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Function Calculator (Table of Values)

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.

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Function Calculator (Table of Values) -

Tag(s) : Functions

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# Function Calculator (Table of Values)

## Function Calculator

### Calculate f for a range of values

Limited to 50 values max

### Table of Values Generator

Limited to 50 values max

## Find Equation from Values

### What is a table of values? (Definition)

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

xf(x)
11
24
39
416

### How to calculate the values of a function?

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.

### How to calculate the preimage of a value?

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

### How to apply a function over a whole table of 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.

### How to choose the values to calculate?

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.

### How to use a table of values to perform interpolations?

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.

## Source code

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Function Calculator (Table of Values) on dCode.fr [online website], retrieved on 2024-07-18, https://www.dcode.fr/function-value-calculator

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