When the base is greater than 1 (a growth), the graph increases, and when the base is less than 1 (a decay), the graph decreases. Purpose of use To easily understand the complex problems with regards on Exponential fuction. com is a place for teachers and students to connect, build, and share rich content. The other two forms mentioned in the Community post are on lines 2 and 3. Scribd is the world's largest social reading and publishing site. The Graph of the Complex Exponential Function. You can find these keyboard shortcuts and more in the help menu in the calculator or by pressing ctrl + / on Windows, command + / on Mac. Desmos Activity Builder, grab a bat. Save your picture on your Desmos account and email it to your teacher. In this lesson students will explore relationships between time and distance of various functions. This website and its content is subject to our Terms and Conditions. Math courses include algebra, geometry, algebra 2, precalculus, and calculus. Click on the orange arrow to drag. This is a versatile graphing calculator that is also easy to use and very inviting for student engagement. White van shoe sales Question. Looking at this graph of f(x) = a x, what is the domain? Looking at the graph of f(x) = a-x, what is the domain? What is the range? Where is it increasing? Decreasing? What is the y-intercept? Graph an Exponential Function. Learning Goal: Build procedural fluency with graphing exponential functions. interpolating spectrum. Families of Graphs. (many tricks around DesmosGraph). To use the application, you need Flash Player 6 or higher. I was even more in love with the activity after this! We have a student at our school with a severe peanut allergy, so I opted to use Skittles instead of M&Ms for this activity. How can you use technology (like Desmos) to solve this?. Taylor series expansion of exponential functions and the combinations of exponential functions and logarithmic functions or trigonometric functions. Attach your graph. A line that a curve approaches more and more. This is all due to major. ” Would you consider a name change to “Two Truths and a Lie (Circle Graphs)”? I use Desmos activities with students and teachers in adult numeracy, where we like to keep the focus on the content adults need, without reminding them what level they are working on. This game requires students to represent the exponential parent function y=2^x numerically, algebraically, graphically and verbally. Apart from allowing you to graph functions easily via an intuitive math input system, it's also possible to add sliders to graphs (allowing you to explore the effect of changing parameters). Converting Between Logarithmic and Exponential Forms - Independent Practice Worksheet Complete all the problems. Not some students. Handouts Completed Notes. Search Search. ___ 2 exponential decay functions with a negative "a" This must create an interesting picture or design. This is what your screen should look like. Intersections of Exponentials and Solutions of Exponentials using Desmos. Right at x is equal to 0, we have y is equal to 1. Classwork What Comes Next? (Desmos) Notes Desmos Exploration Answers Link to Answers Standards Common Core HSF. Once they’ve figured out the parent function ( SPOILER: it’s quadratic. The Graph of the Complex Exponential Function Fold Unfold. Edulastic Extravaganza Contest! Hello All, As you may or may not know, I am a member of the Edulastic Innovator Team. Practice and discussion are required to understand mathematics. Show several examples of how to convert exponential expressions to logarithmic expressions such as $3^2=9\Leftrightarrow \log_3 9=2$. For negative `x`-values, the graph gets very close to the `x`-axis, but doesn't touch it. Loan Balance Situation: A person initially borrows an amount A and in return agrees to make n repayments per year, each of an amount P. See Desmos calculator. Compare: Airbnb. When you graph both the logarithmic function and its inverse, and you also graph the line y = x, you will note that the graphs of the logarithmic function and the exponential function are mirror images of one another with respect to the line y = x. We both teach 4th grade, and we both have similar teaching. To find the y‐intercept, you must set x=0. If x becomes a negative, then 2 will divide itself [-x] times again. Exponential growth also occurs as the limit of discrete processes such as compound interest. Desmos on the Interactive Whiteboard When teaching exponential functions to Year 12, I used Desmos on my IWB to show the graphs of functions such as y = 2 x and y = 3 x. If you haven't worked with Desmos yet and you're interested in geometric and mathematical designs, it's a powerful and easy to use online graphing calculator with many useful bells and whistles. Desmos Activities Desmos is one of the best free online graphing tools. NEW Desmos Right Riemann Sum Calculus Investigation of Areas UPDATED VERSION WITH BORDERS DRAWN BETWEEN RECTANGLES AND DETAILED EXPLANATIONS! The above is an extensive exploration of rectangular approximations to ares under a parabola utilizing the outstanding online graphing calculator, Desmos. You can change the function as you wish. Crespi Integrated Math Here you will find homework and other news about the Integrated Math class at Crespi Carmelite High School in Encino,CA. The points on the X-Axis are, X=-1, X=0, and X=1. THIS IS RELATED TO EXAMPLE 2 FROM TODAY’S LESSON USING DESMOS. Provide lesson plans, worksheets, ExamView test banks, links to helpful math websites for high school math courses. In this lesson you will learn how to write and graph an exponential function by examining a table that displays an exponential relationship. The exponential distribution is the only continuous memoryless random distribution. These activities activities were found at Teacher. To show how you can use the Desmos graphing calculator to do the graphing and calculation. Using table headers or lists are possibilities. (added 9/10/16). Is the pattern linear or exponential? 