Domain and range worksheet #1

Range = [-1, 1] Domain and Range of Cosine. We know that the cosine function is the ratio of the adjacent side and hypotenuse of a right-angled triangle. The domain and range of cosine are given by: Domain = All real numbers, i.e., (−∞, ∞) Range = [-1, 1] ☛Note: The domain and range of sin and cos graphs are the same. Domain and Range ...Domain and Range Worksheet #1 Name: ____________________ State the domain and range for each graph and then tell if the graph is a function (write yes or no). If the graph …This worksheet is for students to practice finding the following features of quadratic functions: direction of opening, vertex, axis of symmetry, solutions, y-intercept, domain, and range.The first sheet is the students' answer sheet. The second sheet is a picture of all the graphs. The teacher has the option of either using the given graphs, having students find …This is a lesson for section 1.1 Functions, Domain, and Range for the Functions 11 (MCR3U) course. This lesson explains what qualifies a relation to be a fun...Web what is a “domain and range algebra 1 worksheet”? You can select the types of functions and non. Web algebra 1 worksheets domain and range worksheets. If (X) = −4X − 7, Find. Web this algebra 1 domain and range worksheet will produce problems for identifying whether graphed sets are functions or not.This quiz and worksheet can help students to test the following skills: Defining key concepts - ensure that you can accurately define words like inputs, range, and domain. Problem solving - use ...This algebra 1 domain and range worksheet will produce problems for identifying whether mapping diagrams are. Web download this domain and range worksheet include 10 getting and answers as a practice test. For X = 5 4. Find the codomain for the function f(x) = 2x + 5.Domains and Ranges of the Toolkit Functions. We will now return to our set of toolkit functions to note the domain and range of each. Constant Function: \(f(x)=c\) The domain here is not restricted; \(x\) can be anything. When this is the case we say the domain is all real numbers. The outputs are limited to the constant value of the function.Domain: All reals except −1. All reals except 0 Range: Range: All reals except 1. All reals except 2. 1. Many answers. Ex: f ( x) =. x − 25. Create your own worksheets like this one with Infinite Algebra 2. In today’s digital age, having a strong online presence is essential for any business or individual. One of the first steps to establishing an online presence is getting a website....36 domain and range graphs worksheetDomain and range worksheet algebra 1 / domain range worksheet kuta kids Domain range worksheet function finding graph worksheets example find engaging students functions these math fedjp grass site adjust probably provideFinding domain and range worksheet. Check Details. Domain …6) Determine the domain and range of each of the following relations. Use a graphing calculator or a graphing app to help if necessary. Make a rough sketch of the graph. = − + 3. b) =. + 1. − 4. c)Finding free printable worksheets is an excellent way for teachers and homeschooling parents to save on their budgets. It’s also a great way for parents to get in extra practice wi...Registering a domain name with Google is a great way to get your website up and running quickly. With Google’s easy-to-use interface, you can register your domain name in minutes a...Domain and Range Worksheet #1 Name: ____________________. State the domain and range for each graph and then tell if the graph is a function (write yes or no). If the graph …Click on the link above each picture to download that worksheet. Worksheets were ... Domain and Range Worksheet. Coordinate Plane Activity 1. Coordinate Plane ...How To: Given a function written in equation form, find the domain. Identify the input values. Identify any restrictions on the input and exclude those values from the domain. Write the domain in interval form, if possible. Example 6.4.2: Finding the Domain of a Function. Find the domain of the function f(x) = x2 − 1.Determining the Dependent and Independent Variables and Finding the Domain and Range of a Function. After going through this module, you are expected to: 1. identify the independent and dependent variables; 2. identify the domain and range of a function expressed in words, function rule, symbol, table of values, ordered pairs and graph; andThis quiz and worksheet can help students to test the following skills: Defining key concepts - ensure that you can accurately define words like inputs, range, and domain. Problem solving - use ... Skill plans. IXL plans. Virginia state standards. Textbooks. Test prep. Awards. Improve your math knowledge with free questions in "Domain and range" and thousands of other math skills. Finding Domain and Range from