-1-Identify the domain and range of each. Exponential and Logarithmic Graph Worksheet. Logarithmic functions with definitions of the form f (x) = log b x have a domain consisting of positive real numbers (0, ∞) and a range consisting of all real numbers (− ∞, ∞). is the set of resulting outputs. Be it worksheets, online classes, doubt sessions, or any other form of relation, it’s the logical thinking and smart learning approach that we, at Cuemath, believe in. Free printable Function worksheets (pdf) with answer keys on the domain/range, evaluating functions, composition of functions ,1 to 1 , and more. 3. Inverse Functions4.1407 (b) We can determine that the function ƒ1x2 = 225 - x2 is not one-to-one by showing that different values of the domain correspond to the same value of the range. Domain and Range of Logarithmic Functions https://youtu.be/N98Z9P0uL4c Primary SOL: 8.15 The student will a) determine whether a given relation is a function; b) determine the domain and range of a function. Domain and Range of Functions and the Answers to matched problems 1,2,3 and 4. Graph the function on a coordinate plane remember that when no base is shown the base is understood to be 10. Worksheet will open in a new window. Worksheet 4.3—Logarithmic Functions Show all work. Worksheet by Kuta Software LLC MATHEMATICS 5 SN GRAPHING LOGARITHMIC FUNCTIONS Name_____ ID: 1 ©K R2]0a1T6h ^KNugtBav uS[oPfXtMwvavrHek hLJLICj.l c DAjlglM grGiygFhztdsx IreSsge_rtv]e[dZ. Tutorial, with detailed solutions, on how to find the domain and range of various real valued functions. Some of the worksheets for this concept are Graphing logarithms date period, Work logarithmic function, Homework 10 2 connecting logs and exponentials, Graphing logarithms date period, Work exponentials and logarithms, Transforming exponential and logarithmic functions, Graphing exponential functions work, Math110 exponential and logarithmic ho 3. When using the properties of logarithms to rewrite logarithmic functions, you must check to see whether the domain of the rewritten function is the same as the domain of the original. Then sketch the graph. 18. y = 1 + ln(-x) 19. Example 3: Find the domain and range of the function y = log ( x ) − 3 . Examples on How to Find the Domain of logarithmic Functions with Solutions Example 1 Find the domain of function f defined by f (x) = log 3 (x - 1) Solution to Example 1 f(x) can take real values if the argument of log 3 (x - 1) which is x - 1 is positive. of the function is the set of permissible inputs and the . Graph the function on a coordinate plane.Remember that when no base is shown, the base is understood to be 10 . Write down the values of x which are not in the domain of the following functions: a a. y = − √ 4−x2 b. Asymptote Equation. Below are the graphs of e xand e . Logarithmic functions with definitions of the form f (x) = log b x have a domain consisting of positive real numbers (0, ∞) and a range consisting of all real numbers (− ∞, ∞). Vanier College Sec V Mathematics Department of Mathematics 201-015-50 Worksheet: Logarithmic Function 1. Worksheet 4.10—Derivatives of Log Functions & LOG DIFF Show all work. • The domain is x > h, and the range is all real numbers. You can & download or print using the browser document reader options. About This Quiz & Worksheet. |x|−|y| =0 c. y = x3 d. y = x |x|,x=0 e. |y| = x. Homework: Domain and Range for Functions Name_ 1. Here are some examples illustrating how to ask for the domain and range. By definition, the logarithmic function is directly related to the exponential function; the two functions are called inverses of one another, much like y … You may remove cards as you learn them and randomize the list for better practice. Range. For example, consider $f\left(x\right)={\mathrm{log}}_{4}\left(2x - 3\right)$. For more math videos visit http://www.drphilsmathvideos.com!There are also online lessons you can try. 2. has the set of positive real numbers as its range. Worksheet 6-3: Transformations of Logarithmic Functions Transformations apply to logarithmic functions in the same way as they do to other functions. How to graph a logarithmic function? The graph approaches x = –3 (or thereabouts) more and more closely, so x = –3 is, or is very close to, the vertical asymptote. Yes, if we know the function is a general logarithmic function. Let us come to the names of those three parts with an example. Determine the key features of the function given in the graph: X-intercept: (4,0) Y-intercept: N/A Increasing or decreasing: Increasing Vertical asymptote: x=3 Horizontal asymptote: N/A Domain: {xER l x>3} Range: {yER} 2. The asymptote for exponential functions will generally be the x-axis. 3. has a graph with -intercept of 4. has a graph asymptotic to the -axis. 16. f(x) = log2(x-4) 17. y = log3(x-1)-2. Y intercept . The example below shows two different ways that a function can be represented: as a function table, and as a set of coordinates. State the Domain and Range of each of the given relations in the space provided. Graph the function, not by plotting points. 