**Functions are mathematical equations that use input and output in place of variables.** The input is the known variable, while the output is the solution. Any time a variable (x) changes in a relationship to equal a new variable, use functions (y).

Functions, a language used in mathematics to depict the relationship between two variables, are most frequently encountered in college algebra and trigonometry. f(x) = x + 4 is a function example. The output or y variable is also the solution, f(x). Simply select a number as the input for x to begin solving the problem.

The formula is x + 4. The equation becomes: f(5) = 5 + 4 if a problem solver wishes to get the result if the input is 5. After solving the issue, the result is 9 since f(5) = 9. This is a relatively simple example, but as the relationship between two variables gets more intricate, functions can turn into really challenging math problems.

Functions have two strict restrictions that help to simplify these problems. Every input and output must have the correct relationship for the function to be valid, which means there can be only one valid output for any input value. The connection between input and output is what qualifies the relationship as a function.