Contextualization

Theoretical Concepts

Function is one of the most fundamental concepts in mathematics, widely used in various areas of knowledge. Essentially, a function is a relationship between two sets where each element of the initial set (domain) has a unique corresponding element in the final set (codomain).

In high school, one of the first topics studied in the context of functions is the 'domain'. The domain of a function is the set of all input values for which the function is defined. In other words, all the values you can input into the function and get a response. The concept of domain is essential for understanding the limitations of a function, that is, in which cases it can or cannot be applied.

For each value in the domain, the function assigns a single value in the codomain. For example, in the function y = 2x, the domain of this function is the set of all real numbers, because for every real number we substitute in place of x, we can calculate a value for y.

Relevance and Application

Now, you might be wondering: 'Why do I need to know this?' Well, the concept of domain is an important tool that mathematicians, engineers, physicists, economists, among other professionals, use to model and solve real-world problems.

For example, suppose you are an engineer designing a bridge. A key factor for the project is the amount of traffic the bridge can support. The domain here would be the maximum number of vehicles the bridge can support simultaneously.

Practical Activity

Activity Title: Conquering the Domain

Project Objective

The objective of this project is to carry out an activity that allows students to understand in a practical and playful way the concept of domain of a function.

Project Description

Students will be divided into groups of 3 to 5 people. Each group will have to choose three different functions (it can be a linear, quadratic, logarithmic, trigonometric function, etc). Once chosen, they must determine the domain of each of these functions and illustrate them on a graph.

To make learning more fun and engaging, we suggest that the groups create a 'board game' based on their functions. In the game, each group must use the chosen functions as 'paths' that the players will follow, where the domain of the function will determine the possible route. Thus, each path will have limitations based on the domain of the corresponding function.

Required Materials

• Cardboard (or any platform to draw the game)
• Paper, pencil, and eraser
• Ruler
• Markers of various colors
• Game pieces (can be small objects, such as coins, Lego pieces, bottle caps)

Step by Step

1. Choose three different functions
2. Determine the domain of each of them
3. Draw the graph of each function on the cardboard, using different colors to differentiate each one. The chosen functions will be the paths of the game.
4. Define the rules of the game, taking into account the domain of each function (players can only move in the spaces defined by the domain of the function)
5. Play! The groups must play against each other to test and clearly understand the practical application of the concept of domain.

Project Delivery

Each group will deliver:

• The developed board game
• A written report composed of:
  • Introduction: Definition and importance of the domain of a function, project objective, and description of the chosen functions.
  • Development: Detailed explanation of how each function was defined, how its domain was determined, description of the game creation process, and discussion of the results obtained.
  • Conclusion: Recap of the main points, lessons learned, and conclusions about the project.
  • Bibliography: Sources used for the project development.

Remember that the report, as well as the discussions during the game, should be elaborated collaboratively, encouraging teamwork and communication among group members.