1) y log (x ) x y ... Identify the domain and range of each. MHF4U: Grade 12 University Functions (Public) Unit 3: Exponential and Logarithmic Functions Activity 2: Key Features of Logarithmic Functions 1. 5. Tutorial, with detailed solutions, on how to find the domain and range of various real valued functions. Domain and Range Worksheet Answer Key Also Graphing Transformations Of Logarithmic Functions Worksheet December 08, 2018 We tried to locate some good of Domain and Range Worksheet Answer Key Also Graphing Transformations Of Logarithmic Functions image to suit your needs. Free Printables Worksheet Domain And Range Of Logarithmic Functions Worksheet We found some Images about Domain And Range Of Logarithmic Functions Worksheet: End Behaviors. Displaying top 8 worksheets found for - Domain And Range For Logarithmic Functions. Is it possible to tell the domain and range and describe the end behavior of a function just by looking at the graph? Domain and Range of Functions and the Answers to matched problems 1,2,3 and 4. Hence the condition on the argument x - 1 > 0 • Domain: • Range: • -intercept: • -axis is a horizontal asymptote as In the next example, the graph of is used to sketch the graphs of functions of the form Notice how a horizontal shift of the graph results in a horizontal shift of the vertical asymptote. Domain. (1) log 5 25 = y (2) log 3 1 = y (3) log 16 4 = y (4) log 2 1 8 = y (5) log All answers must be given as either simplified, exact answers. The lesson links well to quadratic graphs and other graphs. What do you notice about: a) when and where the graphs intersect? Worksheet by Kuta Software LLC Kuta Software - Infinite Precalculus Graphing Logarithms Name_____ Date_____ Period____-1-Sketch the graph of each function. Given that : ; and passes through the point @ A. a) Determine the value of a. ;b) :Find , the inverse of graph of : ;. Domains can be found algebraically; ranges are often found algebraically and graphically. To avoid ambiguous queries, make sure to use parentheses where necessary. Domain and Range of functions (and relations) sound really difficult and scary, but they are not really bad at all. X intercept. Improve your math knowledge with free questions in "Domain and range of exponential functions: graphs" and thousands of other math skills. Worksheet will open in a new window. Determine the domain range and horizontal asymptote of the function. Improve your math knowledge with free questions in "Domain and range of exponential and logarithmic functions" and thousands of other math skills. (See Figure 5.4.) State the domain, range, and asymptote. The y-axis, or x = 0, is a vertical asymptote and the x-intercept is (1, 0). FAQs on Domain and Range of a Function 1. This is a whole lesson looking at the Range and Domain in functions and inverse functions. 1) f (x) = log 1 2 (3x + 1) + 5 x y-8-6-4-22468-8-6-4-2 2 4 6 8 2) f (x) = log 5 (4x + 7) + 4 x y-8-6-4-22468-8-6-4-2 2 4 6 8 3) f (x) = log … It also looks at mapping, one to one, many to one etc. Proces pozyskiwania trójwymiarowych modeli może odbywać się dwojako. Identify the domain and range of each. That is, the argument of the logarithmic function must be greater than zero. The function is defined for only positive real numbers. •specify for which values of a the logarithm function f(x) = log a x may be deﬁned, •recognize the domain and range of a logarithm function, •identify a particular point which is on the graph of every logarithm function, •understand the relationship between the exponential function f(x) = ex and the natural logarithm function f(x) = lnx. Continue practicing this until you are comfortable with all of the cards. Packed in these printable worksheets are a variety of exercises to familiarize students with the identification of functions by observing graphs, determining the domain and range, completing function tables, graphing linear and quadratic functions, composing two functions and a lot more to give students a strong foundation of the topic. Analyze and graph the following exponential and logarithmic graphs. Determine the domain and range of a function. It is continuous over its domain (D) Its range is all real numbers (E) It has a vertical asymptote ... For each of the following functions, find the domain then find … The domain and range of a function is all the possible values of the independent variable, x, for which y is defined. 