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Creating Function Art

If you want to join the competition, we highly recommend that you read this GeoGebra book: https://www.geogebra.org/m/vvs7ubsk. It contains supplementary materials that are not in this course.  

  • Basic understanding of algebraic functions (e.g., polynomial, trigonometric).
  • Familiarity with coordinate plane graphing concepts.
  • Fundamental knowledge of geometric shapes and their properties.
  • General computer literacy and ability to navigate software interfaces.

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Creating Function Art
  • 7 Lessons
  • Intermediate
  • 49 minutes
  • Category STEM
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This course, "Function Art" explores the creative application of mathematical functions to generate artistic designs using GeoGebra software. Participants will learn the fundamentals of GeoGebra, including its interface and graphing capabilities for various functions. A key focus will be understanding and applying transformations of functions, such as vertical and horizontal translations and scaling, to manipulate graphs and create desired shapes. The course will also cover techniques like defining domains for functions and coloring regions between graphs to add depth and visual appeal to the artwork. Through demonstrations and practical exercises, students will gain hands-on experience in using functions to create intricate and expressive art, culminating in their own function-based artworks.  

  • Utilize GeoGebra software for graphing various functions, including polynomial, trigonometric, and conic sections.
  • Apply transformations such as vertical and horizontal translations and scaling to manipulate function graphs.
  • Define specific domains for functions to create segmented graphs.
  • Integrate images into GeoGebra as a guide for creating intricate function art.
  • Create artistic designs by applying various mathematical functions and their transformations within GeoGebra
  • Effectively utilize GeoGebra's features to define function domains
  • Demonstrate a comprehensive understanding of function properties and their graphical representations
Lessons
    • Exploring GeoGebra: Your Introduction to Function Art
      1 Section 0 minutes
      This lesson introduces GeoGebra, a dynamic mathematics software that combines algebra, geometry, calculus, and statistics in one package. You'll become familiar with its user-friendly interface, including the toolbar, input bar, algebra view, and graphics view. This foundational understanding will prepare you to create amazing function-based art.
    • Graphing Functions and Defining Domains in GeoGebra
      1 Section 0 minutes
      Dive into graphing functions in GeoGebra, a crucial skill for creating function art. This lesson covers how to graph functions and define domains for finite graphs. You'll also get a sneak peek at the possibilities of complex artwork that can be created using these techniques.
    • Vertical Translations: Shifting Graphs Up and Down
      2 Sections 0 minutes
      Explore vertical translation, a fundamental function transformation. Learn how adding or subtracting a constant from a function's output shifts its graph up or down on the coordinate plane. GeoGebra will be used to visualize these vertical shifts, building your intuitive understanding of this key concept.
      1 reading
    • Horizontal Translations: Shifting Graphs Left and Right
      2 Sections 0 minutes
      This lesson explores horizontal translations. You'll learn how constants added or subtracted within a function's input shift its graph left or right. GeoGebra demonstrations will build your intuitive understanding of input changes affecting graph position. Mastering this provides precise control for your function art.
      1 reading
    • Vertical Scaling: Stretching and Shrinking Graphs Vertically
      2 Sections 0 minutes
      Explore vertical scaling, changing graph height or flatness. Multiplying a function's output by numbers greater than one stretches it vertically, making it steeper. Multiplying by numbers between zero and one shrinks it, making it flatter. Observe these effects in GeoGebra, controlling your function art's vertical dimension.
      1 reading
    • Horizontal Scaling: Stretching and Shrinking Graphs Horizontally
      2 Sections 0 minutes
      This lesson focuses on horizontal scaling, affecting graph width or compression. Multiplying a function's input by numbers greater than one shrinks the graph horizontally. Conversely, multiplying by numbers between zero and one stretches it horizontally. GeoGebra demonstrations will enable horizontal manipulation of your function-based artwork.
      1 reading
    • Creating Function Art: A Sample Artwork Demonstration
      1 Section 0 minutes
      This lesson demonstrates how to apply all learned function transformations to create a complete artwork. You'll observe the step-by-step process of using various functions and their shifts, stretches, and reflections to form a recognizable image. This practical application will solidify your understanding and inspire your own creative projects.
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