Tool for calculating the different values of a function from its equation f(x) and given values in order to compute their images by the function calculator and make a table of values.

Function Calculator (Table of Values) - dCode

Tag(s) : Functions

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A table of values describing a function is made up of two columns. The first column contains the values of a variable (usually denoted $ x $), and the second column contains the values matched by the function (usually denoted $ f(x) $). Thus, it relates a number to the value obtained by the function, which allows you to have an idea of the behavior of the function.

__Example:__ The square function $ f(x) = x^2 $ has for table of values

x | f(x) |
---|---|

1 | 1 |

2 | 4 |

3 | 9 |

4 | 16 |

The value (or image) of a function $ f(x) $ is the value of the function $ f $ for an indicated value of $ x $.

__Example:__ $ f(x) = 3x $ then for $ x = 2 $ the value of $ f(2) = 6 $

The calculation of the values can be done on the entire domain of definition of the function. Any calculation of a value outside the definition domain will result in an error.

The totality of the values can be represented in a form of curve which is the graphical representation of the function.

dCode has a tool to calculate the preimage by a function, ie the values of $ x $ for which the function has a given value.

It is common to want to apply a function to a variety/sequence/list of values, such as an Excel column. Specifying the mathematical function to apply and dCode will calculate all the values automatically.

The choice of values to calculate in a table of values depends on several factors:

— the objective: Choosing specific values can highlight a particular behavior of the function under certain conditions

— existence of critical values: Identify special values such as the zeros of the function, the inflection points, the maxima, the minima, or the asymptotes.

— scope of the study: Determine the relevant range of values for the application of the function (domain of definition).

— spacing of values: Uniform spacing can be useful for regular analysis, but it may be necessary to bring values closer together in regions of rapid variation of the function.

— constraints: Take into account any constraints imposed such as prohibited or irrelevant values to be excluded from the table of values.

Interpolation involves estimating values between known data. From a table of values, there are interpolation methods (such as Lagrange interpolation) which can predict other neighboring values from the table or find the formula of the function.

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Cite as source (bibliography):

*Function Calculator (Table of Values)* on dCode.fr [online website], retrieved on 2024-07-18,

- Function Calculator
- Find Equation from Values
- What is a table of values? (Definition)
- How to calculate the values of a function?
- How to calculate the preimage of a value?
- How to apply a function over a whole table of value?
- How to choose the values to calculate?
- How to use a table of values to perform interpolations?

calculation,function,image,list,table,value,number

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