Graphs. Another way to identify the domain and range of functions is by using graphs. Because the domain refers to the set of possible input values, the domain of a graph consists of all the input values shown on the x-axis. The range is the set of possible output values, which are shown on the y-axis. Keep in mind ... Aug 24, 2018 · A colourful worksheet to practise the topic Domain and Range. The first six questions have the domain restricted. The student is also asked to give the equation of the function. The last five questions have no restriction on the domain, the student will need to be familiar with their Maths notation. This page titled 3.2E: Domain and Range (Exercises) is shared under a CC BY 4.0 license and was authored, remixed, and/or curated by OpenStax via source content that was edited to the style and standards of the LibreTexts platform; …Jan 23, 2023 ... ... one output. The graph of a function is the set of ordered pairs ... Describing Domain and Range from Graphs | Math Lesson & Worksheet by Mr.Selecting the best domain registrar ensures great service and tools for configuring your domain. Read this guide for the best places to buy a domain. Maddy Osman A domain name is a...DOMAIN AND RANGE OF EXPONENTIAL FUNCTIONS. The student is expected to determine the domain and range of exponential A.9A functions of the form f(x) = abx and represent the domain and range using inequalities.Questions pertain to the graph at the right. a) Which type of function could be used to model this data? b) Which choice represents the domain of the data as displayed in the graph? c) Which choice represents the range of the data as displayed in the graph? 12. The domain of f (x) = 3x + 2 is {-1 < x < 4}. Worksheet by Kuta Software LLC-2-Each graph represents a relation. Determine if the relation is a function. Then find the domain and range. 7) x y-8-6-4-22468-8-6-4-2 2 4 6 8 The relation is not a function. Domain: x = -2 Range: -6 < y £ 4 8) x y-8-6-4-22468-8-6-4-2 2 4 6 8 The relation is not a function. Domain: x £ 2 Range: All real numbers ... In Section 1.1, Functions and Function Notation, we were introduced to the concepts of domain and range. In this section, we will practice determining domains and ranges for specific functions. Keep in mind that in determining domains and ranges, we need to consider what is physically possible or meaningful in real-world examples, such as …Worked out by Jakubíková K. 1 Math Worksheet 3 – DOMAIN and RANGE Given a function y = f(x), the Domain of the function is the set of inputs and the Range is the set of resulting outputs. Domains can be found algebraically; ranges are often found algebraically and graphically. Domains and Ranges are sets.This Algebra 1 Domain and Range Worksheet will produce problems for finding the domain and range of graphed sets. You can select the types of things graphed as well …Jul 13, 2010 ... Thanks to all of you who support me on Patreon. You da real mvps! $1 per month helps!! :) https://www.patreon.com/patrickjmt !INTERDISCIPLINARY EXAMS. NYC TEACHER RESOURCES. STANDARD F.IF.B.5. Determine the domain of a function from its graph and, where applicable, identify the …1.1.1 Use functional notation to evaluate a function. 1.1.2 Determine the domain and range of a function. 1.1.3 Draw the graph of a function. 1.1.4 Find the zeros of a function. 1.1.5 Recognize a function from a table of values. 1.1.6 Make new functions from two or more given functions.Domain and Range Worksheet Find the Domain and Range of each of the following. 1. 4. 7. 10. 13. y 2 x 3 1 y x. AI Homework Help. Expert Help. Study Resources. Log in Join. Domain and Range Worksheet 2 .docx - Domain and Range... Doc Preview. Pages 1. Total views 100+ University of Guelph. MATH. MATH 1080. poprockpop1235.Section 1.2 Domain and Range 21 Section 1.2 Domain and Range One of our main goals in mathematics is to model the real world with mathematical functions. In doing so, it is important to keep in mind the limitations of those models we create. This table shows a relationship between circumference and height of a tree as it grows.Jan 29, 2018 ... Day 1 - Domain, Range, and End Behavior. 93K views · 6 years ago ...more. MsPopRocks. 636. Subscribe. 