**The difference between a function and an equation is determined by the degree of freedom in assigning values to variables and their power of representation.**

In other words, the difference between a function and an equation depends on the power we have to give values to the variables and on the capacity for representation.

## Equation and inequality

An equation is characterized by acting as a bridge between two mathematical expressions. This bridge is the mathematical symbol that we know equally (=) and, as its name indicates, it represents equality. There are equations in which the bridge is not (=), but rather are inequalities that can be complete (>, <) or partial (≥, ≤). In the case that the bridge is not an equality (=) we will talk about inequalities.

To make it easier to remember that it is an equation, we can use its translation into English. The word “equal” (=) translated into English would be “*equal*”. It may be easier to remember “*equal*”Since it is more like the word“ equation ”and, therefore, knowing that we are talking about the symbol (=).

So, for inequalities, since there is the negative prefix in front of (**in**-equations), is similar to saying no equations, therefore, “not equal”. In relation to this, the mathematical symbols that we can find will be:>, <, ≥, ≤.

## Function

A function is similar to an equation in the sense of understanding the concept as a bridge, but in this case the bridge will be one of assignment or dependency. We will not talk about equality or inequality, since when we have a function an equal will appear.

Functions are identified by having an “f (independent variables)” in the equation. In the functions we will differentiate the typology of the variables depending on whether they are independent or dependent:

- Independent variable (x): it can take any value that comes to mind.
- Dependent variable (f (x)): it is limited by the value of the dependent variable.

Generally, for each value of the independent variable X only corresponds a single value of the dependent variable f (X). This statement is true as long as we do not take into account other types of functions that allow the dependent variable f (X) to have more than one value of the independent variable X associated with it.

## Summary

Equation | Function | |

Assignment | The solutions of the variables are bounded by the equation. | The independent variables can take any value and the dependent variables depend on those values. |

Representation | Only the solutions of the equation can be represented. | We can represent the points we want by assigning values to the independent variables of the function. |

## Example

Determine whether the items in the following list are functions or equations:

The answer in order would be: equation, function, equation, function.