8 01 Relations and Functions A relation is
- Slides: 6
8. 01 Relations and Functions
A relation is a set of ordered pairs. { (1 , 3) , (– 3 , 2 ) , ( 2 , 0) , (– 1 , – 4) } The domain of a relation is the set of x – coordinates. These values are sometimes called inputs. The range of a relation is the set of y – coordinates. These values are sometimes called outputs. Domain: {– 3, – 1, 1, 2} Range: {– 4, 0, 2, 3}
A function is a relation where each member of the domain is assigned to exactly one member of the range. { (1 , 3) , (– 3 , 2 ) , ( 2 , 0) , (– 1 , – 4) } Domain: Range: – 3 – 1 1 2 – 4 0 2 3 We say that a relation that is a function is one – to – one.
Determine the domain and range of each relation and determine if it’s a function or not. { ( 0 , 2), (– 1 , 3 ), ( 1 , 0) } D – 1 0 1 R 0 2 3 Yes, it’s a function because each member of the domain is assigned to only one member in the range. { (0 , 1), ( 1 , 3 ), ( 1 , 2) } D 0 1 R 1 2 3 No, it’s not a function because 1 is assigned to both 2 and 3.
Determine the domain and range of each relation and determine if it’s a function or not. D – 2 1 5 x y Input Output – 2 0 1 2 1 1 5 2 3 2 R 0 2 Yes, each member in the domain is assigned to exactly one member in the range. D 1 3 R 0 1 2 No, it’s not a function because 1 is assigned to both 0 and 1.
Try This: Determine the domain and range of each relation and determine if it’s a function or not. { ( 1 , 2), (– 2 , 3 ), ( 1 , 0) } D – 2 1 R 0 2 3 No, it’s not a function because 1 is assigned to both 2 and 0. D 0 2 4 x y 0 0 2 4 4 16 R 0 4 16 Yes, it’s a function because each member in the domain is assigned to exactly one member in the range.
