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 Description  
 Function:  A rule of matching elements of two sets of numbers in which an input value from the first set has only one output value in the second set.
Suppose each audio CD costs $12.00 at a certain store. An equation to determine the change due from a $50.00 bill for the number of CDs you want to purchase is:

c = 50 - 12n


c is a variable representing the change due and n is the variable representing the number of CDs purchased. If you bought 1 CD, then the change is $38.00. If you bought 3 CDs, then the change is $14.00.

If you recieved $26.00 in change, then we can determine the number of CDs purchased. By solving the equation, the solution is 2 CDs purchased.

This situation is a function since there is a single output value for each valid input number. That is,

 change

 number of CDs purchased

 $50.00

 0

 $38.00

 1

 $26.00

 2

 $14.00

 3

 $2.00

 4

 

 5


The graph to the left is a graph of the function c = 50 - 12n. This is a linear function since the graph of the solutions above results in a straight line. Thus, for example, 2 = 50 - 12n is a linear equation whose solution is n = 4.
The red points at left are the some of the solutions to the equation: y = x2. Note that the red points do not fit onto a line. Thus y = x2 is not a linear function. We say y = x2 is a nonlinear function.

Examples of Functions
  • Each person is assigned a unique social security number.
  • Each type and brand of item in a grocery store is assigned a unique bar code number.
  • Each house on a street is assigned a unique address.