Range or y-values?__ ________________ _____________ In particular, theres a certain education startup out there, relentlessly seeking to hijack our Internet browsers and mobile devicesinto a should we say graphing extravaganza. Also calculate the functions explicitly by evaluating the integrals. This is a BLENDED Activity where a hard copy(which is sold separately at my store here) of the activity is also included.Students should feel comfortable with: Identify the Dimension of the given Matrices Determining if the given matrice, I think that when we use technology in the classroom with our students, we should teach them to use technology as a tool. In fact, working on a graph while logged in allows you to give a title to the graph, so that if you decide to save it for later, a simple Ctrl + S will do. By accepting all cookies, you agree to our use of cookies to deliver and maintain our services and site, improve the quality of Reddit, personalize Reddit content and advertising, and measure the effectiveness of advertising. By clicking Accept all cookies, you agree Stack Exchange can store cookies on your device and disclose information in accordance with our Cookie Policy. In Desmos, the integral symbol $\int$ can be typed out using the int command, after which you can use the arrow keys to navigate around and enter the upper/lower limits. Reddit and its partners use cookies and similar technologies to provide you with a better experience. How to move and/or rotate a semi circle or like any equation. Need a. Indeed, if we are given agiant table with4 columns says $x_1$, $x_2$, $x_3$ and $y_1$ then wecanfita linear model for these variablesby simplytyping something along the line of $y_1 \simax_1+bx_2+cx_3 +d$ into the command line, so thateven ifDesmos is not properly equipped to plot graphs involving multiple independent variables, we can continue to run multivariate regression as if nothing happened in the first place! This product includes inquiry, notes summary/template and practice questions, a full complete lesson! Use strict inequalities ( < and > < a n d >) for dotted lines and non-strict inequalities ( and a n d ) for a solid line. Dont believe in the mighty power of Desmos? Frederick April 28, 2023, 7:00pm 1. So what else can you do with the integral operator? By nesting one operator inside another, we can also evaluate complexmathematicalexpressions such as those involving double summation or triple product for instance. Of course, when defining a definite integral, its necessary to include thedifferentialin such a way that the variable of the differential corresponds to the variablein the function you wish tointegrate on. Other times, you might need to use parentheses to group some of yourexpressions together before they can be properly interpreted by Desmos. Source: iphone.apkpure.com Check Details. domain and range restrictions inaction: Bridge, graphed by Brian: In fact, this graphing-in-bulk method has proved to be a formidable techniqueindrastically slowing down / paralyzing ourcomputers andmobile devices! The graph of this function is a straight line with a slope of 14 and y-intercept of 49. for (var i=0; i Answered step-by-step. Feel free to post demonstrations of interesting mathematical phenomena, questions about what is happening in a graph, or just cool things you've found while playing with the graphing program. f'(x) Hi Rayray. QGIS automatic fill of the attribute table by expression, Effect of a "bad grade" in grad school applications, Understanding the probability of measurement w.r.t. You can add an open point manually. how to change belly button shape naturally, anime characters with the birthday august 25, process automation specialist superbadge step 6, sheridan college acceptance rate for international students. To save any updates or changes, you will need to keep saving. Instead, it is probably better known as an innocent-looking mathtool for the scientifically-minded, making applied math ever more palatableand entertaining! In which case, just know thatthe $\le$ symbol can be obtained by typing out < and =in that order, and the$\ge$ symbol by typing out > and =, again in that order. What is the Vertex ? That is, $20+$ times more choices than gummies! Thats quite a bit on an innocent-lookingonline graphing calculator isnt it? Sure, while programmable calculators in general are still pretty muchpopular these days, the graphing calculators from the21st-century are also coming in waves as we speakpotentiallydisrupting the market of scientific computing and educational technology. Graphing and computing using Desmos is quite a topic all on its own, so we thought that keeping everything under one hood would make people lifes easier! Then it makes sense that you create an account, and work on your graphswhile logged into the account. If total energies differ across different software, how do I decide which software to use? As it turns out, Desmos is remarkably receptive to calculus-based expressions as well. Feynman's technique is used here. Practice typing the equations into the left column on the right side of the screen, explore changing the window size by clicking on the wrench. and our If you want to use this inverse in another function, write g (y) = f (x) instead. 