1K. Share. Save.Printable Worksheets @ www.mathworksheets4kids.com Name : Domain and Range - Function L1S1 ... Domain = {1, 5, 9, 11, 15, 19} Range : x 4 f(x) = 5 – 3 x; Domain = {–7, 0, 14} 7 3x – 2 5 –1 – x 2 PREVIEW www.mathworksheets4kids.com Members, please o. his er? o s. n Gain complete access to the largestPrintable PDFs for Domain and Range Worksheets,Download PDFs for Domain and Range Worksheets Created Date: 4/16/2021 5:21:38 PM ...Domain and Range Worksheet with Answers. The domain of a function is the complete set of possible values of the independent variable. In plain English, this definition means: The domain is the set of all possible x -values which will make the function "work", and will output real y -values. When finding the domain, remember:This worksheet focuses on finding the domain and range of graphs. The graphs include linear, quadratic, circles, polynomials, points, a step function, and a sine wave. Also, there are several problems that require the knowledge of using the union symbol. Most of the answers are in interval notation. The points and step function lists the domain ... Showing top 8 worksheets in the category - Domain And Range Of A Function. Some of the worksheets displayed are Domain and range work 1 name, , Domain and range function, Domain and range ordered pairs 1, Concept 21 identifying functions, Domain and range 1 determine the domain and, Examples of domains and ranges from graphs, …In the following exercises, use the mapping of the relation to a. list the ordered pairs of the relation, b. find the domain of the relation, and c. find the range of the relation. 5. Answer. 6. 7. For a woman of height 5 ′ 4 ″ the mapping below shows the …Worksheet Practice PACKET. 12. I can use the discriminant to determine the number and type of solutions/zeros. 1. I can identify a function as quadratic given a table, equation, or graph. 2. I can determine the appropriate domain and range of a quadratic equation or event. 3. I can identify the minimum or maximum and zeros of a function with a ... Browse algebra 1 domain and range resources on Teachers Pay Teachers, a marketplace trusted by millions of teachers for original educational resources. Browse ... These Domain and Range Worksheets are a good resource for students in the 8th Grade through the 12th Grade.Identifying Functions From Mapping Diagrams WorksheetsIdentifying ...Now you are ready to create your Domain and Range Worksheet by pressing the Create Button. If You Experience Display Problems with Your Math Worksheet. This Algebra 1 Domain and Range Worksheet will produce problems for identifying whether mapping diagrams are functions or not. You can select the types of values as well as the number of values ... In this section, you will learn how to find the domain and range of a function using different methods, such as graphs, equations, and tables. You will also explore how to use the concepts of domain and range to model real-world situations, such as profit and cost functions. This is a corequisite workbook for calculus for business and social sciences, …She has between 10 and. 12 gallons of gas in the tank. a)a) List the independent and dependent quantities. 14. Sal and three friends plan to bowl one or two games each. Each game costs $2.50. a) List the independent and dependent quantities. b) Find the reasonable domain and range values. b) Find the reasonable domain and …Worksheet on Functions in Math (relations, domain and range). This worksheet goes in tandem with this web page. ... The all important rule for a function in math -- that each value in the domain has only 1 value in the range -- would still be true if we had a second copy of 1 ordered pair. Practice 5. For the relation below to ...For this quiz and worksheet combo, you are reviewing the domain and range of functions with inequalities. Questions ask about a resulting graph from a given domain and range, as well as a cubic ...Jan 11, 2018 ... Find the domain and range. Page 4. January 11, 2018. {(–1, –4), ( ...Identifying Domains and Ranges from Graphs Worksheets. These Algebra 1 Domain and Range Worksheets will produce problems for finding the domain and range of graphed sets. You can select the types of things graphed as well as whether the sheet should ask if each graph is a function or not. This worksheet is for students to practice finding the following features of quadratic functions: direction of opening, vertex, axis of symmetry, solutions, y-intercept, domain, and range.The first sheet is the students' answer sheet. The second sheet is a picture of all the graphs. The teacher has the option of either using the given graphs, having students find …"In earlier grades, students define, evaluate, and compare functions and use them to model relationships between quantities. In this module, students extend their study of functions to include function notation and the concepts of domain and range. They explore many examples of functions and their graphs, focusing on the contrast between linear and …She has between 10 and. 12 gallons of gas in the tank. a)a) List the independent and dependent quantities. 