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Here's the official definition:

 

A rule is a function if
each element in the domain

goes to
exactly one element in the range
.

Check out this guy:

R = { ( 1, 2 ), ( 2, 3 ), ( 3, 4), ( 1, 4) }

Let's graph those points:

a graph of the vertical line test for { ( 1 , 2 ) , ( 2 , 4 ) , ( 3 , 4 ) , ( 1 , 4 ) }  ...  the x axis are the domain guys  ...  the y axis are the range guys R is NOT a function since one element in the domain (1) goes to two elements in the range
(
2 and 4.) 

Or, you can just say that R is not a function since 1 goes to 2 AND 1 goes to 4.

So, it fails the vertical line test!


YOUR TURN:

Is R = { ( a , 1 ) , ( b , 1 ) , ( c , 2 ) , ( b , 3 ) }

a function?

* put the letters along the bottom since they are the domain guys!

 


Is this a function?

R = { ( 1 , b ) , ( 2 , a ) , ( 3 , a ) , ( 4 , c ) }

* now the numbers go along the bottom!