6- Finding Zeros/Solutions/X-intercepts To get it started, heres a list of inequalities you can tryout andget the juice flowing: And heres what happened when we throw inthese inequalities into Desmos. www.desmos.com/calculator/zpceslgvw2, Chess Board, graphed by Eric: Can anyone help please? In which case, one can always choose tosegment the graphby imposing restrictions on theequation/inequality in question as long as the following syntax rule is being adhered to: \begin{align*} \text{equation/inequality} \, \{ \text{condition 1}\}\{ \text{condition 2} \} \ldots \end{align*}. About Press Copyright Contact us Creators Advertise Developers Terms Privacy Policy & Safety How YouTube works Test new features NFL Sunday Ticket Press Copyright . where, for every input, there is one (and only one) output. Tour Start here for a quick overview of the site Help Center Detailed answers to any questions you might have Meta Discuss the workings and policies of this site On the other hand, any saved graph can also be deleted if needed to by hitting the $\displaystyle \times$ button next tothe name of the graph to be deleted. But there's more: Use Desmos to easily graph inverse trig relations and functions, or to build interactive unit circles and sine wave tracers. Y-intercept _____________for first line A note of caution though: when setting up an integral function especially the ones involving multiple integral operatorsyou want totake that extra care to make sure that the variable of integrationis different fromthe variable(s) in the limits. Unit 6: TikTok or Tick-Tock Probability w/Venn Diagrams, Unit 6: Simple Probability, Set Notation & Venn Diagrams, Unit 5: Graphing Equations using Technology, Unit 5: Circles - Group Assignment Practice, Unit 5: Distance, Midpoint, & Slope Formulas, Unit 4: Applictions of Arc Length Sector Area & Volume, Unit 4: Circle Properties Group Assignment, Unit 4: Circles Vocabulary & Tangent Properties, Unit 3: Missing Sides, Angles, & Cofunctions, Unit 2: Triangle Proportionality Theorems, Unit 2: Spiral into the Golden Ratio Activity, Jeopardy - Congruent Triangles Test Review, Unit 1: Angle Relationships with Parallel lines. Learn Desmos: Trigonometric Graphing. For example, lets say that youwant to estimate the value of the infinite series $\displaystyle \frac{1}{1^2}+\frac{1}{2^2}+\cdots$, then one of the things you can do is to type something like this into the command line: \begin{align*} \sum_{i=1}^{1000} \frac{1}{i^2} \end{align*}. To plot a piecewise function on Desmos, use curly brackets with an x statement inside. NOTE: Your students will need to have access to a comp, Virge Cornelius' Mathematical Circuit Training, I wrote this for our high school algebra one students. Pellentesque dapibus efficitur, ctum vitae odio. You can do this by making a slider on the graph. Ive tried entering it as two separate functions, but that doesnt seem to work. Conic Sections: Parabola and Focus. - Share your creation for the class to see and to inspire an emotion is that the root word of emoji? The Math+Technology series is perfect! f (x) = sin(2x) All that is required is some ability in drawing multiplevertical bars and line segments and perhaps the ability in doing so at the right spots as well. The graph of this function is a parabola opening upwards, passing through the origin. Your output graph should not look differ. Strugglingto model the total distance traveled by an annoying fly? 0x2t dt5x2t dtx02t dtxx+72t dt For part 2 of the lab, let's use the FTC, Part 2 to find the area of I want the total area, so l'd like the cone part to count as positive area even For example, to modela particle moving along a sine-wavetrajectory, all we need to do is toembed an undefined parameterintothe coordinates of the sine wave(as in$(a, \sin 2\pi a)+3$ ), before activatingthe slider for the parameter usingthe play button. This is the same integral as in (a), but with the limits reversed. To be sure, if you name a column as a function of another pre-existingcolumn, then the values underthe new column will be determined by those under the old column. In a similar manner, a function in terms of $y$ can also be assigned a name as well, from whichwe can define and name acompoundfunctionin a command line without having to resort to rewriting the expressions again and again: And in case youre wondering, the polar functions are equally supported in Desmos as well. Choose your method!! Other calculator may not include function on key, Your students will get lots of practice with this Systems of Equations with Three and Four Variables Task Card Resource.This activity is designed for Algebra 2 or PreCalculus. ago. Desmos Is A Powerful Online