4. This math video tutorial explains how to graph linear equations, rational functions, inequalities, logarithmic functions, exponential functions, polar equations, trigonometric functions such as. Calculates the exponential functions e^x, 10^x and a^x. For those of you that get hooked on Desmos, I suggest you also check out the Daily Desmos Challenge). Erf is implemented in the Wolfram Language as Erf[z]. Graphing Form of a Parabola in Desmos (Math) by Greg Ford. Press STAT, then right arrow to highlight CALC, and then press 0:ExpReg. Explore graph, equation and properties of Exponential functions (growth/decay) with this interactive program. Descriptions are borrowed directly from Teacher. The topic of the lesson is Modeling with Exponential Functions. Graph y x2x e. Java Project Tutorial - Make Login and Register Form Step by Step Using NetBeans And. Learners stretch bands around the pegs to form line segments and polygons and make discoveries about perimeter, area, angles, congruence, fractions, and more. When interest is compounded continually (i. ) This session will provide an introduction to the free online graphing calculator Desmos. com and Des-Blog. The inverse of a logarithmic function is an exponential function. It's one of the most popular graphing calculator applications available for iOS and Android devices. They were required to have a minimum of 15 components of their graph, including no more than 4 horizontal or vertical lines. Solve linear equations and inequations, quadratic and simple exponential equation, sand simultaneous equations with two unknowns. Chapter 6 : Exponential and Logarithm Functions. Exponential Power Calculation. e-Exponential regression: y=AeBx What if the value of (A) was forced e. Linear Regression Analysis Many relationships resemble linear relationships of some kind. 80^t) Find the initial value of the car and the value after 12 years. Use This Area for Additional Text. 2: 7-21 Student eTool (Desmos) Click on the link below to access eTool. This is what your screen should look like. Graphing exponential functions is similar to the graphing you have done before. com, a free online graphing calculator. This year I have really shifted my thinking away from the hand-held graphing calculator to the online calculators Desmos and Geogebra. Students will graph their data both by hand on the back of the activity sheet (need graph paper), and using the Desmos graphing calculator app in the next step. If you haven't worked with Desmos yet and you're interested in geometric and mathematical designs, it's a powerful. Any time \(x\) increases by 1, \(f(x)\) increases by a factor of 3. Newton's method is an example of how the first derivative is used to find zeros of functions and solve equations numerically. This algebra activity focuses on exponential functions. The Enlightened Elephant: Zombies and Exponential Functions Update to zombie problem. Free Online Scientific Notation Calculator. The Exponential Function in Excel is also used for also calculating the probability distribution in the statistics also known as the exponential probability distribution. This month, I participated in a fun 'Swap & Share!' I was so excited to be paired with Holly from Fourth Grade Flipper. Odd function effect in desmos. Direct students to the graph URL (included below) Print a copy of the slide image and have students work with pencil and paper only. You will save your work to this account. The TABLE feature of the calculator can be helpful in many different situations. Home Pedagogy. k Worksheet by Kuta Software LLC. Interactive education for every platform, for everyone. Identify the correlation of the scatterplot. These activities activities were found at Teacher. Changes in b. MY GOAL is to try to give you as many resources as possible in order for you to be successful in your math class. Start with a nice algebra activity Central. Algebra II Module 1, Topic C, Overview Students solve polynomial, rational, and radical equations, and apply these types of equations to real-world situations. In the plot above, the dashed circle represents the complex modulus |z| of z and the angle theta represents its complex argument. 