Mathematics is commonly used by some artists, whether they are conscious of it or not. It is possible to start with basic patterns and apply reflections, translations, stretches, and rotations to obtain a greater variety of images. The ability to do this has become much easier and quicker for a graphic designer, an artist who uses a computer to draw. Look at the following pictures. How do you think mathematics or mathematical ideas may have been used to help create each piece?
first image: © fat*fa*tin/4816771/Fotolia; second image: © pureguitarfury/6053388/Fotolia; third image: Hemera/Thinkstock
In this module you will investigate the following questions:
- How are transformed equations and graphs related to the original function?
- How can functions and their transformations be used in design?
To investigate the module questions, you will focus on the lessons and questions in the table.
Lesson |
Topic |
Lesson Questions |
1 |
Horizontal and Vertical Translations | How are the graphs of the functions y = f(x) and y − k = f(x − h) related? |
| How can you graph the function y − k = f(x − h) given y = f(x)? | ||
2 |
Reflections | How is a point related to its reflection? |
How are the graphs of the functions y = f(x), y = f(−x), and y = −f(x) related? |
||
| How can you graph the function y = f(−x) or y = −f(x) given y = f(x)? | ||
3 |
Stretches | How are the graphs of the functions y = f(x) and y = af(bx) related? |
| How can you graph the function y = af(bx) given y = f(x)? | ||
4 |
Combining Transformations | How can multiple transformations be applied to a function? |
| How can you write the equation of a transformed function given the original? | ||
5 |
Inverse of a Relation | How are a function and its inverse related? |
The Module 1 Project: Designing with Transformations will focus on using functions and their transformations to create your own artwork.
Note: Loading times for video and other media may vary depending on your Internet connection. Please be patient.