Basic Concepts of Functions

Note:  This is the second part of the Functions Series. To view the other parts, click the link below.

Part I: Introduction to Functions
Part II: Basic Concepts of Functions

***

In the first part of this series, we have discussed that a function is a relationship between two sets where for each value in the first set, there is exactly one corresponding value in the second set. We have painted large cubes, cut them into unit cubes and found a pattern about the number of cubes with 3, 2, 1 and no painted faces.

Figure 1 – Cubes painted and sliced into unit cubes.

We found out that if a cube has side n units, if we painted all of its faces and cut it into unit cubes, the following relationships hold: » Read more

If you would like to enhance your geometric drawings, then Google Sketchup is one software that I would recommend. Google Sketchup is 3-dimensional modeling software designed for architects, engineers, filmmakers and game developers, and other related professionals (Wikipedia).  It is now used to create models in Google Earth.

What makes Google Sketchup advantageous over other 3d software is that  it is a lot easier to use.  Some of the examples below are the figures I created after only watching several of their video tutorials.

Figure 1 shows the model in perspective showing symmetries of a right rectangular prism.

Figure 1 - Symmetries of a right rectangular prism.

Figure 2 shows the painted cube problem my Introduction to the Concept of Functions post. In the diagram, a big cube is painted yellow and cut into smaller cubes. The problem is to investigate the number of painted faces.

Figure 2 - Cube painted yellow and cut into smaller cubes.

Figure 3 shows different face styles of a cuboctahedron.

Figure 3 - Cuboctahedron in different view types.

Google Sketchup is free, and you can pay if you want a professional version. There are basic, intermediate and advanced video tutorials in its website.

You may also want to read my post on Using Google Sketchup in Teaching Mathematics.