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Input and Output
The expression y=x +5 is an illustration of a function.
There are inputs and outputs in each function. In plain English, the input is what enters the function, and the output is what the function produces.
The input and output variables in the equation y = x + 5 are x andy, respectively. The way the function operates is by converting an input value, suchx = 3, into an output value. If you substitute 3 for the number x in the equationy = x + 5, then becomesy = 3 + 5 = 8. So, y = 8. The output value is this. It is crucial to remember that each input has a single output in a function.
The domain and range are additional names for the input and output variables. The collection of all values that the function will accept as inputs, or its domain, is what makes up the function. The collection of all potential outputs that a function might produce is known as its range. The 3 and 8 in the aforementioned case would both fall under the domain and the range respectively.
Meaning of Input in Mathematics
Keep in mind that the input variable is what the function uses. Although it is frequently the case in mathematics, the input need not be a number. The independent variable is also referred to as the input.
Function notation is a common way to express functions. The equation y = x + 5 mentioned earlier as an example of a function might be written as f (x) = x + 5 in function notation. In this instance,
The input is x.
It is the function, f(x).
The output isx + 5.
The function declares that it will generate the result x + 5 given any inputx. Here are a few more instances of inputs and functions.
| Input | Function |
| n = 15 | f(n) = n – 8 |
| A = -4 | fA = A ×7 |
| 2 | f(2) = 2³ |
Although x is frequently used, as seen in these cases, the input need not bex.
Meaning of Output in Mathematics
Remember that the function’s output is represented by the output variable. Although it is frequently the case in mathematics, the result need not be a number. Because it depends on the value of the input, the output is occasionally referred to as the dependent variable.
Keep in mind that function notation is frequently used to represent functions. f( g ) = g / 3 is an example of a function written in function notation. In this instance,
The input is g.
It is the function, f (g).
The output is g / 3.
According to the function, it will provide an output equal to g / 3 for every given input, g. The result of an input of9 is 9 / 3, or 3. The same examples from before that demonstrated inputs and functions are shown here, but this time the outputs are also shown.
| Input | Function | Output |
| n = 15 | f(n) = n – 8 | 15 – 8 = 7 |
| A = -4 | f(A) = A 7 | -4 7 = -28 |
| 2 | f(2) = 2³ | 2³ = 8 |
Keep in mind that each input in a function only results in one output.
Rules for Function Input and Output
Different formats can be used to express functions, and the same function may appear differently depending on the format. All formats must adhere to the function’s standards for input and output: the function decides which inputs are valid, and the inputs determine the outputs. Tables, graphs, and algebraic expressions are the three most typical formats for expressing functions. The same function is illustrated here in three distinct versions.
Tables
When a function is represented as a table, the table typically has two columns: an inputs column and an outputs column. Between the input and output, a third column might be added to indicate how the input results in the function’s output.
Use the very straightforward function f ( x) = 3x + 2 to avoid the necessity for a third column.
| Input(x) | Output(f(x)) |
| 0 | 2 |
| 1 | 5 |
| 2 | 8 |
| 3 | 11 |
| 4 | 14 |
| 5 | 17 |
This table displays the inputs0, 1, 2, 3, 4, and 5. The table displays the following outputs 2, 5, 8, 11, 14, and 17. It should be noted that each input only results in one output, and the value of the output is dependent upon the value of the input.
Conclusion
In plain English, the input is what enters the function, and the output is what the function produces. The same examples from before that demonstrated inputs and functions are shown here, but this time the outputs are also shown. Between the input and output, a third column might be added to indicate how the input results in the function’s output.