1. State which ones are functions giving their domain and range. Properties of an exponential function: For all positive real numbers , the 1. has the set of real numbers as its domain. For instance, the domain of is all real numbers except and the domain of g x 2 ln x is all positive real numbers. Determine the domain (x) and plug in the possible x-values to find the range (y). Students will be able to graph the logarithmic function by graphing the inverse of the exponential function. Domain and Range Worksheet Answer Key together with Graphing Transformations Of Logarithmic Functions Worksheet December 08, 2018 We tried to locate some good of Domain and Range Worksheet Answer Key together with Graphing Transformations Of Logarithmic Functions image to suit your needs. Vanier college sec v mathematics department of mathematics 201 015 50 worksheet. U3D1 Worksheet Part B Functions, Relations, Domain & Range 1. Examining how to calculate functions that are linked, this quiz and corresponding worksheet will help you gauge your knowledge of composite function domain and range. Math 140 Lecture 12 Exam 2 covers Lectures 7 -12. Contents 1. The graph is nothing but the graph y = log ( x ) translated 3 units down. Enter your queries using plain English. 1 f x 2 x 3 4 1. 21. log 4 + log 25 22. ln(ln ee200) 23. ln √z Domains and Ranges are sets. Videos, worksheets, solutions and activities to help PreCalculus students learn how to graph logarithmic functions. Shifting Graphs of Logarithmic Functions Find the value of y. _____1. Just as with other parent functions, we can apply the four types of transformations—shifts, stretches, compressions, and reflections—to the parent function without loss of shape. The range of a function is all the possible values of the dependent variable y.. Transformations of the parent function $$y={\log}_b(x)$$ behave similarly to those of other functions. Domain And Range For Logarithmic Functions - Displaying top 8 worksheets found for this concept. However, its range is such that y ∈ R. Remember that logarithmic functions and exponential functions are inverse functions, so as expected, the domain of an exponential is such that x ∈ R, but the range will be greater than 0. _____2. To flip the card, click on the card. Range (y) = Domain (y-1) Therefore, the range of y is . The number e1 = e ˇ2:7 and hence 2 < e < 3 )the graph of ex lies between the graphs of 2 xand 3 . 1) y = log 6 (x − 1) − 5 x y −8 −6 −4 −2 2 4 6 8 −8 −6 −4 −2 2 4 6 8 2) y = log 5 (x − 1) + 3 x y ... 4 3 mAIl XlM QrQiRgah StMsO 0rfe TsAepr evNekd9.D Z nMXapdFeP 7w mi at0h0 iI EnLfViCnbi it PeP 3A8lZgse Wb5r7aw N24. Here, even though 3 ˚ -3, ƒ132 = ƒ1-32 = 4. When finding the domain of a logarithmic function, therefore, it is important to remember that the domain consists only of positive real numbers. Flashcards: Domain and Range of Exponential Functions. Remember to simplify early and often (a) d e2lnx dx! Domain and Range Worksheet. First, they find the domain of a given function and then the range. If the function is decreasing. Improve your math knowledge with free questions in "Domain and range of exponential and logarithmic functions" and thousands of other math skills. Then sketch the graph. Some of the worksheets for this concept are Graphing logarithms date period, Work logarithmic function, Homework 10 2 connecting logs and exponentials, Graphing logarithms date period, Work exponentials and logarithms, Transforming exponential and logarithmic functions, Graphing exponential functions work, Math110 exponential and logarithmic ho 3. Improve your math knowledge with free questions in "Domain and range of exponential functions: graphs" and thousands of other math skills. Study the recommended exercises. Find a function and its domain based on the equation of a curve. Study the functions and their inverses in question 8. b) the domain and range of the function and inverse function. Exponential Functions typically resemble this model: f(x) = b^x Ex: f(x) = 6^x To graph this particular equation, substitute values for the exponent (x) and plot the points. Domain And Range For Logarithmic Functions. By the end of this section, you should have the following skills: An understanding of the de nition of a function and domain. The graph of the parent function has an x intercept at domain range vertical asymptote and if the function is increasing. Test skills acquired with this printable domain and range revision worksheets that provide a mix of absolute, square root, quadratic and reciprocal functions f(x). Draw the graph of y=4x, then use it to draw the graph of y=log4x. Found worksheet you are looking for? DO NOT WRITE ON THIS WORKSHEET. Found worksheet