Table of values

In mathematics, a table of values is understood to be a table with two columns or two lines in which the arguments and the associated function values ​​of a function are entered.

Tables of values ​​can be used to create the graph of a function. This means that only discrete values ​​can be specified. It is not clear from this how the function behaves between two value pairs.

Functions that are only defined on a finite set can be used by a value table of classical propositional logic and also some other logics to characterize the semantic properties of the logical connection symbols.

In the empirical sciences, such as physics , a table of values ​​in which individual measurement results are recorded is, conversely, the basis for making assumptions about an underlying relationship in the form of a mathematical function. Again, this is often done by preparing the table entries graphically and then "obviously" lying points on a straight line or another simple curve. In addition, statistical methods such as regression analysis play a role here.

Examples

From the table of values ​​for points gained and the associated curve. ${\displaystyle y=x^{2}}$

To draw the graph of , a table of values ​​is created for. ${\displaystyle y=f(x)=x^{2}}$ ${\displaystyle \{x\in \mathbb {Z} \ |\ 0\leq x\leq 3\}}$

x	f (x)
0	0
1	1
2	4th
3	9

In order to be able to draw the curve progression more precisely, further intermediate values ​​are helpful.

From the table of values ​​for points gained and the associated curve. ${\displaystyle y=(x^{2}-2)^{2}-1}$

To draw the graph of , a table of values ​​for some x -values ​​from −3 to +3 is created. ${\displaystyle y=g(x)=(x^{2}-2)^{2}-1}$

x	−3	−2	−3/2	−1	−1/2	0	1/2	1	3/2	2	3
g (x)	48	3	−15/16	0	33/16	3	33/16	0	−15/16	3	48

The table of values ​​(correctly) suggests that the graph of g is symmetric about the y axis. However, this must be checked formally. The table also suggests that there is a local maximum at and a local maximum at each. A formal check is also important here, because only the first of these statements actually applies. However, assuming continuity , one can at least conclude from the table that between −2 and −1 or between 1 and 2 there is (at least) one local minimum (the local minima are indeed at ). Finally, you can see that there is a zero at and , and that (again assuming continuity), at least one zero must lie between −2 and −1.5 and between 1.5 and 2. The table of values ​​provides a valuable starting point for the numerical search for zeros, for example using the secant method (these two zeros are actually included ). However, one cannot generally assume that every zero of g can be traced using a simple table of values. In the present case, however, all zeros have been found, since a fourth-degree polynomial can only have four zeros. ${\displaystyle x=0}$ ${\displaystyle x=1{,}5}$ ${\displaystyle x=-1{,}5}$ ${\displaystyle x=\pm {\sqrt {2}}}$ ${\displaystyle x=-1}$ ${\displaystyle x=+1}$ ${\displaystyle x=\pm {\sqrt {3}}}$

Value tables for logical functions are also referred to as a truth table . The XOR function is defined, for example, by the following table of values:

(FROM)	A XOR B
(FALSE, FALSE)	NOT CORRECT
(FALSE, TRUE)	TRUE
(TRUE, FALSE)	TRUE
(TRUE, TRUE)	NOT CORRECT

Here the third line means: If A is true and B is false, then “A XOR B” is also true.