33 1 9 3 27 0. com with the student code I give you. Step 1: Find the Slope (or Gradient) from 2 Points. Author thedullguy Posted on March 21, 2017 Categories algebra, curriculum, edtech, teaching Tags Activity Builder, algebra, Algebra 2, Desmos, exponential, Junioritis, learning, MTBoS, re-teach, reflective teacher Leave a comment on Hockey Sticks Observe Me. Converting Between Logarithmic and Exponential Forms - Independent Practice Worksheet Complete all the problems. U7D3 Notes – Transformations of Exponential Functions Name_____ Desmos Marbleslides Exponentials - Go to. Now that we have worked with each type of translation for the exponential function, we can summarize them to arrive at the general equation for transforming exponential functions. Lesson 24: Solving Exponential Equations. Motion Vectors (2-D) Graphs a curve in the plane specified parametrically with radius, velocity, and acceleration vectors. Please use complete sentences where appropriate. com For example, TI calculators use logarithmic transformations for ExpReg, PwrReg, and LnReg, Geogebra uses logarithmic transformations for FitExp, FitGrowth, FitLog, and FitPow, and Excel uses logarithmic transformations in its Exponential, and Power regression lines. Graphs The following slides show the various graph types you should be familiar with for GCSE. There are two parts to the activity. This website and its content is subject to our Terms and Conditions. class code. docx Author: Trevor Jensen Created Date: 20141016234017Z. asymptote Where the function crosses the y‐axis. Have them go through fitting curves for linear, quadratic, and exponential models. I would like some sort of a formula or process that would allow me to enter a starting point and a starting slope and then an ending point and an ending slope. Pairs write their names and draw pictures using a graphing application with a collaborative graphic project. Just as with other parent functions, we can apply the four types of transformations—shifts, reflections, stretches, and compressions—to the parent function [latex]f\left(x\right)={b}^{x}[/latex] without loss of shape. A linear function has one independent variable and one dependent variable. However, because they also make up their own unique family, they have their own subset of rules. The graph of [math]x![/math] on Desmos looks an awful lot like the graph of [math]\Gamma(x+1)[/math]. Hello! Answering your question, graphically and taking in account the idea of bacteria growth, yes! How? Well, take a look at this graphs generated with a free app named Desmos. Log Graphs. And there's only 10 days left. Calculates the exponential functions e^x, 10^x and a^x. Video examples at the bottom of the page. • Students will begin to express ideas of exponential growth and decay in the real-world context of population and how many real-life situations are modeled with exponential growth and decay. Desmos will even plot the residuals (and serve up the correlation coefficient) so you can explore the goodness of the fit. e-x 2 = e (-3 x-4) Desmos does not appear to algebraically solve the equation, yet the answer is displayed as vertical lines at the solutions. Explore the graph of an exponential function. Section 5: Transforming Exponential Functions, and. Just as with other parent functions, we can apply the four types of transformations—shifts, reflections, stretches, and compressions—to the parent function [latex]f\left(x\right)={b}^{x}[/latex] without loss of shape. Exponential growth is common in physical processes such as population growth in the absence of predators or resource restrictions (where a slightly more general form is known as the law of growth). Equation Y = _____ 5. Desmos designs and implements programs arising from financial donations by individuals, companies and charitable financial institutions aiming to meet the needs of vulnerable groups. Odd function effect in desmos. Graphing exponential functions is similar to the graphing you have done before. Desmos Activities Desmos is one of the best free online graphing tools. 1 point: You have incorporated at. Graph y = 2 (x + 3) This is not the same as "2 x + 3". 73 Same y‐intercept. Adjust your sliders until you get the highest possible value for R². Learning Goals: (1)Create a need for the formula(2)Understand that exponential functions have a multiplying rate of change (3)Provide a context for the meaning of a and b. Directions: You are to create a drawing with equations and restrictions using the DESMOS software. Tes Global Ltd is registered in England (Company No 02017289) with its registered office at 26 Red Lion Square London WC1R 4HQ. Welcome to functions! I look forward to a great semester with you. Characteristics of Graphs of Exponential Functions Before we begin graphing, it is helpful to review the behavior of exponential growth. Day 2-Recreate with Desmos: Using Desmos, recreate your Roller Coasters using your knowledge of functions and their transformations. Desmos will automatically generate a table. Answer to Explain a method for solving an exponential equation such as 2 x = 7 algebraically. The Ordered list of interactive Desmos graphs. Your equation art should consist of at least 25 equations and at least 6 different types of equations. See Desmos calculator. Desmos was born out of Luberoff’s own experiences as a math tutor, when he noticed that his younger students were still using the same calculator he had to use in school a decade ago. Desmos Activities for Middle School. Erf