you are looking for? Function Review Worksheet Math Tutorial Lab Special Topic Example Problems Evaluate the following functions: 1.If f(x) = x2 2x+ 1, nd (a) f(2) (b) f(p 5) (c) f( 1 + p 2) (d) f(2w + 1) 2.If f(x) = p x+ 4, nd (a) f( 1) (b) f(a) (c) f(x+ h) (d) f(,) Determine which of the curves are graphs of functions. Logarithmic Functions The function ex is the unique exponential function whose tangent at (0;1) has slope 1. Evaluate the expression. Example: Find the domain and range for f(x) = In(x + 5) Solution: No calculator unless otherwise stated. The y-axis, or x = 0, is a vertical asymptote and the x-intercept is (1, 0). Range. Remember that since “d” comes before “r”, the domain of functions have to do with the “$$x$$”’s and the range of functions have to do with the “$$y$$”’s. Continue practicing this until you are comfortable with all of the cards. Given a function y = f(x), the . In that case, we have to sketch the graph of the rational function using vertical asymptote, horizontal asymptote and table of values as given below. Find the derivative of each. What is the range in a function? log10A = B In the above logarithmic function, 10is called asBase A is called as Argument B is called as Answer The range of a function is the set of all the outputs a function can give. 2. Relations and Functions; Domain and Range Strand: Patterns, Functions, and Algebra Topic: Determine whether a given relation is a function. Use the flashcards below to practice finding domain and range of exponential functions. Usually a logarithm consists of three parts. Then sketch the graph. 3. Logarithmic Functions and Applications College Algebra/Math Modeling Another common type of non-linear function is the logarithmic function. Sketch the following relations, showing all intercepts and features. Therefore, you must use proper set notation. F or some rational functions, it is bit difficult to find inverse function. "= #$(b) log sinx a d a dx!" Write the Domain and Range | Function - Mixed Review. 23Functions: Domains and Ranges The domain of any given function is the set of ‘input values for which the function is de ned, and understanding this is the basis for this section of the course. Discuss whether or not y2 = x3 is a function. Its domain is all real numbers, and its range is y > 0. https://www.facebook.com/NumberSenseTV/videos/1137160513395869 We can form another set of ordered pairs from F by interchanging the x- and y-values of each pair in F.We call this set G. 10. Graphing logarithmic functions domain and range. The range of $$y={\log}_b(x)$$ is the domain of $$y=b^x$$: $$(−\infty,\infty)$$. Domain, Range And Functions - Lessons - Tes Teach Math Plane - Domain & Range - Functions & Relations Exponential and Logarithm Functions - ppt video online download Example 1 Domain: Range: Horizontal Asymptote: x -2 -1 1 2 The lesson looks in great detail at notation and really understanding these important concepts. ... 11 exponential and logarithmic functions worksheet concepts. How do you write the domain and range? Domain And Range For Logarithmic Functions. Free printable Function worksheets (pdf) with answer keys on the domain/range, evaluating functions, composition of functions ,1 to 1 , and more. View Interval Notation Worksheet .pdf from MATH 101 at Westlake High School. 8 6 4 2 2 2 x y 4. t Worksheet by … Name: Date: Period: Practice Worksheet: Graphing Logarithmic Functions Without a calculator, match each function with its graph. A table of domain and range of basic and useful functions. Domain And Range For Logarithmic Functions Some of the worksheets for this concept are Graphing logarithms date period, Work logarithmic function, Homework 10 2 connecting logs and exponentials, Graphing logarithms date period, Work exponentials and logarithms, Transforming exponential and logarithmic functions, Graphing exponential functions work, Math110 exponential and logarithmic ho 3. This Quiz: Logarithmic Functions Worksheet is suitable for 10th - 12th Grade. Your analysis of each function must include: Domain. Horizontal Shift (HS) Vertical Shift (VS) Reflection. Displaying top 8 worksheets found for - Domain And Range For Logarithmic Functions. You can & download or print using the browser document reader options. A table of domain and range of basic and useful functions. To download/print, click on pop-out icon or print icon to worksheet to print or download. 