A function is a set of ordered pairs where each element in the set represents a distinct output. Each input is given a real number by the function, and each output is a real number as well. This is written as f(x) = y in mathematical notation. The graph of a function is a visual representation of how the function behaves. It shows the input values on the x-axis and the output values on the y-axis. The graph can help us to identify the inverse of a function.  Not all inverses are functions.

The applications of functions are everywhere. Function plays a significant role in the design of various structures, from bridges to buildings, and knowing the fundamentals of how to apply them is a crucial ability for any aspiring engineer. We can see the use of functions in artificial intelligence, machine learning, robotics, navigation system, astronomy, economics, and even in biology. We are familiar with the Automated Teller Machine (ATM). The ATM’s internal software runs a process to link the number on the card to your bank account when the card is entered into the device. This is actually a one-to-one mapping, i.e., function. This is probably a widespread and most popular application of the function.

Therefore, understanding functions is a crucial component of mathematics and has applications in many different areas. You can gain from learning more about functions whether you’re a student, instructor, or just someone who needs to brush up on the fundamentals of math. In this course, we will look at the basics of functions and how they can be used to solve problems. We will also explore some simple examples that illustrate different types of functions and their properties.  So if you’re looking to build a solid foundation in mathematics, go on!