Differentiate between formula and function

A formula and a function are both mathematical concepts, but they are used in different contexts and have different purposes.

1. Formula: A formula is a mathematical relationship or rule expressed in symbols. It is a concise way of expressing information symbolically as in a mathematical or chemical formula. The main purpose of a formula is to show the relationship between different quantities. For example, the formula for the area of a circle is A = πr², which shows the relationship between the area (A) and the radius (r).

2. Function: A function, on the other hand, is a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output. It is like a machine that has an input and an output, and the output depends on the input. For example, the function f(x) = x² is a rule that assigns to each number x its square x².

In summary, a formula is a statement of a fact or a rule, while a function is a special type of relation where every input has a unique output.