3.4 Function concepts -- four ways to represent a function

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: $\mathrm{2x}+6$ . Note that in an algebraic representation, the input number is represented as a variable (in this case, an $x$ ).
3. Numerical - This can be done as a list of value pairs, as $(4,14)$ — meaning that if a 4 goes in, a 14 comes out. (You may recognize this as $(x,y)$ 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.