Graphing Calculator That Can Be. I use this in my Algebra 2 classrooms a few days before a test to review all these topics. This is a fun activity to introduce exponential functions with technology. By reversing the roles of $x$ and $y$, functions in terms of $y$ can also be typed out into a command line as follows: \begin{align*} x = \text{some algebraic expressions in terms of }y \end{align*}. Required fields are marked, Get notified of our latest development and resources, Yeah. How can I add an x-intercept in Desmos? ______________________________ This integral is a bit different from the previous ones, as the limits are now functions of x. algebra 1 calculator technology activities. Web welcome to a quick introduction to the desmos graphing calculator. Create A Table From A Function. Graph the following functions in Desmos. there is a way in desmos to do and function you have to do something called nesting(putting a conditanal in a conditanol) example {{a=5:1}+{b=2:1}=2:f(x)}, $$y=f(x)\{\text{cond1}\}\{\text{cond2}\}\{\text{cond3}\}$$, $$y=(x^2-x)\left\{x^2>1\right\}\left\{x^4<3\right\}$$, $$\text{cond1} = \left(\{\text{subcond1}:1,0\}\{\text{subcond2:1,0}\}\{\text{subcond3:1,0}\}=1\right)$$, $$ The graph of this function is also a parabola opening upwards, but shifted 5 units to the right and 25 units downwards. link, For complex piecewise functions, you can use this hack: Do you see how the calculations match up with the graphs? Directions: Begin in Cell #, Students will work on 12 Solving Exponential Equation problems. If you're looking for help with your homework, our team of experts have you covered. So, what kinds of functions are supported in Desmos? If you need help with your homework, our expert writers are here to assist you. Watch this quick tutorial to learnhow: Who knew piecewise notation could be so fun! Command + Shift + A. You can easily fill out our order form to get started. Oh, here comes another one! Click Save to save the graph to your account. And with all of our knowledge of Graphing Using Transformations and Piecewise Functions, we are now able to discuss Symmetry. By the way, if youve manage to make it this far, you are already a true hero on your way tobecoming a power user of Desmos! To see this process in action, watch this tutorial! Just remember tostart the link with ahttpor https prefix though. None of the problems require the use of a calculator; exact answers only are given (no decimals). Why did DOS-based Windows require HIMEM.SYS to boot? And if the point is meant to be moving along a circular path instead, putting an expression such as $(3\cos a 5, 3\sin a + 6)$ into the command line would do. Use a table to determine where your point of discontinuity is. Five Lock boxesa. y=\left\{\\\color{red}{\left\{x^2>1:1,0\right\}\left\{x^4<3:1,0\right\}=1:\left(x^2-x\right)},\\\color{blue}{\left\{x^2>1.8:1,0\right\}\left\{x^4+x^2<25:1,0\right\}=1:x},\\\color{green}{-1}\right\}$$ t can be any variable besides y. , As a middle-grade student, my knowledge is basic. When lookingata seriesof points and itsassociatedscatter plot, its only natural that we seek to further understandthe nature of relationship if any between the two variables in question. Quizzes with auto-grading, and real-time student data. Graph functions, plot points, visualize algebraic equations, add sliders, animate graphs, and more. How do vector graphics engines (like adobe illustrator) render lines of prescribed thicknesses? 3- Finding Y-intercept and Maximum or Minimum values, Just click on the "functions" tab on the right hand side of the panel and scroll down. In which case, it makes sense that we useregression models to explain and predict the behaviors of one variable from another. Discord Server: https://discord.gg/vCBupKs9sB, Scan this QR code to download the app now. As for thefactorial, weve got an interesting fact for you:Desmos can calculatethe factorial of a number up to $170!$, which iseasily more than double of what can be achieved usinga TI-83 or any of itsvariants for that matter! To change the point from a closed circle to an open circle, click and long-hold the color icon next to the expression. Indeed, this is something that Desmos does incredibly well despite having a user interface that appears to bedeceptively simple. Heres a list of native, unary statistical commands supported in Desmos: Additionally, heres a list ofbinary statistical commands supported in Desmos, with slightly more delicate syntax: To be sure, the fact that these are about the only native commands supported in Desmos doesnt mean that these are the only statistical measures we are restricted to. (for the record, a new variable doesnt includeany of the pre-defined variablessuch as $x$ and $y$. 