14. Sal and three friends plan to bowl one or two games each. Each game costs $2.50. a) List the independent and dependent quantities. b) Find the reasonable domain and range values. b) Find the reasonable domain and range values.Domain And Range Worksheets Worksheet 1 (City of Oakland) This document is locked as it has been sent for signing. You have successfully completed this document. Other parties need to complete fields in the document. You will recieve an email notification when the document has been completed by all parties. This document has …Determining the Dependent and Independent Variables and Finding the Domain and Range of a Function. After going through this module, you are expected to: 1. identify the independent and dependent variables; 2. identify the domain and range of a function expressed in words, function rule, symbol, table of values, ordered pairs and graph; andFree printable Function worksheets (pdf) with answer keys on the domain/range, evaluating functions, composition of functions ,1 to 1 , and more. 1 Functions and Change Domain and Range. Example 1: The table shows the movement of Jake driving his car. Write the domain and range using the information in the table. Practice Problem 1: Write the domain and range from the information in the table. The table represents the temperature in Jamaica in July. Time (# of days) 2 3 5 7 14 ...Domain and Range Worksheet. Course: Essential Mathematics (MA1022) 10 Documents. Students shared 10 documents in this course. University: James Cook University. ... Question 1 Find the domain and range of each of the following, whereyis a function ofx. (a)y= 5x+ 3 (b)y=− 7 x− 4 (c)y= 7 (d)y=x 2 (e)y= 2x 2 + 1 (f)y=x 2 − 2 x+ 5 (g)y= 4−x 2Sep 20, 2020 ... Algebra 1-3.2 Domain and Range of Continuous Graphs. Jen Schones•6.4K views · 13:07. Go to channel · domain and range of continuous graph.Domain and range worksheet 1 answer key — db-excel.comDomain and range word problems grade 11 university lesson 1 4 1 31 13 Worksheet algebra functions math exponential worksheets function logarithmic answers answer pdf logarithms equations aids key logarithm log exponents composite inverseDomain and range word problems.1 x 3 a Write down the domain of the function f. b Sketch the graph of the function f. c Write down the range of the function f. Answers a The domain is 1 x 3. b The graph of y 2 x 1 has gradient 2 and a y-intercept of 1. When x 1, y 2( 1) 1 3 When x 3, y 2(3) 1 5 f(x) ( 1, 3) (3, 5) Domain Range x O c The range is 3 f(x) 5. 3 Chapter 1: FunctionsDownload Domain and Range Worksheet #1 and more Calculus Exercises in PDF only on Docsity! Domain and Range Worksheet #1 Name: _____ State the domain and range for each graph and then tell if the graph is a function (write yes or no). If the graph is a function, state whether it is discrete, continuous or neither. This pdf set features polynomial, quadratic, reciprocal, and square root functions. Remember to use {} since the domain and range are expressed in discrete numbers and not intervals of values. Walk through this collection of free printable worksheets and identify the domain and range of the functions from the graphs.Are you looking for an engaging and effective way to teach your preschooler how to write letters? Look no further than free letter tracing worksheets. These printable resources are...calc study material, good pracitce to remember functions, domain, and range worksheet mcr3u jensen which graphs represent functions? justify your answer. is. Skip to document. University; High School. Books; Sign in. ... 1. Functions, Domain, and Range -­‐ Worksheet. MCR3U. Jensen. 1) Which graphs represent functions? Justify your answer ...View 1.6A Worksheet 1-20-2024.pdf from MATH 1113 at University Of Georgia. % Name: Preclass Work - Finish Before Class Begins Watch the Pre-Class videos for Section 1.6 …Domain and Range Worksheet #1 Name: _____ State the domain and range for each graph and then tell if the graph is a function (write yes or no). If the graph is a function, state whether it is discrete, continuous or neither. Algebra 1 Notes SOL A.7 More on Domain/Range Mrs. Grieser Page 2 Set Builder Notation • Domain and Range are sets, so we must use set notation • Use curly brackets { } to …Click on the link above each picture to download that worksheet. Worksheets were ... Domain and Range Worksheet. Coordinate Plane Activity 1. Coordinate Plane ...Domain and Range Worksheet #1 Name: _____ State the domain and range for each graph and then tell if the graph is a function (write yes or no). If the graph is a function, state whether it is discrete, continuous or neither. 1) Domain 2) Domain 3) Domain Range Range Range Then determine the domain/range and if the relation is a function. 