FUNCTIONS

We often need to pair up numbers.
(i.e. : Age with Salary,
Height in Inches with Height in Centimeters,
Number of Shirts to be printed with Total Cost,
Time in a Taxi with the Cost of the Ride, ...)

Sometimes the 1st item has more than one
2nd partner, sometimes each 1st quantity
has one 2nd partner [a FUNCTION], and there
are even cases where each 1st member of the pair
has a unique 2nd partner [This type of FUNCTION
has an INVERSE - each 2nd member has
only one first member for a partner].

A RELATION is a set of ordered pairs.
Example 1 : {(4,2) , (4,-2) , (9,3) , (9,-3)}
Example 2 : f = {(5, 13) , (7, 17) , (2,7)}

A FUNCTION is a RELATION in which
each first number "x" has
one second number "y" for a partner.

Thus, Example 2 is a FUNCTION and
Example 1 is NOT a FUNCTION.
In most cases the relationship
between "x" and "y" has some hidden rule.
Example 1's Rule has "x" as the square of "y".
x = y * y or x = y^2

Example 2's Rule
takes "x" and first multiples by 2 and then
3 is added to create the "y" value.
y = 2x +3 or f(x) = 2x + 3

OLD FAITHFULL is predictable:

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