Editing Function (mathematics) (section)

=== Tables ===
{{Main|Mathematical table}}
A function can be represented as a table of values.  If the domain of a function is finite, then the function can be completely specified in this way.  For example, the multiplication function <math>f:\{1,\ldots,5\}^2 \to \mathbb{R}</math> defined as <math>f(x,y)=xy</math> can be represented by the familiar [[multiplication table]]

{| class="wikitable" style="text-align: center;"
! {{diagonal split header|{{mvar|x}}|{{mvar|y}}}}
! 1  !! 2  !! 3  !! 4  !! 5
|-
! 1
| 1  || 2  || 3  || 4 || 5
|-
! 2
| 2  || 4  ||6 || 8  || 10
|-
! 3
| 3  || 6  || 9  || 12 || 15
|-
! 4
| 4  || 8  || 12 || 16 || 20
|-
! 5
| 5  || 10 || 15 || 20 || 25
|}

On the other hand, if a function's domain is continuous, a table can give the values of the function at specific values of the domain.  If an intermediate value is needed, [[interpolation]] can be used to estimate the value of the function.  For example, a portion of a table for the sine function might be given as follows, with values rounded to 6 decimal places:

{| class="wikitable" style="text-align: center;"
! {{mvar|x}} !! {{math|sin ''x''}}
|-
|1.289 || 0.960557
|-
|1.290 || 0.960835
|-
|1.291 || 0.961112
|-
|1.292 || 0.961387
|-
|1.293 || 0.961662
|}

Before the advent of handheld calculators and personal computers, such tables were often compiled and published for functions such as logarithms and trigonometric functions.