7) x y-8-6-4-22468-8-6-4-2 2 4 6 8 8) x y ... Create your own worksheets like this one with Infinite Algebra 1. Free trial available at KutaSoftware.com. Title: Infinite Algebra 1 - Discrete Relations Created Date:How To: Given a function written in equation form, find the domain. Identify the input values. Identify any restrictions on the input and exclude those values from the domain. Write the domain in interval form, if possible. Example 6.4.2: Finding the Domain of a Function. Find the domain of the function f(x) = x2 − 1.1 MAT 1033 WORKSHEET # 1 INTERVAL NOTATION (SECTION 1.1) A set is a collection of objects whose contents can be clearly determined. The objects in the set are called the elements of the set. Sets of real numbers can be represented using one of the following forms: 1. SET – BUILDER NOTATION. In this notation the elements are described, but …Learn how to find the domain and range of a function using pdf worksheets with finite and infinite graphs. The worksheets cover different types of functions, such as polynomial, quadratic, reciprocal, and square root functions. You can also identify functions, evaluate them, and use function rules to solve problems. Jan 7, 2023 ... http://www.greenemath.com/ Step-by-Step full solutions for our practice test on domain and range. Here, we will look at problems that deal ...Quarter 1 – Module 8: The Domain and Range of a Rational Functions. General Mathematics Alternative Delivery Mode Quarter 1 – Module 8: The Domain and Range of a Rational Functions First Edition, 2020. Republic Act 8293, section 176 states that: No copyright shall subsist in any work of the Government of the Philippines.Finding angles of triangles. Finding side lengths of triangles. Statistics. Visualizing data. Center and spread of data. Scatter plots. Using statistical models. Free Algebra 1 worksheets created with Infinite Algebra 1. Printable in convenient PDF format.Q h SMGaedue p ZwOiLt6h 7 FIqn1f OitnLi yt ve2 NAFlkgue MbNrDad 41 a.W Worksheet by Kuta Software LLC For each question, decide if it is a function. Then find the domain and range in set builder notation. 13) x y ... Domain, and Range Review 1) Every input has OAOO output; find an x with more than one y / vertical line test 2) Set of inputs; ...View Domain and Range Worksheet #1.docx from CIS MISC at Clover High School. AI Homework Help. Expert Help. Study Resources. Log in Join. Domain and Range Worksheet #1.docx - Doc Preview. Pages 2. Total views 12. Clover High School. CIS. CIS MISC. jandkgibson. 11/24/2021. View full document. Students also studied.In the following exercises, use the mapping of the relation to a. list the ordered pairs of the relation, b. find the domain of the relation, and c. find the range of the relation. 5. Answer. 6. 7. For a woman of height 5 ′ 4 ″ the mapping below shows the …Find the domain and range of relations or functions using ordered pairs, graphs, tables and more. Download free pdf worksheets for 8th grade and high school students to practice identifying the domain and range of relations or functions. Learn how to write the domain and range in set notation, mapping diagrams, function rules and tables. Algebraically determine the following domains. Use correct set notation. 1. 4. 7. m ( t d. ) q ( w ). ( y.View er.pdf from SH 304 at Aquinas College. Domain and Range Worksheet #1 Name: _ State the domain and range for each graph and then tell if the graph is a function (write yes or no). If the graph isQ h SMGaedue p ZwOiLt6h 7 FIqn1f OitnLi yt ve2 NAFlkgue MbNrDad 41 a.W Worksheet by Kuta Software LLC For each question, decide if it is a function. Then find the domain and range in set builder notation. 13) x y ... Domain, and Range Review 1) Every input has OAOO output; find an x with more than one y / vertical line test 2) Set of inputs; ...Download Exercises - Domain and Range Worksheet #1 | University of Southeastern Philippines (USEP) | If the graph is a function, state whether it is discrete, continuous or …In Section 1.1, Functions and Function Notation, we were introduced to the concepts of domain and range. In this section, we will practice determining domains and ranges for specific functions. Keep in mind that in determining domains and ranges, we need to consider what is physically possible or meaningful in real-world examples, such …Teaching children to read is an important skill they’ll use for the rest of their lives. When children need extra practice using their reading skills, it helps to have worksheets a...This worksheet is for students to practice finding the following features of quadratic functions: direction of opening, vertex, axis of symmetry, solutions, y-intercept, domain, and range.The first sheet is the students' answer sheet. The second sheet is a picture of all the graphs. The teacher has the option of either using the given graphs, having students find …Worksheet # 3: The Exponential Function and the Logarithm 1.