Functions in calculus represent the relationship between two variables, which are the independent variable and the dependent variable. Let’s consider the following diagram.
There is an INPUT, a black box, and an OUTPUT. For example, suppose we want to make a pizza. We would need the following basic ingredients.
- Pizza Base
- Pizza Sauce
- Cheese
- Seasoning
The above real-life example can be represented in the form of a function as explained below,
The taste of our pizza depends on the quality of the ingredients. Let’s take another example
Suppose that: y = x2
| Value of x | Value of y |
| 1 | 1 |
| 2 | 4 |
| 9 | 81 |
| 11 | 121 |
Using the diagram given above, we get:
We can see that the value of y depends on the value of x. We can conclude that
- INPUT is independent of the OUTPUT
- OUTPUT depends on the INPUT
- Black Box is responsible for the transformation of the INPUT to the OUTPUT
In calculus,
- INPUT is an independent variable
- OUTPUT is a dependent variable
- Black Box is a function