Project: Functions in Real Life

Introduction

Let's begin our learning journey to understand inputs and outputs of functions in mathematics. In mathematical terms, a function is a relation between a set of inputs and a set of possible outputs. It is significant to note that each input relates to exactly one output. Let's understand this concept in more depth.

The foundation of a function relies on two major components: the domain and the range. The domain comprises all possible input values for a function, whereas the range includes all possible output values. These two concepts form the basis of functions and are essential to understanding how functions operate in mathematics.

Visualizing a function is another valuable way to grasp this concept. The graph of a function is the pictorial representation of all the input and output pairs. Indeed, if we correctly understand the graph of a function, we can predict the output for any input value and vice versa.

Functions in Context

So, why is it important to understand functions, their inputs, and outputs? It is because functions apply to almost every aspect of our daily lives. For example, knowing how to calculate functions is crucial to understanding how the weather changes over time or to predict the return on a financial investment.

In fact, a sound understanding of the concept of functions is a vital skill for many careers. Professionals such as engineers, physicists, economists, and even artists use functions in their everyday work. Even at home, things like the speed of your internet connection or the growth of a plant can be understood through functions.

Hands-on Activity: "Functions in Real Life"

Project Objective

The project consists of conducting a team-based inquiry into the application of functions in the real world, culminating in developing a function model that represents a chosen phenomenon. The goal is to apply mathematical concepts of functions, domain, range, inputs, and outputs to analyze a real-world situation.

Detailed Project Description

Divided into groups of 3 to 5 students, each team will identify and describe a real-world phenomenon that can be represented by a mathematical function. This phenomenon can vary widely: it could be the changing price of gas, the growth of a plant, the speed of a car, the phases of the moon, or many others.

After selecting a phenomenon, the team should conduct research to understand the variables involved and how they correlate. Based on this research, the team should then model a mathematical function that represents this phenomenon.

Materials Required

• Mathematics textbooks and/or online references for researching mathematical functions.
• Graphing calculator software (preferably free and online, such as Desmos, GeoGebra, etc.).
• Notebook or binder for documenting the research process, function modeling, and the writing of the final report.

Step-by-Step Guide for Completing the Activity

1. Form groups of 3-5 students.
2. Choose a real-world phenomenon to be studied and represented by a mathematical function.
3. Conduct research on the phenomenon, focusing on understanding the variables involved and how they correlate.
4. Model a function that accurately represents the chosen phenomenon.
5. Use graphing calculator software to test and visualize the modeled function.
6. Document the research process, modeling, analysis, and conclusions in a final report.

Project Deliverables and How They Should Connect to the Suggested Activities

Following the hands-on component of the project, students should develop a detailed report using the following outline:

1. Introduction: Students should describe the chosen phenomenon, its real-world relevance, and the purpose of this project.
2. Development: Students should thoroughly explain the chosen phenomenon, the theory behind the function that represents it, the detailed implementation of the hands-on activity, the methodology used in their investigation, and the results obtained from modeling the function. It is important for students to explain how they handled the inputs and outputs of the modeled function.
3. Conclusion: Students should summarize the main points of their work, articulate what they learned, and draw conclusions about the practical application of functions in representing their chosen phenomenon.
4. References: Students should cite the sources they used to complete the project, such as books, web pages, videos, etc.

Note that the report should be submitted in a written document format, either hard copy or digital, and is an essential part of the project, complementing and demonstrating the extent of the hands-on work.