1 Designing with Transformations Purpose In this project you will be relating and explaining the concepts from function transformations to create your own artwork. Presentation The most important part of your project presentation is to clearly explain and support your reasoning with relevant visuals and equations. Carefully check the project rubric to be sure you are clear about the expectations for the project. You can choose any format you prefer for the final presentation of this project. Some options include a written document, a virtual or real poster, a website, a video, an oral report, a PowerPoint, or other format. Project Introduction Design is seen in many areas, such as art, crafts, and architecture. In Designing with Transformations you will have a chance to design your own work of art using the transformations studied in this module. In some works of art you can clearly see how shapes or images have been transformed by reflections, stretches, and/or translations. An example is shown. What transformations do you see in the artwork? Project Requirements In this project you will design your own work of art on a grid. This could be a drawing of a logo or a picture. Your image must include the three functions shown plus at least one original function. These functions must then be translated, reflected, and stretched to create your final image. The three functions that must be in your design include the following: 2 You must also include at least one function of your own design. Sketch each original function of your own design on Original Function Grid Template. Draw your final image or logo on Final Image Grid Template. Project Checklist The functions in your design must include the transformation of at least four functions: the transformations of all three required functions the transformation of a function of your own design Of the four functions in your design one function must include a combination of stretches, reflections, and translations one function must be produced by reflecting a different function in the line y = x Highlight four transformed functions you have used in your artwork. For each function, complete the following: Describe the series of transformations of each function from the original function. Determine an equation for the new function in terms of the original function. State the domain and range of the original function and the transformed function. Determine whether the inverse is a function. Explain why. Explain the relationship between the domain and range of the function and its inverse. Describe how your image connects to the ideas learned in this unit. Project Sample Here is a sample of how two transformed functions could be used to create the image of an ice cream cone. Your creation is obviously not allowed to be an ice cream cone! Add colour, text, and other design elements that you need to make your final image look complete. Conclusion Write a brief conclusion to your Module 1 Project. Include a personal reflection of what you learned from the project during and after completion. Be sure to explain why you felt the way you did. 3 Original Function Grid Template 4 Final Image Grid Template 5 PROJECT RUBRIC Criteria Standards Graphs, Diagrams, and/or Models Demonstrates an Understanding of the Concept Demonstrates Reasoning Skills Communicates Understanding to Others Excellent Graphs, diagrams, and/or models are accurate and greatly add to the understanding. Responses to questions are insightful and reflect a comprehensive understanding of the concept. Equations are efficient and correct. The student demonstrates reasoning by making in-depth comparisons or connections and draws insightful conclusions. The student uses specific mathematical language to explain understanding and provides in-depth support for conclusions. Proficient Graphs, diagrams, and/or models are logical and easy to understand. Responses to questions are clear and reflect a thorough understanding of the concept. Errors in equations don't detract from understanding. The student demonstrates reasoning by making relevant comparisons or connections and draws meaningful conclusions. The student uses appropriate mathematical language to explain understanding and provides clear support for conclusions. Adequate Graphs, diagrams, and/or models are partially accurate and somewhat difficult to understand. Responses to questions are simplistic and reflect a reasonable understanding of the concept. Calculation errors detract from understanding. The student demonstrates reasoning by making superficial comparisons or connections and draws sketchy conclusions. The student uses everyday language to explain understanding and provides minimal support for conclusions. Limited Graphs, diagrams, and/or models are flawed and difficult to understand. Responses to questions are superficial and reflect an undeveloped understanding of the concept. Equations are incorrect. The student demonstrates reasoning by making irrelevant comparisons or connections and draws flawed conclusions. The student uses inappropriate language to explain understanding and provides few, if any, support for conclusions.