is implemented in the Wolfram Language as Erf[z]. Both of these functions are very important and need to be understood by anyone who is going on to later math courses. A Different Look at Linear Functions ~Teacher Notes. Exponential Growth and Decay: Zombies, Word Problems, and M&Ms's Hi guys! After returning from Fall Break, I decided to do exponential growth and decay, and I think that most of the kids enjoyed it. We work with digital media but we think. Writing Exponential Equations Worksheet Level 4: Goals: Write an exponential equation with a decay factor Practice #1 Graph these three equations using www. You will be working on Desmos Quadratics today. Before starting polynomials, we did a small unit on solving quadratics. This is a versatile graphing calculator that is also easy to use and very inviting for student engagement. Thus, the exponential regression curve is not the best-fit curve in the "strict" sense. Solve logarithmic equations including some challenging questions. Derivate of exponential functions: Investigating e x and lnx (Autograph) Gradients of tangents to the exponential function (Casio) Reduction to linear form (Casio) Gradient of tangent to y=e kx (Casio) Derivative of y=e kx (Desmos) Graph of y=ka x (Desmos) Graph of y=ka x (GeoGebra) Derivate of exponential functionsy=e kx (GeoGebra) 14: Data. The idea of Graphing Designs could span linear, exponential, quadratic and conic equations. Finding short discovery activities is a challenge. Some fun(ish) worksheets I'm going to try to get my box. Similarly the cube root of 10 is written 10 1/3, the fifth root of 10 as 10 1/5 and so on. It doesn't work of course but here is my logic: NOTATION: a is the initial angle b is the angle of increase r is the radius x original x-cord x' new x-cord y original y-cord y' new y-cord so: x = r * show more I've always wondered. Desmos is an incredible calculator which will help you to draw a graph of any function. Creating one logarithm from a sum. 265x)-1 and it matched up with the black line in the picture. Setting up an exploratory activity to identify transformations on Desmos is easy and engaging! When introducing exponential functions, we started with a very short activity. Can you find the five parametric equations to recreate this graph? Bowtie Draw. But, this time we modeled both exponential growth and exponential decay. How to Calculate Exponential Growth Rates. You can copy data from a spreadsheet and paste it into a blank expression in the calculator. T HE LOGARITHMIC FUNCTION WITH BASE b is the function. Falling Shopper, London. Sketch a graph with all three lines to the right. For those of you that get hooked on Desmos, I suggest you also check out the Daily Desmos Challenge). How to Find the Inverse of a Function 1 - Cool Math has free online cool math lessons, cool math games and fun math activities. Desmos Faces from the 2014-2015 School year. The screenshot at the top of the investigation will help them to set up their calculator appropriately (NOTE: The table of values is included with the first function so that points will be plotted on. You will need to know that the "carrot key" (Looks like ^ , right under the "Clear" key on TI-83s and 84s) is what you use to type out your exponents. Exponential Functions. Starting off with a recent creation in Desmos, Here is an array of 200 exponential functions bounded by a circle, and a straight line through the middle. Students will use their knowledge of tables and graphs to discover concepts of exponential functions and restrictions on the domain and range of those functions. Its ubiquitous occurrence in pure and applied mathematics has led mathematician W. Classwork What Comes Next? (Desmos) Notes Desmos Exploration Answers Link to Answers Standards Common Core HSF. Desmos is an interactive website that helps students with graphing and plotting points, building functions, and creating tables. Got It: Misconception/Error. ProblemSet#2-- - - - Name:_____-Homework-H-Show-all-work-on-separate-paper. If you make wise choices and focus carefully as you use each resource, even if math is difficult for you, I believe you will find success. Graphs The following slides show the various graph types you should be familiar with for GCSE. Statistical functions require an argument in order to be used. There are four exponential growth problems further down this page. Create a Picture Using Equations, Inequalities, and/or Systems of Inequalities Create a picture by graphing a variety of equations, inequalities and/or systems of inequalities. Exponential Function Every exponential function can be written in the following format: f x a b() x Starting Value Base or “Multiplier” Always 1 more than # increased by. pdf), Text File (. To find the y‐intercept, you must set x=0. com and Des-Blog. y = f(x) = a + bx. exponential function minimum and maximum, how can i find minimum value of 4 exponential equation, finding the maximum value of an exponential decay function, finding maximum and minimum of an exponetial function, how to determine the maximum and minimum point of exponential function, determine the maximum value of a parabola and exponential,. n --> ), the compound interest equation takes the form: Demonstration of Various