Terminology

Introduction

A function is a mathematical relationship that assigns exactly one output to each input. Think of it as a machine: you put something in (the input), and the machine does something specific to it to give you an output.

For example, consider a function that adds $2$ to any number.

• Input : $3$ $\implies$Output : $5$
• Input : $0$ $\implies$Output : $2$
• Input : $-4$ $\implies$Output : $-2$

More formally, the function we just described can be written as $f(x)=x+2$

• $f$ is the name of the function.
• $x$ is the input of the function.
• $f(x)$ is the output of the function, which is equal to $x+2$.

Characteristics of Functions

A function :

• Takes an input (usually represented as $x$) and an output (usually represented as $y$).
• The function follows a specific rule, such as adding, multiplying, or squaring the input.
• For every input, there is exactly one output (one-to-one relationship). This is what makes it a function.

For example, if $f(x)=x^2$ and the domain is $\{1,2,3\}$ then the range is $\{1,4,9\}$