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01 Function Concepts -- Four Ways to Represent a Function

Module by: Kenny M. Felder. E-mail the author

Summary: This module discusses how it is possible to describe one function four different ways.

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Modern Calculus texts emphasize that a function can be expressed in four different ways.

  1. Verbal - This is the first way functions are presented in the function game: “Double and add six.”
  2. Algebraic - This is the most common, most concise, and most powerful representation: 2x + 6 2x + 6 . Note that in an algebraic representation, the input number is represented as a variable (in this case, an x x ).
  3. Numerical - This can be done as a list of value pairs, as ( 4 , 14 ) ( 4 , 14 ) — meaning that if a 4 goes in, a 14 comes out. (You may recognize this as ( x , y ) ( x , y ) points used in graphing.)
  4. Graphical - This is discussed in detail in the section on graphing.

These are not four different types of functions: they are four different views of the same function. One of the most important skills in Algebra is converting a function between these different forms, and this theme will recur in different forms throughout the text.

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