**What is Input & Output in Math?**

The concept of the terms input and output refers to what is taken in (input) and what is produced (output), and it can be used in multiple contexts like functions, algorithms, computers, and so on. This blog will cover what these terms mean from a mathematical standpoint.

So before going further into what input and output could mean in math, you need to know about the term function.

**What Is a Function and What Does It Mean in the Context of Math?**

Essentially, a function connects each input value to a unique output value. The concept of a function is frequently compared to a coin stamping machine by mathematicians. When you insert a coin into the machine, the output is a flattened piece of metal with something stamped on it. A function can only give you one result, just like the machine can only give you one flattened piece of metal. You can check if a mathematical relationship is a function by inputting different values and ensuring that the output has only one result.^{1}

Although this is a simple example, as the relationship between two variables becomes more complicated, functions can become very complex problems in advanced math. Functions have two strict rules to help simplify these issues: First, the function must be a correct relationship for each input and output, that is, there must be only one output for each input; and second, it must work for all input values.^{2}

So, based on the preceding example, what do you think is** the Input and the Output?**

Yes! The coin is the input, and the stamped metal is the output.

The number you enter into the expression is the input, and the output is what you get once the look-up or calculations are completed. A function’s input and output are both variables, which means they change. The input variables can be chosen by you, but the output variables are always determined by the function’s rules. The input variable is commonly denoted by the letter* x* and the output by *f (x)*, which is read as “*f of x*,” but the input variable and the function itself can be denoted by any symbol or letter. You’ll also come across functions that have one variable (usually *y*) equal to an expression with another variable (*x*).^{1}

It is not necessary for the input to be a number, but it is frequently the case in math. In some cases, the input is referred to as the independent variable. In the same way, the output does not have to be a number, though it is frequently in the context of math. The output, on the other hand, is sometimes referred to as the dependent variable because its value is determined by the value of the input.^{3}

This is the fundamental understanding of input and output. In addition, there are input and output variables, which can be scalars, matrices, strings, or vectors. There are input and output functions, input and output tables, and so much more that you can explore.^{4}

If this blog post piqued your interest in the fundamentals of what input and output mean in math, and if you wish to learn more about this and similar concepts, go to BYJU’s FutureSchool blog.

References:

*Differences Between Absolute Value & Linear Equations*. (n.d.). Retrieved June 1, 2022, from https://sciencing.com/differences-absolute-value-linear-equations-8222278.html*What Does Input and Output Mean in Math?*(n.d.). Retrieved June 1, 2022, from https://www.reference.com/world-view/input-output-mean-math-47a57db89ac7a3eb*Math Input & Output Function Formats & Examples | How to Find Input and Output – Video & Lesson Transcript | Study.com*. (n.d.). Retrieved June 1, 2022, from https://study.com/learn/lesson/math-input-output-function-formats-examples-how-to-find.html*Input and output math – How To Discuss*. (n.d.). Retrieved June 1, 2022, from https://howtodiscuss.com/t/input-and-output-math/109524