Introduction

Mathematics, one of the oldest and most fascinating sciences, is the universal language that allows us to understand and describe the world we live in. In mathematics, each concept has its own reason for being and its respective relevance. Within this universe, we find functions, pillars of mathematics and essential tools in many fields of science.

Functions are mathematical relations, described by formulas or rules, that determine the correspondence of each element of a set to another element of a second set. In this context, the concepts of codomain and range are crucial. The codomain of a function is the set of all real numbers that can be obtained by substituting values in place of the function's variable. The range, on the other hand, is the values that are actually reached by the function.

Understanding these concepts is crucial, not only for solving problems in class or on exams, but also for everyday life. They are also fundamental for many real-world applications. For example, in physics, functions are used to describe natural phenomena, such as the motion of an object in free fall, the amount of light that passes through a lens, or the conversion of temperature units.

Similarly, in economics, functions are used to understand and predict consumer behavior patterns, determine how efficiently a business produces goods and services, and analyze market trends. Therefore, a clear understanding of these concepts is essential.

For further study on the topic, we suggest the following sources:

1. Book "Fundamentals of Elementary Mathematics" - Volume: Functions - Gelson Iezzi, Carlos Murakami (ISBN-13: 978-8516057249)
2. Khan Academy page on functions, range, and codomain: Khan Academy
3. Videos from the channel Matemática Rio with Prof. Rafael Procopio: Matemática Rio

Hands-on Activity - "Function Exploration: Unveiling Codomain and Range"

Project Objective

Students will work in groups of 3 to 5 to create a dynamic and creative video presentation explaining the concepts of function, codomain, and range, as well as differentiating them, and presenting practical examples that demonstrate the applicability of these concepts in real life.

Detailed Project Description

Each group will be responsible for creating a video, approximately 10 to 15 minutes in length, acting as a team of "function explorers". The idea is to turn the video into a kind of "guided tour", where the team will explore the "world of functions" explaining, in a simplified and didactic way, what functions, codomain, and range are, and how these concepts are applied in different scenarios.

Students may use animations, drawings, graphs, enactments, and any other visual aids they deem appropriate to convey the information clearly and engagingly.

Required Materials

• Video recording equipment (can be a smartphone, tablet, or camera)
• Video editing software (several are available for free)
• Internet access for research

Detailed Step-by-Step Activity Instructions

1. Research and Planning: Divide tasks within the group. Everyone should research the topic, but each person can delve deeper into a specific subtopic (functions, codomain, range).
2. Script: Write a detailed script for the video. The script should include the introduction of the concepts and practical examples that illustrate each one of them in real life.
3. Production: Record the video according to the script. Be creative, but remember: the goal is to teach about functions, codomain, and range.
4. Editing: Edit the video to make it dynamic and engaging.
5. Review: Watch the final video and check if the concepts are clear and the examples are coherent.

Project Deliverables

In addition to the video, each group must submit a written report with the following sections:

Introduction: Tell the story behind the creation of the video, why you chose this topic, and the relevance of function, codomain, and range in the real world. Explain the project objectives clearly.

Development: Here, explain the theory behind the concepts of function, codomain, and range. Describe the activity you carried out, the steps you followed, and the methodology adopted. Present and discuss the results obtained. For example, what was the reaction of the colleagues who watched the video? Did they understand the concepts explained?

Conclusion: Summarize the main points of the work, explain the lessons learned, and the conclusions drawn from the project. You can reflect, for example, on whether there were any difficulties during the development of the project and how they were overcome.

Bibliography: List the research sources used to work on the project, such as books, web pages, videos, etc.

Remember: the video and the written report are complementary. Be creative, but always focused on the main objective: to learn and teach about function, codomain, and range.