7- Writing the Factored form For mine, I chose to limit the domain to between -10 and 10, and have step counts. This integral." y=\left\{\\\color{red}{\left\{x^2>1:1,0\right\}\left\{x^4<3:1,0\right\}=1:\left(x^2-x\right)},\\\color{blue}{\left\{x^2>1.8:1,0\right\}\left\{x^4+x^2<25:1,0\right\}=1:x},\\\color{green}{-1}\right\}$$, How to use AND condition in Desmos [closed], Improving the copy in the close modal and post notices - 2023 edition, New blog post from our CEO Prashanth: Community is the future of AI, Desmos help - making a finite length line with origin on a sine wave move along it and vary angle orthogonal to sine wave line, In Desmos, function fills entire screen unless $y$ is used in some denominator. Similar to the cases with thesummation and product operators, you are also free to stack up as many integral symbols as you like, and use Desmos to evaluate, say, a double integral (e.g., the volume of a geometrical figure) or even a triple integral (e.g., the total mass of a metal rod). Hmm, what are we talking about here? For example, to graph the function $x^2$ withthe domain restricted to only the positive numbers, the following line would do: \begin{align*} y=x^2 \, \{ x>0 \} \end{align*}. Who knows, maybe you can even turn some of yourinspiration into afruitful, creative process with perhaps a bit of technical twist along the way! . Click the graphs below to see For complex piecewise functions, you can use this hack: To complete the circuit, they will have to complete all of the problems. Domain or x-values? The best answers are voted up and rise to the top, Not the answer you're looking for? A note is exactly that: a note for yourself and others looking atyourgraph and command lines. This is a great handout for kids who already know how to calculate slope, but do not yet know slope intercept formula. Once you've mastered this feature you'll be cranking out incredible graph art in no time. Hi William. Piecewise Functions play by their own rules, but that doesnt mean they have to be hard to handle. Now, if a function in terms of $x$ is meant to be referred on a repeated basis, then a name can be assignedto it by replacing the $y$ on the left-hand side with, say, $f(x)$. Calculus: Fundamental Theorem of Calculus This site uses cookies from Google to deliver its services and to analyze traffic. b. For mine, I chose to limit the domain to between -10 and 10, and have step counts. Once afolder is created, itcan be given a label, after which a command line can be dragged in or out of the folder with ease, and the triangular arrow iconnext to it can be used to expand/collapse thefolder as one wishes. Furthermore, by naming the mathematical expression we want to compute, we can pass down the output of the computation into a new variable, subsequently using it for other fancier purposes such as building elaborate computations or graphicalizing the outputof the computations intofiguresand animations. However, do note that in this case, the functions will have to be typed out using$r$ and $\theta$ as the designated variablesinstead (e,g., $r=\frac{1}{2} \theta^2$). Ready for the recap? Students practice solving systems of equations with three or more variables. Now, does that mean that you always have to produce a table in Desmos from scratch? 1- Finding Vertex Are you getting the free resources, updates, and special offers we send out every week in our teacher newsletter? Information about your use of this site is shared with Google. 56 likes, 2 comments - Curious Mind (@curious_math) on Instagram: "My solution to the problem by @vibingmath ! All right. For the record, the $\sum$ symbol can betyped out using the sum command, after which you will have to use the arrow keys to navigate around and specify the lower/upperlimits. Interpreting the angles in either degree or radian. Methods such as inverse matrices, augmented matrices, or utilization of onli, This is a project I use in my Algebra 2 Honors classroom to help my students practice graphing a system of linear equations.. 1. I can help you figure out mathematic tasks. Andif instead of having one function change its shape, you are interested in seeing several functions under a common parameter moving all at once, then you can for example try typing out$y=ax$, $y=ax^2$, $y=ax^3$ into three command lines, activate the slider, and watch as the polynomials move in tandem with pride! 0x2t dt5x2t dtx02t dtxx+72t dt For part 2 of the lab, let's use the FTC, Part 2 to find the area of I want the total area, so l'd like the cone part to count as positive area even. Why xargs does not process the last argument. Heres a figure illustratinghow implicit functions and parametric equations work out in Desmos: Think that wasquite a list of equations already? When it comes to graphing, equation is one of those first words that comes to mind. For a quadratic model, you can type insomething along the line of $y_1 \sim a{x_1}^2+b x_1 + c$, and a parabolashould be ready for you in a blink of aneye. Similarly, the derivative of a function in terms of $y$ can also be graphed by appending $\dfrac{d}{dy}$ in front of it. Do you see how the calculations match up with the graphs? Course Hero is not sponsored or endorsed by any college