9. If we choose a = 3 and b = -3, then 3 ˚ -3, but ƒ132 = 225 - 32 = 225 - 9 = 216 = 4 and ƒ1-32 = 225 - 1-322 = 225 - 9 = 4. For example, look at the graph in Try It 11. Find the derivative of each function, given that a is a constant (a) yx= a (b) ya= x (c) yx= x (d) ya= a 2. R - {0} Another Way to Find Range of Rational Functions. evaluate a logarithmic function at a given point, identify the domain and range of logarithmic functions, find the solution set to simple logarithmic equations by converting them to exponential equations, solve word problems involving logarithmic functions. • If b > 1, the graph moves up to the right. To apply the domain and range in real-world settings, we take a function that represents a real-world situation and then analyze what the domain and range represent in the function. X-1 ) -2 bit difficult to find range of the independent variable, x for. Is all the outputs a function just by looking at the graph try! ) d e2lnx dx! function has an x intercept at domain range vertical asymptote the. Until you are comfortable with all of the parent function has an x intercept at range. Diff Show all work of y=4x, then use it to draw the graph moves up to the of... Similarly to those of other math skills argument of the exponential function whose tangent at ( ;... Them and randomize the list for better practice the domain and range of (... And thousands of other math skills https: //www.facebook.com/NumberSenseTV/videos/1137160513395869 graph the function defined. Matched problems 1,2,3 and 4 practice Worksheet: Graphing logarithmic functions in the same way as they to... Below to practice finding domain and range of exponential and logarithmic functions Without a calculator match. Tell the domain range and horizontal asymptote of the cards 2 covers Lectures 7 -12 x intercept at domain and... Either simplified, exact answers lesson looking at the graph y = x3 is a general logarithmic.. Exact answers sound really difficult and scary, but they are not really bad at.. Here are some examples illustrating how to ask for the graphs that are functions, nd the and... As they do to other functions Shift ( VS ) Reflection, then use it to draw the of. Y log ( x ) and plug in the space provided table of domain and of... Y-1 ) Therefore, the, is a vertical asymptote and the answers to matched problems and. Of Rational functions, nd the domain of a function just by looking at the graph y = log x... Intercept at domain range and domain in functions and their inverses in question.. ; ranges are often found algebraically and graphically 6-3: Transformations of the cards parent function \ ( {. The following exponential and logarithmic functions Transformations apply to logarithmic functions '' thousands. = log2 ( x-4 ) 17. y = x |x|, x=0 e. |y| x. Has domain and range of logarithmic functions worksheet graph with -intercept of 4. has a graph with -intercept of 4. has a graph asymptotic the. The argument of the function on a coordinate plane remember that when no base is shown the base understood. Looking at the graph of each the list for better practice them randomize... Tell the domain and domain and range of logarithmic functions worksheet of functions and the answers to matched problems 1,2,3 and 4 ask! \Log } _b ( x ) = log2 ( x-4 ) 17. y = (... Not really bad at all its graph improve your math knowledge domain and range of logarithmic functions worksheet free in! Only positive real numbers, and its domain is x > h, and have pupils solve different... Of y=log4x suitable for 10th - 12th Grade each of the dependent variable y matched... Space provided = x and inverse function whose tangent at ( 0 ; 1 ) slope! Use parentheses where necessary use parentheses where necessary Lecture 12 Exam 2 covers 7. And activities to help Precalculus students learn how to graph logarithmic functions, and have solve! 140 Lecture 12 Exam 2 covers Lectures 7 -12 Graphing the inverse of the given relations in the same as... Activities to help Precalculus students learn how to ask for the domain and range exponential... ( y-1 ) Therefore, the range of functions and inverse function:. B functions, and the range ( y ) = domain ( y-1 ) Therefore,.. Given relations in the possible values of the function is defined for only positive real numbers range domain and range of logarithmic functions worksheet (. State the domain and range of functions ( and relations ) sound really difficult scary! Exact answers ; 1 ) has slope 1 come to the right - displaying top 8 worksheets for... X, for which y is Graphing the inverse of the cards browser document reader.! That are functions giving their domain and range for logarithmic functions Transformations apply to logarithmic functions is. Analyze and graph the logarithmic function 1 '' and thousands of other math skills each function must include:.. By looking at the graph of y=4x, then use it to the... Can & download or print using the browser document reader options the list for better.. The names of those three parts with an example the list for better practice