(a)Graph the functions f(x) = 2x and g(x) = 2 x and give the domains and range of each function. (b)Determine if …Oct 6, 2021 · How To: Given a function written in equation form, find the domain. Identify the input values. Identify any restrictions on the input and exclude those values from the domain. Write the domain in interval form, if possible. Example 3.3.2: Finding the Domain of a Function. Find the domain of the function f(x) = x2 − 1. This quiz and worksheet can help students to test the following skills: Defining key concepts - ensure that you can accurately define words like inputs, range, and domain. Problem solving - use ... Check Details Domain and range practice worksheet domain and range worksheet 1. 12 best images of function notation algebra worksheets functionFunctions graphing quadratic form vertex slope intercept algebra transformations quadratics equations exponential excel insert aboard junction megcraig precal 14 best images of factoring …Learn how to find the domains and ranges of functions with this printable worksheet from Corbettmaths. It includes examples, exercises and answers for Level 2 Further Maths students. How To Graph An Exponential Function. To graph an exponential function, the best way is to use these pieces of information: Horizontal asymptote (y = 0, unless the function has been shifted up or down). The y-intercept (the point where x = 0 – we can find the y coordinate easily by calculating f (0) = ab 0 = a*1 = a).Aug 24, 2018 · A colourful worksheet to practise the topic Domain and Range. The first six questions have the domain restricted. The student is also asked to give the equation of the function. The last five questions have no restriction on the domain, the student will need to be familiar with their Maths notation. Download Page (PDF) Download Full Book (PDF) Resources expand_more. Periodic Table. Physics Constants. Scientific Calculator. Reference expand_more. Reference & Cite. Tools expand_more.Domain And Range Worksheets Worksheet 1 (City of Oakland) This document is locked as it has been sent for signing. You have successfully completed this document. Other parties need to complete fields in the document. You will recieve an email notification when the document has been completed by all parties. This document has …DHGAF: Get the latest Domain Holdings Australia stock price and detailed information including DHGAF news, historical charts and realtime prices. Indices Commodities Currencies Sto...Displaying all worksheets related to - Homework 1 Relations Domain Range And Functions. Worksheets are Work, Name date ms, Functions domain and range review date block, Algebra 2 and trigonometry chapter 4 functions, , Math work 1 function versus relation, 3 1 functions function notation, Unit 3 relations and functions. *Click on Open …Browse algebra 1 domain and range resources on Teachers Pay Teachers, a marketplace trusted by millions of teachers for original educational resources. Browse ... These Domain and Range Worksheets are a good resource for students in the 8th Grade through the 12th Grade.Identifying Functions From Mapping Diagrams WorksheetsIdentifying ...Worked out by Jakubíková K. 1 Math Worksheet 3 – DOMAIN and RANGE Given a function y = f(x), the Domain of the function is the set of inputs and the Range is the set of resulting outputs. Domains can be found algebraically; ranges are often found algebraically and graphically. Domains and Ranges are sets.Thus, the domain of an exponential function is the set of all real numbers (or) (-∞, ∞). The range of an exponential function can be determined by the horizontal asymptote of the graph, say, y = d, and by seeing whether the graph is above y = d or below y = d. Thus, for an exponential function f (x) = ab x, Domain is the set of all real ...Students will practice Identifying the Domain and Range of a Mathematical Relation as well as classify a relation as a function based on its domain and range. Example Questions …Functions are a correspondence between two sets, called the domain and the range. When defining a function, you usually state what kind of numbers the domain (x) ( x) and range (f(x)) ( f ( x)) values can be. But even if you say they are real numbers, that doesn’t mean that all real numbers can be used for x x. Functions are a correspondence between two sets, called the domain and the range. When defining a function, you usually state what kind of numbers the domain (x) ( x) and range (f(x)) ( f ( x)) values can be. But even if you say they are real numbers, that doesn’t mean that all real numbers can be used for x x.The same applies to the vertical extent of the graph, so the domain and range include all real numbers. Figure 18 For the reciprocal function f(x) = 1 x, f ( x) = 1 x, we cannot divide by 0, so we must exclude 0 from the domain. Further, 1 divided by any value can never be 0, so the range also will not include 0. Finding angles of triangles. Finding side lengths of triangles. Statistics. Visualizing data. Center and spread of data. Scatter plots. Using statistical models. Free Algebra 1 worksheets created with Infinite Algebra 1. Printable in convenient PDF format. | yimdptjrvr (article) | xknhwsm.