or university. a. Being primarily a graphing calculator in nature, Desmos seems to prefer presentinga new table withtwo humble columns by default: the first column $x_1$ presumably for the $x$-values, and the second column $x_2$ for the $y$-values. To define a piecewise function in Desmos, wecanuse the following syntax on a command line: \begin{align*} y \ (\text{or }x) = \{ \text{condition 1}: \text{definition 1}, \text{condition 2}: \text{definition 2}, \ldots \} \end{align*}. And with all of our knowledge of Graphing Using Transformations and Piecewise Functions, we are now able to discuss Symmetry. Explore math with our beautiful, free online graphing calculator. Actually, we are not quite done with the computational commands yet. Not really. There is no innate function for x-intercept for good reason because a function or an equation can have 0 or multiple copies of them. Furthermore,ifthe trajectory of a movable point actually defines a function, then Desmos will automatically make the pointdraggable across the $x$-axis, making it easier to manipulate than ever! Definition: A function is a relation between a set of inputs and outputs where, for every input, there is one (and only one) output. Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. The function I'm working with is f (x) = { 2x + 1 if x 0, 4x - 3 if x > 0 }. I need an x-intercept, but I only know how to do a y-intercept and Google is failing me. The community reviewed whether to reopen this question 3 months ago and left it closed: Original close reason(s) were not resolved. How can I control PNP and NPN transistors together from one pin? Heres five more interesting unary operations for your pleasure: If you look closely at the above figure with the Desmos keypad, you mightnotice something that looks like a summation sign, along with the Pi product symbol right next to it. In particular, well see how to use Desmos to tweak around thegraph setting, create notes, organizing lines into folders, and make use ofthe saving and sharing functionalities! When you enter a line of mathematical expression containing anundefined parameter, Desmos will give you to option to include a slider for that parameter, which has the capability of allowingyou toadjust ofits value manually or even better yet create an animationout of it byallowing the value of the parameter to increase/decrease automatically. Yep. The students have a great time helping each other if made into a game with prizes! Because itll then beour duty tobeg to differ, and attempt to convince you otherwise. Thatsan astoundingimprovement from the age of programmable calculators! c. What is the equation for the derivative of f (x) = sin(2x) ? Actually, why nottoy around withthe sliders a bit first and observe how the shape of the graph changes during this process! Hi everyone, Im currently trying to graph a piecewise function in Desmos, but Im not quite sure how to do it. Untitled Graph. Nam lacinia pulvinar tortor nec facilisis. (google draw)c. Lock 3 Exponential Growth and Decay from tables. I have used this as individual assignments, but the most effective strategy is to work in small groups or centers. Lock 2 Evaluating exponential functions given This is a matching activity. Fortunately, this is a feature wellsupported in Desmos, where animage can be added to the graph the sameway a folder is addedtoa command line. By the way, did you notice the circle icons on the top of mostcolumns? Desmos is a powerful . In fact, by creating as many columns as we want, we can extend this point-plotting feature a bit tothree or four functions simultaneously, All we have to do is to make sure that function columns are labeledas a function of $x_1$, and watch as Desmos auto-fills the rest of the table and graph for us. For delimiters whichserve to group an algebraic expression together, use parentheses instead. Of course, the restriction could have been an inequality on$y$ as well, as in the graph of the function $x^2$ where $y$ is restricted to the interval $[5,15]$: \begin{align*} y=x^2 \, \{ 5 \le y \le 15 \} \end{align*}. Graphing of course! Ctrl + alt + =. Please show your work so I can learn more from your response. Similar to the case with a note, a folder can be created by first clicking on the command line where the folder should appear, and then by accessing the Add Item menuviathe $+$ icon nearthe upper-left corner. I can use correct notation to restrict the domain of a graph. A minor scale definition: am I missing something? In other words, a function is a relation, Functions are typically solved for the dependent variable (y) and instead written as, Today we will explore a graphing utility at. Elimination, Substitution, Matrices, or the Graphing Calculator. Students should be familiar with vocabulary such as correlation, relationship, causation, extrapolation, interpolation, linear, non-linear, prediction, correlation coefficient, though in all honesty, the circuit leads them through these ideas.There is