Precalculus

Topic 1: Functions 1.1      Relations An ordered pair of two elements is called relation. The first element of the ordered pair is the object and a set of objects is called the domain of the relation. The second element of the ordered pair is the image and a set of images is called the range of the relation. There are four types of relations, namely one-to-one, many-to-one, one-to-many and many-to-many relations. Example 1 Relation = {(1, 2), (3, 5), (4, 8)} Domain = {1, 3, 4} Range = {2, 5, 8} Since one object has one and only one image and vice versa, thus this is a one-to-one relation. Example 2 Relation = {(1, 2), (3, 2), (4, 8)} Domain = {1, 3, 4} Range = {2, 8} Since one object has one and only one image while one image has at least one object, thus this is a m any-to-one relation. Example 3 Relation = {(1, 2), (1, 5), (4, 5)} Domain = {1, 4} Relation = {2, 5} Since one object has at least one image and one image has at least one object, thus this is ...