section_path: Representing a function/Tables
section_name: Tables
paragraph_text: Tables
  
  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 f: { 1, …, 5 } 2 → R {\displaystyle f:\{1,\ldots,5\}^{2}\to \mathbb {R} } defined as f (x, y) = x y {\displaystyle f(x,y)=xy} can be represented by the familiar multiplication table
  
  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:
  
  Before the advent of handheld calculators and personal computers, such tables were often compiled and published for functions such as logarithms and trigonometric functions.