no answer key included since the answers are part of the, This is a project I use in my Algebra classroom to help my students practice graphing linear equations given in standard form using technology such as Geogebra, Desmos calculator or a graphing calculator. And it gets even better: by using an undefined parameter as the upper limit and configuring the slider accordingly. However, it's still a simple integral of a linear function. A subreddit dedicated to sharing graphs created using the Desmos graphing calculator. There are 15 questions provided. To plot a piecewise function on Desmos, use curly brackets with an x statement inside. Thats definitely something Desmos can handle for sure! Otherwise, its not our fault if Desmos refuses to parse your expressions like its crazy! In Desmos, any mathematical expression involving addition, subtraction, multiplication (*), division (/) and exponentiation (^) can be put into a command line,so that ifthe expression entered contains no variable whatsoever, then the output can becalculated and returned right back to you usually in a blink of aneye. 9. Thank you! XD. How to check for #1 being either `d` or `h` with latex3? Dont take this for granted by the way, because this is whereyou get to configure the range of the variable $t$, which in essencedeterminesthe portion of the parametric equations that is actually displayed on the graph. It is intended that students, This activity has 3 scavenger hunts: Solving Systems of Equations by Graphing Solving Systems of Equations by Substitution, and Solving Systems of Equations by Elimination.Graphing:There are 16 cards (with 16 questions) that drills the understanding of how to: Identify the solution from a given graph Solve the system by graphing by HAND Solve the system by graphing using TECHNOLOGY (Graphing Calculator or Desmos) Determining whether a given point is a solution to a system or not Without, ** This activity is available as a "GOOGLE INTERACTIVE" product HERE** This product is a NO PREP - SELF CHECKING activity that engage students in "Multiplication of Matrices". Ctrl + option + shift + right arrow. Stack Exchange network consists of 181 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. Because then you can actually savethese graphs for real, andshare them with other like-minded individuals! Experts are tested by Chegg as specialists in their subject area. I haven't found a built-in conjunction function, so you might find helpful my workaround: For simple domain restrictions, you can use a product of conditions: y = f ( x) { cond1 } { cond2 } { cond3 } y = ( x 2 x) { x 2 > 1 } { x 4 < 3 } link. Alternatively, you can also use integrals to define an equation or an inequality (e.g., integral function), and do all kinds of stuffs with it such as verifying the FirstFundamental Theorem of Calculus! Sounds a bit obscure? which is pretty cool. Example: t = g (y)^2. For mine, I chose to limit the domain to between -10 and 10, and have step counts. If you intend to havethevalues under the first column to be equally spaced, but are too lazy to enter the values yourself manually, then you can auto-fill the first column by pressingEnterrepeatedly after entering the first two values into thecolumn. $$y=f(x)\{\text{cond1}\}\{\text{cond2}\}\{\text{cond3}\}$$ example. In doing so, you are in effect removing yourself from the need ofpunching Desmos for real, in casethe expression doesntturn out to be exactly Desmos-interpretable. Browse other questions tagged, Start here for a quick overview of the site, Detailed answers to any questions you might have, Discuss the workings and policies of this site. And thats just astart! Connect and share knowledge within a single location that is structured and easy to search. In which case, youcan use the arrow keysto help younavigate around theexpression and type out what you want. example If you look at the upper-right corner of Desmos user interface, you should be able to see an icon with a wrenchon it. I have included a blank web for you to be creative! Because you might remember this thing called theTexas Instrument TI-83from the old days. Then graph the point on a separate expression line. What is a function & how is it different from an equation? Calculus: Integral with adjustable bounds. For instance, we could try plotting out the $n$th-degree Taylor polynomials of $\cos x$ by leaving$n$ asanundefined parameter, so that once we turn on slider with $1$ as the step-size, we should start to see a bunch of functions flashinglike crazy! **Want to see what's inside? Andif youre feeling a bit adventurous, you can certainly try entering an equation/inequality with multiple parameters, each of which isdefined as a list on its own with equal sizes. Hi Yif. In fact, with just a bit of imagination, we can eventurn the result of computations into ananimated graph, by convertingthe numbers into an animated line segment, or if we so prefer convert the numbers into a comparative diagram of our liking!