Function Calculator (Table of Values)

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.

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

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.