FUNCTION TABLE Meaning and
Definition
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A function table, also known as an input-output table or a mapping table, is a mathematical tool used to represent the relationship between the input values and corresponding output values of a function. It is a tabular representation of a function that organizes and displays pairs of input and output values in a systematic manner.
In a function table, the inputs, often referred to as independent variables or domain values, are listed in the first column. These inputs can be any numbers, variables, or other mathematical entities that are valid for the function. The output values, also known as dependent variables or range values, are displayed in the subsequent columns.
The function table provides a clear and structured presentation of the different input-output pairs for a specific function. By analyzing the table, one can identify patterns or trends that may exist in the relationship between the inputs and outputs. This information can be used to make predictions or to understand how the function behaves for different input values.
Function tables are widely used in mathematics and are particularly useful in algebra, where they are employed to explore and graph various types of functions. They play a crucial role in illustrating the concept of a function and its corresponding values, helping to visualize the relationship between variables and their corresponding outcomes.
Etymology of FUNCTION TABLE
The word "function" originates from the Latin word "functio", which means "performance" or "execution". In mathematics, a function is a relation that associates each element in a particular set (the domain) to exactly one element in another set (the codomain).
The term "table" can be traced back to the Latin word "tabula", which means "board" or "tablet". In this context, a table refers to a grid or a list of values arranged in rows and columns.
When combined, "function table" refers to a tabular representation of a mathematical function, where inputs and corresponding outputs are organized in a systematic manner. Such a table can be used to provide a visual representation of the function's behavior and allow for easy reference or calculation of values for a given input.