Compounding. You should memorize the 2nd page of [3-1] which contains the Logarithm Properties. We work with digital media but we think. Investment Project - Desmos. Graphing exponential functions is similar to the graphing you have done before. Graph f(x) = 2 x. Hello! Answering your question, graphically and taking in account the idea of bacteria growth, yes! How? Well, take a look at this graphs generated with a free app named Desmos. I would like some sort of a formula or process that would allow me to enter a starting point and a starting slope and then an ending point and an ending slope. Let’s say for example your function is [math]y = 5^x[/math]. Graph exponential functions and find the appropriate graph given the function. Exponential functions follow all the rules of functions. A=5 without using the above equation of A, how can we get the value of (B)? Thanks!. From simplify exponential expressions calculator to division, we have got every aspect covered. ___ 2 exponential decay functions with a negative "a" This must create an interesting picture or design. One is for students to see how the parameters of linear and exponential functions affect the shapes of their graphs. The staff picked graphs fall into two categories namely, “Math Examples” and “Creative Art”. Students will test their ideas by launching the marbles, and have a chance to revise before trying the next challenge. com Blogger 27 1 25 tag:blogger. Desmos Activities for Middle School. • How can I create and analyze exponential functions to model and solve real-world problems? • How can I manipulate exponential function models using graphing technology (desmos) to demonstrate mastery of each of the effects of each parameter in an exponential function? Technology Standards - What technology standard(s) will this unit cover?. Graph Individual (x,y) Points - powered by WebMath. We hope it will improve our conversations externally as well, with the broader community of math educators we’re proud to serve. CPM Student Tutorials CPM Core Connections eTools & Videos CC Algebra eTools Chapter 7 CCA 7. Statistical Functions. Exponential Growth Formula. Online Exponential Regression. Compare the equation Desmos. Exponential functions. Following on from this is a set of questions designed to probe understanding and get students. The Falling Shopper is painted around 7 meters above the ground on Bruton Lane. Delta Math is loading (this could take a moment). Calculate a determinant of the main (square) matrix. Graphing technology is also essential to see the meaning of all of the numbers in the tables: otherwise students can only observe trends in the data but this is not enough to determine which models are the most accurate. Another way to say this is that it grows by equal factors over equal intervals. This algebra activity focuses on exponential functions. Desmos Classroom Activities keyboard_arrow_up Back to Top I have adored using the free Desmos Graphing Calculator in my lessons for a few years now, but have only recently discovered the power of Desmos Classroom Activities , which allow students to investigate, and you to monitor, record and facilitate collaboration and discussion. Of course, we suspected that all along. Most exponential graphs resemble this same basic shape. Exponential growth is common in physical processes such as population growth in the absence of predators or resource restrictions (where a slightly more general form is known as the law of growth). After three days, Raj told his friend Helen about the game. What are their general characteristics? How easy are they to spot? 2) To model objects with parabolic shape with quadratic equations. Classwork What Comes Next? (Desmos) Notes Desmos Exploration Answers Link to Answers Standards Common Core HSF. ) Unit 0 Graphing Lines Geogebra Links (Slope-Intercept Form) https://www. Remember, Desmos is a cloud-based application after all, which means that every time you save a graph and publish it somewhere online, you are in effect contributing to an ever-growing database of Desmos modules — all in the name of science and technology!. You should be able to complete this activity purely on the functions you learned from Part 1 of this Unit. ___ 2 exponential decay functions with a negative "a" This must create an interesting picture or design. The other two forms mentioned in the Community post are on lines 2 and 3. Follows • 2. Create a Picture Using Equations, Inequalities, and/or Systems of Inequalities Create a picture by graphing a variety of equations, inequalities and/or systems of inequalities. Polynomial Regression Online Interface This interface is designed to allow the graphing and retrieving of the coefficients for polynomial regression. Population growth, inﬂation, and radioactive decay are but a few examples of the various phenomenon that exponential functions can be used to. I would like some sort of a formula or process that would allow me to enter a starting point and a starting slope and then an ending point and an ending slope. Desmos Modeling Bundle. In a semilogarithmic graph, one axis has a logarithmic scale and the other axis has a linear scale. Address comments / suggestions about this document to

