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Function Concepts -- Four Ways to Represent a Function

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

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Summary: This module discusses how it is possible to describe functions in four different ways: graphically, verbally, algebraically, and numerically.

Note: Your browser may not currently support MathML. See our browser support page for additional details. You can always view the correct math in the PDF version.

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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