# What Does Input and Output Mean in Math?

**Mathematical equations called functions use input and output replace the variables in an equation.** The input is the known variable, while the output is the solution. Use functions any time a variable (x) transforms in a relationship to equal a new variable (y).

Functions are mathematical language to show the relationship of two variables, most often found in college level algebra and trigonometry. An example of a function is f(x) = x + 4. The solution, f(x) is also the y variable, or output. To solve the equation, simply choose a number for x, the input. The relationship is x + 4. If a problem solver wants to find the output if the input is 5, then the equation becomes: f(5) = 5 + 4. Then by completing the problem, f(5) = 9, 9 is the output. This is a very basic example, however, functions can become very complex problems in advanced math as the relationship between two variables becomes more complicated. To simply these issues, functions have two stringent rules. The function must be a correct relationship for every input and output, meaning for every input there is only one output and it must work for every input value. This is what makes the relationship between input and output a function.