[email protected] Modeling with Linear, Quadratic, and Exponential Models. class code. 3 that a power function has the form y = axb. Give an overview of the instructional video, including vocabulary and any special materials needed for the instructional video. Since most pictures have lines that do not go on forever, this is a very useful tool. How DESMOS changed the way I teach. Crespi Integrated Math Here you will find homework and other news about the Integrated Math class at Crespi Carmelite High School in Encino,CA. Exponential growth is a topic that deserves especially thoughtful treatment as part of a high school education because a person who has thought deeply about this ubiquitous phenomenon pays attention to and conceptualizes certain critical issues in, for example, science, economics, and social science, in a fundamentally different way than one who Read more…. I attempted by drawing both graphs but im searching for answers through algebra manipulation. As the x-values increase to the right, the graph's y-values grow faster and faster, shooting quickly off the top of the graph. Create a Desmos Piece - wise Equation with 4 - interval functions: - Exponential - Logarithmic - Linear - Your Choice (The Story/Graph must include at least one graph which increases and decreases. Integrated Math: Two years ago we stopped teaching the traditional progression of Algebra 1, Geometry, Algebra 2 and replaced it with Math 1, Math 2, and Math 3. After fitting THEIR best curves, have them use the regression built into Desmos. Free math lessons and math homework help from basic math to algebra, geometry and beyond. Then when we go to solve |x-3| = 7, they can find the solution graphically first and work up to an algebraic solution. This shows you how to do Exponential Regression in DESMOS- you will need to know how to do this for Friday's activity of modeling the population of Massachusetts using an exponential function. Graphing exponential functions is similar to the graphing you have done before. Before starting polynomials, we did a small unit on solving quadratics. Not some students. ” - Sincerely, Dr. Desmos Demo Horizontal Shifts, Vertical Shifts, and Change in Steepness. But having the resource of Desmos there (that kids like using and see the value in), makes it simple for them to see the connection. Match my Exponential Graph Inspired by Michael Fenton's fantastic looking "Match my Line" and "Match my Parabola" resources I have created a similar activity to explore exponential functions using Desmos's new activity builder. This algebra activity focuses on exponential functions. Range of y (y min to y max) is optional; if not specified, the function-grapher engine tries to evaluate it for the specified x range. com/files/Favicon/favicon. As he played, he found that his score, S, doubled after every day, x, he played according to the equation S = 2x. Change the window of your graph so I can see how much money you will make over 30 years. Return to Exercises. With those informations you can assemble a function (squared if parabolic, linear if it's a straight stroke or exponential if it's funky) and if you then restrict it with an intervall, you can replicate that specific area of the stretch. 2: 7-21 Student eTool (Desmos) CCA 7. at first, has a lower rate of growth than the linear equation f(x) =50x; at first, has a slower rate of growth than a cubic function like f(x) = x 3, but eventually the growth rate of an exponential function f(x) = 2 x, increases more and more -- until the exponential growth function has the greatest value and rate of growth!. It forces students to create a t-table (with x-values already supplied), and then a graph for an exponential growth function. A linear function has the following form. Undo: ctrl + z. I just made my first Marbleslides in Desmos! It was incredibly easy, and the students said it was a really fun way to learn. A two-argument form giving is also implemented as Erf[z0, z1]. The points on the X-Axis are, X=-1, X=0, and X=1. Applications of Exponential Functions Group Work. Download Flash Player. You may choose to graph an equation or write an equation from a graph. Use the links or image on each slide to take you to a Desmos page where you can use the sliders to explore how the graphs change. The logarithmic function is defined as the inverse of the exponential function a property that you may explore: Logarithmic Function and its Inverse the Exponential - HTML5 applet For B > 0 and B not equal to 1, Note: The logarithm to the base e is written ln(x). As a result, the pictures on the screen are not something that your browser can easily print. In these cases, "a" is used to represent a list or table header previously defined by the user in the calculator. I tell them that once we get to the lab they need all the time they can get to input functions into Desmos and mess with colors. So, an initial value of -2, and a common ratio of 1/7, common ratio of 1/7. Algebra 2, Math Activities, Student Engagement, Functions. Exponential Transformations Worksheet 4) Write the equation for the function that results from each transformation applied to the base function (𝑓 )=(13) 𝑥 a) reflect in the x- axis (vertical reflection) b) stretch vertically by a factor of 3.