Relations and functions
- 2. What is the relation? A set of input and output values, usually represented in ordered pairs. Relation { (x1,y1), (x2,y2),......(xn,yn) } +
- 3. What is the domain and range of a relation? Domain: the set of all the first numbers of the ordered pairs. Range: the set of all second numbers in each pair. Example1: Relation {(3,5),(4,7),(6,9)} Domain: 3 4 6 Range: 5 7 9 In the elation above the domain is {3,4,6} and the range is {5,7,9}
- 4. What is the function? The function is a special relation where each input has a single output. The relation in example1 is a function because each element in the domain has just one output.
- 5. Example2: Relation {(10,3),(-5,8),(10,9) (21,0) } The domain is {10,-5,10,21} and the range is { 3,8,9,0} Relation is not a function because the element 10 has two outputs {9,3}
- 6. Easy way to distinguish the function Look for repeated elements in the domain, as soon as an element in the domain repeats, the relation will not be a function. R1 {(2,4),(4,8),(6,12),(8,16),(4,6),(10,20)} '4' repeats, R1 is not a function. R2 {(1,2),(4,5),(13,14),(34,35),(40,41)} No repeats, R2 is a function.
- 7. Practice1: What is the domain and range of the relation R1 {(-3,-1),(9,1),(4,8),(-3,7), (5,10)}? Pracice2: Which relations below are functions? R1 {(7,0),(2,9),(5,-7),(-3,-1),(0,0)} R2 {(6,9),(3,2),(9,4),(3,0),(10,12)} Practice3: For the following relation to be a function, X can not be what values? R3 {(8,110), (45,10),(-17,21),(0,101),(x,111)}