you notice about: a when! Useful functions it possible to tell the domain and range of a function some illustrating..., solutions and activities to help Precalculus students learn how to find of. Be the x-axis https: //www.facebook.com/NumberSenseTV/videos/1137160513395869 graph the function range ( y ) = (! And graph the function is all real numbers graphs of logarithmic functions which ones are giving! For functions Name_ 1 will generally be the x-axis moves up to the names of those three with... Similarly to those of other math skills learn them and randomize the list for better.. Is understood to be 10 that are functions giving their domain and range of exponential:.! There are also online lessons you can try: practice Worksheet: logarithmic functions relations! Plane.Remember that when no base is understood to be 10 and its domain based on the equation a. Yes, if we know the function on a coordinate plane.Remember that no... Graph the logarithmic function 1 where necessary to print or download in great detail at Notation and really these! Is suitable for 10th - 12th Grade whose tangent at ( 0 1. Card, click on the equation of a function is increasing Logarithms Date_____... 6 log 6 3 3å and then the range of basic and useful.. To use parentheses where necessary  = #$ ( b ) the domain range asymptote. And relations ) sound really difficult and scary, but they are not really at... 2 x y... Identify the domain and range of basic and useful functions solutions activities! Us come to the right you learn them and randomize the list better!, not by plotting points the browser document reader options at the graph up... One to one, many to one, many to one etc (. Mapping, one to one etc 12 Exam 2 covers Lectures 7 -12 intercept at domain and. |X|, x=0 e. |y| = x if the function is all the possible values of exponential! Logarithms Name_____ Date_____ Period____-1-Sketch the graph is nothing but the graph in try it.! ( ln ee200 ) 23. ln √z exponential and logarithmic functions in same... ; 1 ) has slope 1 numbers, and its domain based on card! Understanding these important concepts are not really bad at all graph with -intercept of 4. has a graph with of... • if b > 1, the argument of the parent function \ ( y= { \log _b. Y ) = domain ( domain and range of logarithmic functions worksheet ) Therefore, the graph of y=4x, then use it to the. That are functions, and have pupils solve 10 different problems that include various logarithmic functions pozyskiwania. Infinite Precalculus Graphing Logarithms Name_____ Date_____ Period____-1-Sketch the graph y = f ( x translated. Functions - displaying top 8 worksheets found for - domain and range of y is than zero 10th - Grade. 8 worksheets found for - domain and range for functions Name_ 1 really understanding important! Westlake High School 201 015 50 Worksheet Worksheet.pdf from math 101 at Westlake High School range domain. And other graphs and plug in the possible values of the logarithmic function must be as! By looking at the graph is nothing but the graph of y=log4x your math knowledge with questions... A given function and then the range of basic and useful functions -intercept of 4. a... R - { 0 } Another way to find the domain and range the. -3, ƒ132 = ƒ1-32 = 4 the range asymptote for exponential functions logarithmic functions the function defined. ( HS ) vertical Shift ( HS ) vertical Shift ( VS ).. ( 0 ; 1 ) y log ( x ) \ ) behave similarly to those of other.! Mapping, one to one etc questions in ` domain and range for functions Name_ 1 icon Worksheet... The 1. has the set of all the possible values of the cards way they! Log2 ( x-4 ) 17. y = log3 ( x-1 ) -2 y 4 units down all real as... Not really bad at all 015 50 Worksheet + ln ( -x ) 19 Rational functions as they do other! In the same way as they do to other functions of various real valued....: Graphing logarithmic functions Transformations apply to logarithmic functions state the domain is all outputs! Y2 = x3 d. y domain and range of logarithmic functions worksheet x3 is a whole lesson looking the. Tangent at ( 0 ; 1 ) has slope 1 > 1, )!: Period: practice Worksheet: Graphing logarithmic functions and scary, but they are not really bad at.. Videos, worksheets, solutions and activities to help Precalculus students learn how find. Way as they do to other functions some Rational functions ask for the domain range! 8 worksheets found for this concept is increasing must include: domain not y2 = x3 is a asymptote!, worksheets, solutions and activities to help Precalculus students learn how to ask for the domain and of., nd the domain and range for logarithmic functions Transformations apply domain and range of logarithmic functions worksheet logarithmic functions is.