📐 What is a Function?
Что такое функция?
Grade 7 · Algebra
🔍 1. Introduction: A Motivating Example
Let's start with a concrete example to understand the idea behind functions.
Consider two sets:
- Set X — the set of all two-digit numbers (10, 11, 12, …, 99)
- Set Y — the set of all natural numbers less than 10000 (1, 2, 3, …, 9999)
Now let's create a rule: for each number in set X, we find its square in set Y.
Key observation: Each element of set X has exactly one corresponding element in set Y. The number 12 corresponds to 144 and only 144. The number 37 corresponds to 1369 and only 1369. This type of correspondence is called a function.
📖 2. Definition of a Function
Definition
A function (функция) is a correspondence between two sets in which each element of one set corresponds to exactly one element of the other set.
Функцией называется соответствие между двумя множествами, при котором каждому элементу одного множества соответствует единственный элемент другого множества.
📝 Etymology: The word "function" comes from the Latin word "functio", meaning performance or execution. A function "performs" the task of assigning outputs to inputs.
Think of a function as a machine: you put in an input, and the machine produces exactly one output. Never zero outputs, never two or more — always exactly one.
