A function is a process or a relation that associates each elementxof asetX, thedomainof the function, to a single elementyof another setY(possibly the same set), thecodomainof the function. It is customarily denoted by letters such asf,gandh.
Functions as define by mathematicians above will seems to be another inapplicable topic to our daily life unless you are, for example, a mathematician or a Programmemer. Which lead us to a simpler and open definition that can be understood by all.
The concept of function can be made simpler to understand by the use of the idea of a function machine i.e. an input goes in the machine; something happens to it inside the machine; an output comes out. Another input goes in; another output comes out. What is going in will determine what will come out. For example in the image below the oil is serving as the function machine:
Functions, continuous functions, discrete functions, etc. are fundamental concepts in mathematics. In itself they are too general to have much value, but they are very useful for organizing things that we want to study in mathematics and elsewhere.
Think of any process where an input produces an output; that process is a function. Here’s a few examples
Functions in the real world
A soda, snack, or stamp machine the user puts in money, punches a specific button, and a specific item drops into the output slot. (The function rule is the product price. The input is the money combined with the selected button. The output is the product, sometimes delivered along with coins in change, if the user has entered more money than required by the function rule.)
Measurement:
Temperature: when taking body temperature the temperature of the body will act as the input while the measurement that comes out as either in degree Celsius and Fahrenheit scales is the function output.
Weight: when you take your weight usually by standing on a scale your body weight will serve as the input while the measurement usually in kilogram is your output.
Fuel Efficiency: A car’s efficiency in terms of kilometer per litre of fuel consumes is a function. If a car typically gets 10L per 100km and you input 50L of fuel, it will be able to travel roughly 500km. The car’s efficiency may be a function of the car’s design (including weight, tires, and aerodynamics), speed, temperature inside and outside of the car, and other factors.
Basic economics and money math:
Monthly Salary: When you receive your monthly salary what you are been paid is a function of the hourly pay rate and the number of you worked for that month.
Income Tax: When calculating your income tax you will observe that you made use of a mathematical function why your salary serve as your input and your tax result is the output. You will observe that the higher your income the higher your income tax.
Compound interest: when interest calculated on an investment the compound interest is a function of initial investment, interest rate, and time or interval of the investment.
Supply and demand: when trying to forecast the price of product and service daily we mad use of functions. The price of the product or services acts as the input why the demand serves as the output of the function. As price goes up, demand goes down and vice versa.
Machine Learning
Most of the operation carried out in our phone, system and other electronic devices is as a result of the application of function. Examples:
- Mapping image to the names of the people on the images.
- Mapping digital songs to author/genres/song name
- Mapping MRI scan data to medical diagnosis
- Mapping online answers to subject/categories
- Relating name and number as well as other information about a contact in your phone
- One of the most widely used applications for functions at the present time is in working with Microsoft Excel Worksheets.
All around us daily we made use of function to make life easy either with or without our knowledge.
References
Wendy, P. (2020). Function in the real world. Education World https://www.educationworld.com/a_curr/mathchat/mathchat010.shtml
Peter, R. (2019) What are the applications of functions in real life? https://quora.com/what-are-the-applications-of-functions-in-real-life
Agada Apeh Andrew is a Lecturer II at the Department of Mathematical Sciences, School of Sciences and Information Technology at the Skyline University Kano, Nigeria. He obtained his BSc in Mathematics from Benue State University, Makurdi
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