What is a Function?
A function is a way of dealing with an "input" , applying some "rule" (the function), and then getting an "output" .
A function is a set of ordered pairs in which no two different ordered pairs have the same -coordinate. An equation that produces such a set of ordered pairs defines a function.
We can call the input , the rule , and then the output is , read " of ".
This DOES NOT mean " times " , it's just a notation device to record the input and output.
For example, find the output of the function when the input, .
To find the output value when , substitute for in the function.
means times .
(Note: is not times )
Think of as ; that way you can safely plug in negative numbers or even other expressions:
Functions and Relations
A function is a special type of relation . A relation is just a set of ordered pairs . In formal mathematical language, a function is a relation for which:
if and are both in the relation, then .
This just says that in a function, you can't have two ordered pairs with the same -value but different -values.
If you have the graph of a relation, you can use the vertical line test to find out whether the relation is a function.