6-A-3: My Definition of Equations and Functions
Equation – a statement of equivalence between two quantities
Arithmetic Example: 4 + 5 =
Answer: 4 + 5 = 9
Algebraic Example: 14 = y – 3
Answer: y = 17
Function – a statement of equivalence between two variables (one input and one output) where the output value depends on the input value. Therefore, the output variable is the dependent variable while the input is the independent variable. For every input value there is one and only one output value.
Examples: y = 3x
Output = Input + 5
F(x) = -2x – 3
*To graph these functions (and any others of your choosing), go to:
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Sowers Math Weblog 
Shawn, some thoughts about your definition of a function. It is important that you mentioned that for every input there is only one output. If the function was 1/x, or some other expression where the output is undefined, does that still meet your conditions? One and only one means that there must be one output value. If one output is undefined, is this still a function?
Also, does the output need to be a variable? Can it be a constant, such as 10 or f(x) = 10? Is there a more general term you could use for the output?
Tom
Comment by tescott | October 23, 2008