find } g ( - 5 ) , g ( \sqrt { 3 } ) , \text { and } g ( x - 5 )$, $g ( x ) = x ^ { 2 } + 1 ; \text { find } g ( - 1 ) , g ( \sqrt { 6 } ) , \text { and } g ( 2 x - 1 )$, $f ( x ) = x ^ { 2 } - x - 2 ; \text { find } f ( 0 ) , f ( 2 ) , \text { and } f ( x + 2 )$, $f ( x ) = - 2 x ^ { 2 } + x - 4 ; \text { find } f ( - 2 ) , f \left( \frac { 1 } { 2 } \right) , \text { and } f ( x - 3 )$, $h ( t ) = - 16 t ^ { 2 } + 32 ; \text { find } h \left( \frac { 1 } { 4 } \right) , h \left( \frac { 1 } { 2 } \right) , \text { and } h ( 2 a - 1 )$, $h ( t ) = - 16 t ^ { 2 } + 32 ; \text { find } h ( 0 ) , h ( \sqrt { 2 } ) , h ( 2 a + 1 )$, $f ( x ) = \sqrt { x + 1 } - 2 \text { find } f ( - 1 ) , f ( 0 ) , f ( x - 1 )$, $f ( x ) = \sqrt { x - 3 } + 1 ; \text { find } f ( 12 ) , f ( 3 ) , f ( x + 3 )$, $g ( x ) = \sqrt { x + 8 } ; \text { find } g ( 0 ) , g ( - 8 ) , \text { and } g ( x - 8 )$, $g ( x ) = \sqrt { 3 x - 1 } ; \text { find } g \left( \frac { 1 } { 3 } \right) , g \left( \frac { 5 } { 3 } \right) , \text { and } g \left( \frac { 1 } { 3 } a ^ { 2 } + \frac { 1 } { 3 } \right)$, $f ( x ) = x ^ { 3 } + 1 ; \text { find } f ( - 1 ) , f ( 0 ) , f \left( a ^ { 2 } \right)$, $f ( x ) = x ^ { 3 } - 8 ; \text { find } f ( 2 ) , f ( 0 ) , f \left( a ^ { 3 } \right)$, $f ( x ) = 2 x - 3 ; \text { find } x \text { where } f ( x ) = 25$, $f ( x ) = 7 - 3 x ; \text { find } x \text { where } f ( x ) = - 27$, $f ( x ) = 2 x + 5 ; \text { find } x \text { where } f ( x ) = 0$, $f ( x ) = - 2 x + 1 ; \text { find } x \text { where } f ( x ) = 0$, $g ( x ) = 6 x + 2 ; \text { find } x \text { where } g ( x ) = 5$, $g ( x ) = 4 x + 5 ; \text { find } x \text { where } g ( x ) = 2$, $h ( x ) = \frac { 2 } { 3 } x - \frac { 1 } { 2 } ; \text { find } x \text { where } h ( x ) = \frac { 1 } { 6 }$, $h ( x ) = \frac { 5 } { 4 } x + \frac { 1 } { 3 } ; \text { find } x \text { where } h ( x ) = \frac { 1 } { 2 }$.

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