Classifying Relationships

 The definition of a function is:  A function is a relation that maps each element in the domain to one and only one element in the range.  What???  What is domain?  Domain is the “x” values.  What is range?  Range is the “y” values.  So a function in plain English is:  A relation where “x” is not repeated.

 There are different ways to determine if a relation is a function depending on how the relation is presented.  If you have a list of points, look to see if “x” is repeated.  {(1, 2), (4, 6), (5, 5), (-2, -1)}  Function – nothing repeats  {(-2, -2), (5, -2). (4, 6), (-5, -2)}  Function – it is still a function if “y” repeats  {(-1, 2), (4, 4), (6, 5), (4, 8)}  Not a function – 4 is repeated

 When information is presented as a map, look at the arrows. Multiple arrows from the first column mean not a function.  This is a function because each time has its own event. Start Time 1 pm 3 pm 5 pm 7 pm Athletic Event Football Volleyball Soccer Basketball

 This is not a function because 7 pm is used twice. Start Times 1 pm 3 pm 7 pm

 When you are give a picture, use the vertical line test.  To do the vertical line test, draw a vertical line on the picture.  If it crosses more than once, it is not a function. Not a function Function Not a function Not a Function Function